Neutrino oscillation

2734: 1579: 2729:{\displaystyle {\begin{aligned}U&={\begin{bmatrix}U_{e1}&U_{e2}&U_{e3}\\U_{\mu 1}&U_{\mu 2}&U_{\mu 3}\\U_{\tau 1}&U_{\tau 2}&U_{\tau 3}\end{bmatrix}}\\&={\begin{bmatrix}1&0&0\\0&c_{23}&s_{23}\\0&-s_{23}&c_{23}\end{bmatrix}}{\begin{bmatrix}c_{13}&0&s_{13}e^{-i\delta }\\0&1&0\\-s_{13}e^{i\delta }&0&c_{13}\end{bmatrix}}{\begin{bmatrix}c_{12}&s_{12}&0\\-s_{12}&c_{12}&0\\0&0&1\end{bmatrix}}{\begin{bmatrix}e^{i\alpha _{1}/2}&0&0\\0&e^{i\alpha _{2}/2}&0\\0&0&1\\\end{bmatrix}}\\&={\begin{bmatrix}c_{12}c_{13}&s_{12}c_{13}&s_{13}e^{-i\delta }\\-s_{12}c_{23}-c_{12}s_{23}s_{13}e^{i\delta }&c_{12}c_{23}-s_{12}s_{23}s_{13}e^{i\delta }&s_{23}c_{13}\\s_{12}s_{23}-c_{12}c_{23}s_{13}e^{i\delta }&-c_{12}s_{23}-s_{12}c_{23}s_{13}e^{i\delta }&c_{23}c_{13}\end{bmatrix}}{\begin{bmatrix}e^{i\alpha _{1}/2}&0&0\\0&e^{i\alpha _{2}/2}&0\\0&0&1\\\end{bmatrix}},\end{aligned}}} 1080:) and would thus quickly cease any meaningful oscillation. More importantly, no mechanism in the Standard Model is capable of pinning down a charged lepton into a coherent state that is not a mass eigenstate, in the first place; instead, while the charged lepton from the W boson decay is not initially in a mass eigenstate, neither is it in any "neutrino-centric" eigenstate, nor in any other coherent state. It cannot meaningfully be said that such a featureless charged lepton oscillates or that it does not oscillate, as any "oscillation" transformation would just leave it the same generic state that it was before the oscillation. Therefore, detection of a charged lepton oscillation from W boson decay is infeasible on multiple levels. 4419: 780: 10250: 3991: 7409: 7399: 7371: 4414:{\displaystyle {\begin{aligned}P_{\alpha \rightarrow \beta }=\delta _{\alpha \beta }&{}-4\,\sum _{j>k}\,\operatorname {\mathcal {R_{e}}} \left\{\,U_{\alpha j}^{*}\,U_{\beta j}\,U_{\alpha k}\,U_{\beta k}^{*}\,\right\}\,\sin ^{2}\left({\frac {\Delta _{jk}m^{2}\,L}{4E}}\right)\\&{}+2\,\sum _{j>k}\,\operatorname {\mathcal {I_{m}}} \left\{\,U_{\alpha j}^{*}\,U_{\beta j}\,U_{\alpha k}\,U_{\beta k}^{*}\,\right\}\,\sin \left({\frac {\Delta _{jk}m^{2}\,L}{2E}}\right)~,\end{aligned}}} 7431: 5195: 7453: 7421: 1102:. Although such matter–antimatter oscillation had not been observed, this idea formed the conceptual foundation for the quantitative theory of neutrino flavor oscillation, which was first developed by Maki, Nakagawa, and Sakata in 1962 and further elaborated by Pontecorvo in 1967. One year later the solar neutrino deficit was first observed, and that was followed by the famous article by Gribov and Pontecorvo published in 1969 titled "Neutrino astronomy and lepton charge". 7443: 6213:). The first pendulum is set in motion by the experimenter while the second begins at rest. Over time, the second pendulum begins to swing under the influence of the spring, while the first pendulum's amplitude decreases as it loses energy to the second. Eventually all of the system's energy is transferred to the second pendulum and the first is at rest. The process then reverses. The energy oscillates between the two pendulums repeatedly until it is lost to 10505: 4837: 6161: 44: 6175: 6189: 5624: 10517: 4892: 6857: 3980: 6147: 8130:. However, for all practical situations, the other particles in the decay may be well localized in time and space (e.g. to within a nuclear distance), leaving their momentum with a large spread. When these partner states are projected out, the neutrino is left in a state that for all intents and purposes behaves as the simple superposition of mass states described here. For more information, 4541: 5377: 5190:{\displaystyle A_{\mathsf {CP}}^{(\alpha \beta )}=P(\nu _{\alpha }\rightarrow \nu _{\beta })-P({\bar {\nu }}_{\alpha }\rightarrow {\bar {\nu }}_{\beta })=4\,\sum _{j>k}\,\operatorname {\mathcal {I_{m}}} \left\{\,U_{\alpha j}^{*}\,U_{\beta j}\,U_{\alpha k}\,U_{\beta k}^{*}\,\right\}\,\sin \left({\frac {\Delta _{jk}m^{2}\,L}{2E}}\right)} 5388: 7043: 6638: 7211: 3752: 6060: 1068:

travels. No analogous mechanism exists in the Standard Model that would make charged leptons detectably oscillate. In the four decays mentioned above, where the charged lepton is emitted in a unique mass eigenstate, the charged lepton will not oscillate, as single mass eigenstates propagate without oscillation.

4832:{\displaystyle {\frac {\Delta _{jk}(mc^{2})^{2}\,L}{4\hbar c\,E}}={\frac {{\rm {GeV}}\,{\rm {fm}}}{4\hbar c}}\times {\frac {\Delta _{jk}m^{2}}{{\rm {eV}}^{2}}}{\frac {L}{\rm {km}}}{\frac {\rm {GeV}}{E}}\approx 1.27\times {\frac {\Delta _{jk}m^{2}}{{\rm {eV}}^{2}}}{\frac {L}{\rm {km}}}{\frac {\rm {GeV}}{E}}~,} 6225:

different frequencies because the second involves the (weak) spring while the first does not. The initial state of the two-pendulum system is a combination of both normal modes. Over time, these normal modes drift out of phase, and this is seen as a transfer of motion from the first pendulum to the second.

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The next simplest addition would be to add into the Standard Model right-handed neutrinos that interact with the left-handed neutrinos and the Higgs field in an analogous way to the rest of the fermions. These new neutrinos would interact with the other fermions solely in this way and hence would not

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of the three neutrino mass states advance at slightly different rates, due to the slight differences in their respective masses. This results in a changing superposition mixture of mass eigenstates as the neutrino travels; but a different mixture of mass eigenstates corresponds to a different mixture

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when particle concentrations and temperatures were high, neutrino oscillations could have behaved differently. Depending on neutrino mixing-angle parameters and masses, a broad spectrum of behavior may arise including vacuum-like neutrino oscillations, smooth evolution, or self-maintained coherence.

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The smallest modification to the Standard Model, which only has left-handed neutrinos, is to allow these left-handed neutrinos to have Majorana masses. The problem with this is that the neutrino masses are surprisingly smaller than the rest of the known particles (at least 600,000 times smaller

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If three neutrinos are considered, the probability for each neutrino to appear is somewhat complex. The graphs below show the probabilities for each flavor, with the plots in the left column showing a long range to display the slow "solar" oscillation, and the plots in the right column zoomed in, to

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Eigenstates with different masses propagate with different frequencies. The heavier ones oscillate faster compared to the lighter ones. Since the mass eigenstates are combinations of flavor eigenstates, this difference in frequencies causes interference between the corresponding flavor components of

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which is an eigenstate for a "flavor" that is fixed by the electron's mass eigenstate, and not in one of the neutrino's own mass eigenstates. Because the neutrino is in a coherent superposition that is not a mass eigenstate, the mixture that makes up that superposition oscillates significantly as it

994:

neutrino after traveling some distance. Since the quantum mechanical phase advances in a periodic fashion, after some distance the state will nearly return to the original mixture, and the neutrino will be again mostly electron neutrino. The electron flavor content of the neutrino will then continue

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The addition of right-handed neutrinos has the effect of adding new mass scales, unrelated to the mass scale of the Standard Model, hence the observation of heavy right-handed neutrinos would reveal physics beyond the Standard Model. Right-handed neutrinos would help to explain the origin of matter

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oscillation experiments, it is known that two mixing angles of the MNS matrix are large and the third is smaller. This is in sharp contrast to the CKM matrix in which all three angles are small and hierarchically decreasing. The CP-violating phase of the MNS matrix is as of April 2020 to lie

3035: 8035:

There are alternative ways to modify the standard model that are similar to the addition of heavy right-handed neutrinos (e.g., the addition of new scalars or fermions in triplet states) and other modifications that are less similar (e.g., neutrino masses from loop effects and/or from suppressed

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is measured using electron anti-neutrinos from nuclear reactors. The rate of anti-neutrino interactions is measured in detectors sited near the reactors to determine the flux prior to any significant oscillations and then it is measured in far detectors (placed kilometres from the reactors). The

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below.) All available neutrino sources produce a range of energies, and oscillation is measured at a fixed distance for neutrinos of varying energy. The limiting factor in measurements is the accuracy with which the energy of each observed neutrino can be measured. Because current detectors have

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of oscillation. If the two pendulums are identical then one normal mode consists of both pendulums swinging in the same direction with a constant distance between them, while the other consists of the pendulums swinging in opposite (mirror image) directions. These normal modes have (slightly)

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The above formula is correct for any number of neutrino generations. Writing it explicitly in terms of mixing angles is extremely cumbersome if there are more than two neutrinos that participate in mixing. Fortunately, there are several meaningful cases in which only two neutrinos participate

3728: 3545: 5209: 6605: 5619:{\displaystyle A_{\mathsf {CP}}^{(\alpha \beta )}=16\,\sin \left({\frac {\Delta _{21}m^{2}\,L}{4E}}\right)\sin \left({\frac {\Delta _{32}m^{2}\,L}{4E}}\right)\sin \left({\frac {\Delta _{31}m^{2}\,L}{4E}}\right)\,J\,\sum _{\gamma }\,\varepsilon _{\alpha \beta \gamma }} 6885: 7951:

Since experiments observing neutrino oscillation measure the squared mass difference and not absolute mass, one might claim that the lightest neutrino mass is exactly zero, without contradicting observations. This is however regarded as unlikely by theorists.

6852:{\displaystyle V={\frac {m}{2}}{\begin{pmatrix}x_{a}&x_{b}\end{pmatrix}}{\begin{pmatrix}{\frac {g}{L_{a}}}+{\frac {k}{m}}&-{\frac {k}{m}}\\-{\frac {k}{m}}&{\frac {g}{L_{b}}}+{\frac {k}{m}}\end{pmatrix}}{\begin{pmatrix}x_{a}\\x_{b}\end{pmatrix}}.} 3975:{\displaystyle P_{\alpha \rightarrow \beta }\,=\,{\Bigl |}\,\left\langle \,\left.\nu _{\beta }\,\right|\,\nu _{\alpha }(L)\,\right\rangle \,{\Bigr |}^{2}\,=\,\left|\,\sum _{j}\,U_{\alpha j}^{*}\,U_{\beta j}\,e^{-i{\frac {m_{j}^{2}\,L}{2E}}}\,\right|^{2}~.} 7391:

display the fast "atmospheric" oscillation. The parameters used to create these graphs (see below) are consistent with current measurements, but since some parameters are still quite uncertain, some aspects of these plots are only qualitatively correct.

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offer the greatest control over the neutrinos being studied. Many experiments have taken place that study the same oscillations as in atmospheric neutrino oscillation using neutrinos with a few GeV of energy and several-hundred-km baselines. The

1284: 8009:, where right-handed neutrinos with very large Majorana masses are added. If the right-handed neutrinos are very heavy, they induce a very small mass for the left-handed neutrinos, which is proportional to the reciprocal of the heavy mass. 5877: 6228:

The description of the system in terms of the two pendulums is analogous to the flavor basis of neutrinos. These are the parameters that are most easily produced and detected (in the case of neutrinos, by weak interactions involving the

1075:

decay is more complicated: W boson decay is sufficiently energetic to generate a charged lepton that is not in a mass eigenstate; however, the charged lepton would lose coherence, if it had any, over interatomic distances

2874: 5736: 5372:{\displaystyle \operatorname {\mathcal {I_{m}}} \left\{\,U_{\alpha j}^{*}\,U_{\beta j}\,U_{\alpha k}\,U_{\beta k}^{*}\,\right\}=J\,\sum _{\gamma ,\ell }\varepsilon _{\alpha \beta \gamma }\,\varepsilon _{jk\ell }~,} 3586: 3383: 7918:; for these values the oscillations become visible for neutrinos traveling several hundred kilometres, which would be those neutrinos that reach the detector traveling through the earth, from below the horizon. 7377:

The blue curve shows the probability of the original neutrino retaining its identity. The red curve shows the probability of conversion to the other neutrino. The maximum probability of conversion is equal to

7929:

oscillation is observed as an apparent disappearance of electron anti-neutrinos in the far detectors (i.e. the interaction rate at the far site is lower than predicted from the observed rate at the near site).

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Following the theories that were proposed in the 1970s suggesting unification of electromagnetic, weak, and strong forces, a few experiments on proton decay followed in the 1980s. Large detectors such as

6448: 3375: 804:. Neutrinos produced in nuclear reactors have energies similar to solar neutrinos, of around a few MeV. The baselines of these experiments have ranged from tens of meters to over 100 km (parameter 7987:

than the mass of an electron), which, while it does not invalidate the theory, is widely regarded as unsatisfactory as this construction offers no insight into the origin of the neutrino mass scale.

8791:

An, F.P.; Bai, J.Z.; Balantekin, A.B.; Band, H.R.; Beavis, D.; Beriguete, W.; et al. (Daya Bay Collaboration) (23 April 2012). "Observation of electron-antineutrino disappearance at Daya Bay".

1331: 6294: 3996: 1584: 591:

in 1957, neutrino oscillation has since been observed by a multitude of experiments in several different contexts. Most notably, the existence of neutrino oscillation resolved the long-standing

9090:

Aartsen, M.G.; Ackermann, M.; Adams, J.; Aguilar, J.A.; Ahlers, M.; Ahrens, M.; al Samarai, I.; Altmann, D.; Andeen, K.; Anderson, T.; et al. (IceCube Collaboration) (12 April 2018).

7038:{\displaystyle {\begin{pmatrix}x_{a}\\x_{b}\end{pmatrix}}={\begin{pmatrix}\cos \theta &\sin \theta \\-\sin \theta &\cos \theta \end{pmatrix}}{\begin{pmatrix}x_{1}\\x_{2}\end{pmatrix}}} 2862: 1390: 1105:

The concept of neutrino mixing is a natural outcome of gauge theories with massive neutrinos, and its structure can be characterized in general. In its simplest form it is expressed as a

8048:

can break the lepton number and lead to neutrino masses. These interactions are normally excluded from theories as they come from a class of interactions that lead to unacceptably rapid

7983:. This type of mass applies for electrically neutral particles since otherwise it would allow particles to turn into anti-particles, which would violate conservation of electric charge. 7206:{\displaystyle V={\frac {m}{2}}{\begin{pmatrix}x_{1}\ x_{2}\end{pmatrix}}{\begin{pmatrix}\lambda _{1}&0\\0&\lambda _{2}\end{pmatrix}}{\begin{pmatrix}x_{1}\\x_{2}\end{pmatrix}}} 7304: 7272: 638:

A great deal of evidence for neutrino oscillation has been collected from many sources, over a wide range of neutrino energies and with many different detector technologies. The 2015

1119: 606:

interest, as the precise properties of the process can shed light on several properties of the neutrino. In particular, it implies that the neutrino has a non-zero mass outside the

6390: 5641: 3144: 6233:). The description in terms of normal modes is analogous to the mass basis of neutrinos. These modes do not interact with each other when the system is free of outside influence. 3097: 6432: 6348: 3738:

causes it to be possible to observe a neutrino created with a given flavor to change its flavor during its propagation. The probability that a neutrino originally of flavor

3256: 1536: 1207: 1006:

In contrast, due to their larger masses, the charged leptons (electrons, muons, and tau leptons) have never been observed to oscillate. In nuclear beta decay, muon decay,

8012:

If it is assumed that the neutrinos interact with the Higgs field with approximately the same strengths as the charged fermions do, the heavy mass should be close to the

6055:{\displaystyle P_{\alpha \rightarrow \beta ,\alpha \neq \beta }=\sin ^{2}(2\theta )\,\sin ^{2}\left(1.27\,{\frac {\Delta m^{2}L}{E}}\,{\frac {\rm {\,}}{\rm {}}}\right)~.} 9986:

Fogli; Lisi; Marrone; Montanino; Palazzo; Rotunno (2012). "Global analysis of neutrino masses, mixings, and phases: Entering the era of leptonic CP violation searches".

3291: 1426: 8730:

Y., Abe; et al. (Double Chooz collaboration) (28 March 2012). "Indication for the disappearance of reactor electron antineutrinos in the Double Chooz experiment".

1466: 8036:

couplings). One example of the last type of models is provided by certain versions supersymmetric extensions of the standard model of fundamental interactions, where

767:

experiment provided a very precise measurement of neutrino oscillation in an energy range of hundreds of MeV to a few TeV, and with a baseline of the diameter of the

4533: 3172: 7342:

When the number of oscillators (particles) is increased to three, the orthogonal matrix can no longer be described by a single angle; instead, three are required (

1494: 7402:

Electron neutrino oscillations, long range. Here and in the following diagrams black means electron neutrino, blue means muon neutrino and red means tau neutrino.

3557:

This limit applies to all practical (currently observed) neutrinos, since their masses are less than 1 eV and their energies are at least 1 MeV, so the

3218: 3196: 8552:

Ahmad, Q.R.; Allen, R.C.; Andersen, T.C.; Anglin, J.D.; Bühler, G.; Barton, J.C.; et al. (SNO Collaboration) (25 July 2001). "Measurement of the rate of

8019:

There are other varieties of seesaw and there is currently great interest in the so-called low-scale seesaw schemes, such as the inverse seesaw mechanism.

3030:{\displaystyle \left|\,\nu _{j}(t)\,\right\rangle =e^{-i\,\left(\,E_{j}t\,-\,{\vec {p}}_{j}\cdot {\vec {x}}\,\right)}\left|\,\nu _{j}(0)\,\right\rangle ~,} 2797:— i.e. if the neutrino is identical to its antineutrino (whether or not they are is unknown) — and do not enter into oscillation phenomena regardless. If 10135: 5857:{\displaystyle P_{\alpha \rightarrow \beta ,\alpha \neq \beta }=\sin ^{2}(2\theta )\,\sin ^{2}\left({\frac {\Delta m^{2}L}{4E}}\right)\quad {\text{ .}}} 533: 470: 1089: 7501:= 0 (If the actual value of this phase is large, the probabilities will be somewhat distorted, and will be different for neutrinos and antineutrinos.) 7799: 1569:

When the standard three-neutrino theory is considered, the matrix is 3×3. If only two neutrinos are considered, a 2×2 matrix is used. If one or more

1039:

because of its large mass. Weak-force couplings compel the simultaneously emitted neutrino to be in a "charged-lepton-centric" superposition such as

750: 8860:

Kim, Soo-Bong; et al. (RENO collaboration) (11 May 2012). "Observation of Reactor Electron Antineutrino Disappearance in the RENO Experiment".

8066: 813:). Mikaelyan and Sinev proposed to use two identical detectors to cancel systematic uncertainties in reactor experiment to measure the parameter 3723:{\displaystyle \left|\,\nu _{j}(L)\,\right\rangle =e^{-i\,\left({\frac {\,m_{j}^{2}\,L\,}{2\,E}}\right)}\,\left|\,\nu _{j}(0)\,\right\rangle ~.} 10279: 3540:{\displaystyle E_{j}={\sqrt {\,p_{j}^{2}+m_{j}^{2}\;}}\simeq p_{j}+{\frac {m_{j}^{2}}{\,2\,p_{j}\,}}\approx E+{\frac {m_{j}^{2}}{\,2\,E\,}}~,} 904:

appeared in Spring 2007 and contradicted the results from LSND, although they could support the existence of a fourth neutrino type, the

10387: 941:, using a neutrino beam directed through 295 km of earth and the Super-Kamiokande detector, measured a non-zero value for the parameter 337: 8166:

The mass of the electron and the mass of the Z boson are examples of particle masses set by the Standard Model fundamental mass scale.

862: 795:. No oscillations were found until a detector was installed at a distance 1–2 km. Such oscillations give the value of the parameter 733: 237: 10558: 7367:

In the approximation where only two neutrinos participate in the oscillation, the probability of oscillation follows a simple pattern:

10521: 6600:{\displaystyle V={\frac {m}{2}}\left({\frac {g}{L_{a}}}x_{a}^{2}+{\frac {g}{L_{b}}}x_{b}^{2}+{\frac {k}{m}}(x_{b}-x_{a})^{2}\right).} 4427: 10264: 7834:

together with the K2K and MINOS long baseline accelerator neutrino experiment have determined the so-called atmospheric parameters

6081:

in atmospheric mixing, since the electron neutrino plays almost no role in this case. It is also appropriate for the solar case of

1555: 3304: 966:

of neutrinos. That is, the three neutrino states that interact with the charged leptons in weak interactions are each a different

10128: 8093: 721:

detectors confirmed the deficit, but neutrino oscillation was not conclusively identified as the source of the deficit until the

526: 8624:

Fukuda, Y.; et al. (Super-Kamiokande Collaboration) (24 August 1998). "Evidence for oscillation of atmospheric neutrinos".

6316:

is the horizontal displacement of the pendulum. As an isolated system the pendulum is a harmonic oscillator with a frequency of

257: 8052:

if they are all included. These models have little predictive power and are not able to provide a cold dark matter candidate.

1014:

decay, when a neutrino and a charged lepton are emitted, the charged lepton is emitted in incoherent mass eigenstates such as

10382: 9709: 8206: 897: 746: 332: 17: 8978:

Abe, K.; et al. (T2K Collaboration) (August 2013). "Evidence of electron neutrino appearance in a muon neutrino beam".

8016:. Because the Standard Model has only one fundamental mass scale, all particle masses must arise in relation to this scale. 1295: 732:. At energies above 5 MeV, solar neutrino oscillation actually takes place in the Sun through a resonance known as the 7870: 840: 187: 6243: 10465: 7991:

be directly observable, so are not phenomenologically excluded. The problem of the disparity of the mass scales remains.

7960:

The question of how neutrino masses arise has not been answered conclusively. In the Standard Model of particle physics,

928: 475: 192: 10121: 10088: 519: 9824: 6236:

When the pendulums are not identical the analysis is slightly more complicated. In the small-angle approximation, the

2828: 1354: 10289: 9761:

Mohapatra, R.N. & Valle, J.W.F. (1986). "Neutrino mass and baryon number nonconservation in superstring models".

35: 10470: 1566:, then the flavor eigenstates would be the same as the mass eigenstates. However, experiment shows that it is not. 480: 222: 7948:

type (making the neutrino its own antiparticle), it is then possible that the MNS matrix has more than one phase.

9253: 7350:. This requires the introduction of complex phases in addition to the rotation angles, which are associated with 3735: 10430: 2798: 1196:{\displaystyle \left|\nu _{i}\right\rangle =\sum _{\alpha }U_{\alpha i}^{*}\left|\nu _{\alpha }\right\rangle ,} 427: 7277: 7245: 5720:{\displaystyle U={\begin{pmatrix}\cos \theta &\sin \theta \\-\sin \theta &\cos \theta \end{pmatrix}}.} 10321: 10269: 114: 10480: 8098: 6353: 3102: 996: 722: 623: 490: 147: 3050: 1003:

for neutrino oscillations, this microscopic quantum effect becomes observable over macroscopic distances.

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of flavor states. For example, a neutrino born as an electron neutrino will be some mixture of electron,

900:

appear to be in conflict with the oscillation parameters measured in other experiments. Results from the

10107: 10035:

Forero; Tortola; Valle (2012). "Global status of neutrino oscillation parameters after Neutrino-2012".

6403: 6319: 757:

have observed a deficit in the ratio of the flux of muon to electron flavor atmospheric neutrinos (see

607: 581: 6442:) of equal mass but possibly unequal lengths and connected by a spring, the total potential energy is 10435: 10103: 9820: 8126:

state with the other bodies in the decay or reaction, and the mixed state is properly described by a

1279:{\displaystyle \left|\nu _{\alpha }\right\rangle =\sum _{i}U_{\alpha i}\left|\nu _{i}\right\rangle ,} 442: 267: 252: 232: 9562: 8486: 3225: 10440: 9637:

Abe, K.; Akutsu, R.; Ali, A.; Alt, C.; Andreopoulos, C.; Anthony, L.; et al. (15 April 2020).

8452:

Gonzalez-Garcia, M.C. & Maltoni, Michele (April 2008). "Phenomenology with massive neutrinos".

8379:

Subhasish Chakrabarty; Amitabha Lahiri (2019). "Geometrical contribution to neutrino mass matrix".

970:

of the three (propagating) neutrino states of definite mass. Neutrinos are emitted and absorbed in

452: 302: 1511: 893:

experiments have all independently observed muon neutrino disappearance over such long baselines.

10548: 10509: 10354: 10222: 10212: 9295: 8517:

Davis, Raymond; Harmer, Don S.; Hoffman, Kenneth C. (1968). "Search for Neutrinos from the Sun".

3298: 627: 182: 3267: 1395: 10227: 10200: 8481: 8024: 6133:

is very small and because two of the mass states are very close in mass compared to the third.

2809:; this has not yet been observed experimentally. If experiment shows this 3×3 matrix to be not 1504:, the complex conjugate should be removed from the first equation and inserted into the second. 1106: 779: 771:; the first experimental evidence for atmospheric neutrino oscillations was announced in 1998. 714: 639: 592: 432: 422: 367: 357: 142: 94: 1430: 10475: 10349: 10316: 10095:"Neutrino Oscillatons and the Solar Neutrino Puzzle (Lecture - 09) by Professor G Srinivasan" 9549: 6871: 967: 686:

energy uncertainties of a few percent, it is satisfactory to know the distance to within 1%.

485: 447: 262: 242: 177: 52: 49: 8284: 4518: 10425: 10364: 10359: 10180: 10054: 10007: 9958: 9939:

Maltoni; Schwetz; Tortola; Valle (2004). "Status of global fits to neutrino oscillations".

9911: 9841: 9772: 9727: 9660: 9591: 9582: 9455: 9397: 9348: 9304: 9262: 9213: 9160: 9103: 9062: 8997: 8944: 8879: 8810: 8749: 8696: 8643: 8582: 8526: 8473: 8398: 8353: 8326: 8312: 8297: 8289: 8259: 8230: 8225: 8123: 3150: 877: 873: 706: 698: 603: 412: 307: 172: 167: 162: 9508: 8921:

Agafonova, N.; et al. (OPERA Collaboration) (26 July 2010). "Observation of a first ν

8245: 1473: 8: 10392: 9604: 9577: 9544:

Olive, K.A.; et al. (Particle Data Group) (2014). "2014 Review of Particle Physics".

9424: 7972: 7608: 6202: 954:, using the same beam as MINOS with a baseline of 810 km, is sensitive to the same. 718: 599: 577: 10058: 10011: 9962: 9915: 9845: 9776: 9731: 9664: 9595: 9459: 9401: 9375: 9352: 9308: 9266: 9217: 9172: 9164: 9107: 9066: 9001: 8948: 8883: 8814: 8753: 8700: 8647: 8586: 8530: 8477: 8425: 8402: 8357: 8344:

V. De Sabbata; M. Gasperini (1981). "Neutrino oscillations in the presence of torsion".

8330: 8301: 8263: 7970:). These interactions require both left- and right-handed versions of the fermion (see 10543: 10420: 10190: 10070: 10044: 10023: 9997: 9974: 9948: 9927: 9901: 9743: 9717: 9704: 9684: 9650: 9639:"Constraint on the matter–antimatter symmetry-violating phase in neutrino oscillations" 9471: 9445: 9229: 9203: 9176: 9150: 9052: 9021: 8987: 8960: 8934: 8903: 8869: 8842: 8800: 8773: 8739: 8712: 8686: 8659: 8633: 8572: 8499: 8463: 8388: 8103: 3580:

is the distance traveled and also dropping the phase factors, the wavefunction becomes

3203: 3181: 647: 342: 272: 212: 9816: 10306: 10027: 9988: 9978: 9931: 9867: 9798: 9763: 9739: 9688: 9676: 9619: 9475: 9436: 9388: 9360: 9339: 9293:; Don S. Harmer; Kenneth C. Hoffman (May 1968). "Search for neutrinos from the Sun". 9290: 9013: 8964: 8895: 8834: 8826: 8765: 8677:

Mikaelyan, L.; Sinev, V. (2000). "Neutrino oscillations at reactors: What is next?".

8606: 8598: 8503: 8410: 8202: 8088: 6868: 2794: 1497: 695: 618:. The experimental discovery of neutrino oscillation, and thus neutrino mass, by the 550: 417: 197: 79: 10074: 9970: 9638: 9233: 9180: 9025: 8907: 8846: 8777: 8716: 6201:

The basic physics behind neutrino oscillation can be found in any system of coupled

999:. Since mass differences between neutrino flavors are small in comparison with long 580:

to have a different lepton family number. The probability of measuring a particular

10485: 10232: 10217: 10158: 10062: 10015: 9966: 9919: 9857: 9849: 9788: 9780: 9747: 9735: 9668: 9609: 9599: 9467: 9463: 9405: 9356: 9334: 9312: 9270: 9221: 9168: 9121: 9111: 9075: 9070: 9040: 9005: 8956: 8952: 8891: 8887: 8822: 8818: 8761: 8757: 8704: 8663: 8651: 8590: 8534: 8491: 8406: 8361: 8308: 8280: 8241: 8000: 7980: 7945: 7831: 6863: 6301: 6237: 5201: 4886:

is zero), then the second sum is zero. Otherwise, the CP asymmetry can be given as

2814: 1570: 1095: 1000: 971: 924: 905: 890: 764: 736:, a different process from the vacuum oscillation described later in this article. 619: 615: 588: 495: 407: 362: 8594: 8495: 584:

for a neutrino varies between three known states, as it propagates through space.

10407: 10274: 9330: 9248: 8563:

interactions produced by B Solar neutrinos at the Sudbury Neutrino Observatory".

8454: 8317: 8250: 8196: 6210: 1563: 792: 380: 297: 202: 9316: 9289: 8655: 8538: 1098:, who proposed that neutrino–antineutrino transitions may occur in analogy with 10445: 10144: 10066: 10019: 9428: 9116: 9091: 9009: 8372: 8337: 8127: 8061: 7938: 7933: 7347: 6611: 3558: 2810: 1099: 938: 920: 886: 643: 611: 104: 99: 65: 10094: 9923: 9672: 7408: 4846:. In this form, it is convenient to plug in the oscillation parameters since: 10537: 10415: 10374: 9853: 9784: 9409: 9017: 8830: 8602: 7398: 7336: 3045: 981:

As a neutrino superposition propagates through space, the quantum mechanical

754: 561: 392: 325: 227: 207: 7370: 5635:

significantly. In this case, it is sufficient to consider the mixing matrix

1573:

are added (see later), it is 4×4 or larger. In the 3×3 form, it is given by

10397: 10328: 10237: 10195: 10185: 9871: 9832: 9680: 9623: 9141:

Akhmedov, Evgeny Kh. (26 September 2007). "Do charged leptons oscillate?".

9039:

Cohen, Andrew G.; Glashow, Sheldon L. & Ligeti, Zoltan (13 July 2009).

8899: 8838: 8769: 8610: 8049: 8040:

is not a symmetry. There, the exchange of supersymmetric particles such as

7964:

only have intrinsic mass because of interactions with the Higgs field (see

7874: 7351: 7343: 6221: 4879: 1501: 982: 826: 694:

The first experiment that detected the effects of neutrino oscillation was

402: 387: 352: 312: 119: 9802: 7430: 10311: 10205: 10173: 10168: 9522: 9450: 9423:

Eidelman, S.; Hayes; Olive; Aguilar-Benitez; Amsler; Asner; et al. (

8313:"Neutrino Experiments and the Problem of Conservation of Leptonic Charge" 8285:"Neutrino Experiments and the Problem of Conservation of Leptonic Charge" 7966: 7452: 7420: 6400:

is the displacement. With a mass attached it oscillates with a period of

3293:

is the current position of the particle relative to its starting position

2806: 975: 963: 942: 814: 805: 796: 437: 282: 277: 152: 109: 89: 84: 56: 9208: 8577: 7442: 4511:

The phase that is responsible for oscillation is often written as (with

9953: 9906: 9793: 9722: 9614: 9275: 9126: 8691: 8638: 8365: 8146:

The Standard Model fundamental mass scale can be taken as the scale of

8078: 7231: 4865: 2865: 1110: 788: 573: 247: 9862: 9225: 759: 9422: 8708: 8013: 7897:

For atmospheric neutrinos the relevant difference of masses is about

7464:

The illustrations were created using the following parameter values:

7354:

but do not influence the observable effects of neutrino oscillation.

1077: 901: 397: 292: 59:

produced by colliding protons decaying into hadron jets and electrons

9889: 9092:"Search for nonstandard neutrino interactions with IceCube DeepCore" 8378: 7638:(solar), obtained from KamLand, solar, reactor and accelerator data. 962:

Neutrino oscillation arises from mixing between the flavor and mass

10490: 9655: 8430: 8393: 8045: 8037: 6214: 6206: 5868: 4843: 3259: 710: 565: 554: 500: 347: 287: 217: 157: 10049: 10002: 9373: 9155: 9057: 8992: 8939: 8874: 8805: 8744: 8468: 7976:). However, only left-handed neutrinos have been observed so far. 1094:

The idea of neutrino oscillation was first put forward in 1957 by

43: 27:

Phenomenon in which a neutrino changes lepton flavor as it travels

10163: 10113: 8083: 8041: 7961: 6230: 6160: 1072: 995:

to oscillate – as long as the quantum mechanical state maintains

701:

in the late 1960s, in which he observed a deficit in the flux of

6220:

The behavior of this system can be understood by looking at its

6065:

This formula is often appropriate for discussing the transition

951: 8195:

Barger, Vernon; Marfatia, Danny; Whisnant, Kerry Lewis (2012).

6174: 4502:{\displaystyle \Delta _{jk}m^{2}\ \equiv m_{j}^{2}-m_{k}^{2}~.} 3175: 932: 650:

for their early pioneering observations of these oscillations.

558: 9194:

Waltham, Chris (June 2004). "Teaching neutrino oscillations".

6188: 10101:. International Centre for Theoretical Sciences. 18 May 2018. 7339:(though that angle applies to quarks rather than neutrinos). 6136: 4874:, in modern experiments are typically on order of MeV or GeV. 1559: 991: 882: 768: 9760: 9089: 7937:

somewhere between −2 and −178 degrees, from the

7584: 3554:

is the energy of the wavepacket (particle) to be detected.

3370:{\displaystyle \left|{\vec {p}}_{j}\right|=p_{j}\gg m_{j}~,} 2864:

are mass eigenstates, their propagation can be described by

2801:

occurs, these factors influence its rate. The phase factor

9825:"Nonlinear neutrino oscillations in the expanding universe" 9429:"Chapter 15: Neutrino mass, mixing, and flavor change" 9337:(20 January 1969). "Neutrino astronomy and lepton charge". 9246: 8925:

candidate event in the OPERA experiment in the CNGS beam".

7878: 6126:

These approximations are possible because the mixing angle

3792: 1011: 1007: 987: 916: 912: 787:

Many experiments have searched for oscillation of electron

725:

provided clear evidence of neutrino flavor change in 2001.

569: 505: 9938: 7242:

describe normal modes which oscillate with frequencies of

6146: 5730:

Then the probability of a neutrino changing its flavor is

9985: 9525:. The demonstration allows exploration of the parameters. 8343: 7382:. The frequency of the oscillation is controlled by Δm. 7346:). Furthermore, in the quantum case, the matrices may be 1083: 729: 702: 9576:

Nakamura, K.; et al. (Particle Data Group) (2010).

9329: 8914: 8551: 8065:

The physics for this system is non-trivial and involves

7611:

combination of Daya Bay, RENO, and Double Chooz results.

9890:"Neutrino Masses and Mixing: Evidence and Implications" 8005:

The most popular conjectured solution currently is the

7362: 9249:"Remarks on the Unified Model of Elementary Particles" 8451: 8194: 7979:

Neutrinos may have another source of mass through the

7168: 7118: 7079: 7000: 6937: 6894: 6811: 6701: 6663: 6358: 6260: 6248: 5656: 2611: 2199: 2076: 1982: 1859: 1765: 1602: 1326:{\displaystyle \ \left|\nu _{\alpha }\right\rangle \ } 8055: 7280: 7248: 7057: 6888: 6641: 6451: 6406: 6356: 6322: 6246: 5880: 5739: 5644: 5391: 5212: 4895: 4544: 4521: 4430: 3994: 3755: 3589: 3386: 3307: 3270: 3228: 3206: 3184: 3153: 3105: 3053: 2877: 2831: 1582: 1514: 1476: 1433: 1398: 1357: 1298: 1210: 1122: 8190: 8188: 8186: 8184: 8182: 7475:) = 0.10 (Determines the size of the small wiggles.) 6289:{\displaystyle {\tfrac {1}{2}}{\tfrac {mg}{L}}x^{2}} 9702:Valle, J.W.F. (2006). "Neutrino physics overview". 8790: 974:processes in flavor eigenstates but travel as mass 739: 10034: 9887: 9038: 8617: 8516: 8134: 7298: 7266: 7205: 7037: 6851: 6599: 6426: 6384: 6342: 6288: 6209:connected by a weak spring (a spring with a small 6054: 5856: 5719: 5618: 5371: 5189: 4831: 4527: 4501: 4413: 3974: 3722: 3539: 3369: 3285: 3250: 3212: 3190: 3166: 3138: 3091: 3029: 2856: 2805:is non-zero only if neutrino oscillation violates 2728: 1530: 1488: 1460: 1420: 1384: 1325: 1278: 1195: 9247:Z. Maki; M. Nakagawa; S. Sakata (November 1962). 8179: 6632:, which can also be written as a matrix product: 4857:, are known to be on the order of 10 eV = (10 eV) 3841: 3779: 682: 10535: 9815: 8275: 8273: 8220: 8218: 6862:The 2×2 matrix is real symmetric and so (by the 2857:{\displaystyle \left|\,\nu _{j}\,\right\rangle } 2793:are physically meaningful only if neutrinos are 1385:{\displaystyle \ \left|\nu _{i}\right\rangle \ } 705:neutrinos with respect to the prediction of the 653:Neutrino oscillation is a function of the ratio 9636: 9502: 9500: 9498: 9496: 9494: 9492: 9490: 9488: 8122:More formally, the neutrinos are emitted in an 7385: 2820: 774: 10280:Mathematical formulation of the Standard Model 8676: 8510: 8423: 3565:, is greater than 10 in all cases. Using also 3220:is the time from the start of the propagation, 10129: 9701: 8545: 8307: 8279: 8270: 8240: 8215: 8067:neutrino oscillations in a dense neutrino gas 7802:have measured the so-called solar parameters 689: 527: 9575: 9485: 4864:, in modern experiments are on the order of 868: 728:Solar neutrinos have energies below 20 9543: 7955: 7412:Electron neutrino oscillations, short range 861:These results have since been confirmed by 10136: 10122: 8670: 8426:"Neutrino 'flip' wins physics Nobel Prize" 7654:at 90% confidence level, corresponding to 6420: 6336: 6137:Classical analogue of neutrino oscillation 3436: 717:. Many subsequent radiochemical and water 534: 520: 42: 10048: 10001: 9952: 9905: 9861: 9792: 9721: 9654: 9613: 9603: 9449: 9274: 9207: 9154: 9125: 9115: 9074: 9056: 8991: 8938: 8920: 8873: 8804: 8784: 8743: 8690: 8637: 8576: 8485: 8467: 8445: 8392: 7830:Atmospheric neutrino experiments such as 7798:Solar neutrino experiments combined with 7585:Observed values of oscillation parameters 7293: 7261: 6423: 6339: 6008: 5985: 5959: 5937: 5796: 5599: 5588: 5584: 5565: 5513: 5461: 5427: 5346: 5313: 5301: 5282: 5268: 5254: 5235: 5168: 5131: 5125: 5106: 5092: 5078: 5059: 5036: 5019: 4628: 4602: 4587: 4382: 4345: 4339: 4320: 4306: 4292: 4273: 4250: 4233: 4199: 4155: 4149: 4130: 4116: 4102: 4083: 4060: 4043: 3954: 3937: 3907: 3893: 3874: 3863: 3856: 3852: 3837: 3831: 3811: 3805: 3790: 3784: 3776: 3772: 3708: 3688: 3682: 3669: 3663: 3659: 3643: 3635: 3615: 3595: 3527: 3523: 3519: 3488: 3477: 3473: 3402: 3123: 3119: 3079: 3057: 3015: 2995: 2982: 2947: 2943: 2929: 2923: 2903: 2883: 2848: 2837: 9630: 9140: 7451: 7441: 7429: 7419: 7407: 7397: 7306:. When the two pendulums are identical ( 7299:{\displaystyle {\sqrt {\lambda _{2}\,}}} 7267:{\displaystyle {\sqrt {\lambda _{1}\,}}} 3742:will later be observed as having flavor 923:particle in a muon neutrino beam in the 778: 9569: 9378:(1 November 1980). "Neutrino masses in 9193: 8094:Lorentz-violating neutrino oscillations 7869:, has been measured by the experiments 7434:Muon neutrino oscillations, short range 2817:or some other new physics is required. 713:-based detector. This gave rise to the 610:, which requires a modification to the 14: 10536: 8723: 8623: 7456:Tau neutrino oscillations, short range 7424:Muon neutrino oscillations, long range 7357: 6350:. The potential energy of a spring is 6205:. A simple example is a system of two 5401: 5398: 4905: 4902: 1540:Pontecorvo–Maki–Nakagawa–Sakata matrix 1090:Pontecorvo–Maki–Nakagawa–Sakata matrix 1084:Pontecorvo–Maki–Nakagawa–Sakata matrix 931:, 730 km away from the source in 783:Illustration of neutrino oscillations. 681:is the neutrino's energy. (Details in 258:de Sitter invariant special relativity 238:N = 4 supersymmetric Yang–Mills theory 10117: 9809: 9539: 9537: 9535: 9533: 9041:"Disentangling neutrino oscillations" 7944:If the neutrino mass proves to be of 7446:Tau neutrino oscillations, long range 6385:{\displaystyle {\tfrac {1}{2}}kx^{2}} 3985:This is more conveniently written as 3139:{\displaystyle ~i^{2}\,\equiv \,-1~,} 10516: 10106:was elected in 1984 a fellow of the 8853: 8417: 7363:Two neutrino probabilities in vacuum 5871:and the convention introduced above 5629: 3092:{\displaystyle (\,c=1,\hbar =1\,)~,} 188:6D (2,0) superconformal field theory 9506: 9416: 8977: 8859: 7994: 3734:each mass eigenstate. Constructive 1558:describing the analogous mixing of 1333:is a neutrino with definite flavor 683:§ Propagation and interference 193:Noncommutative quantum field theory 55:particle detector data depicting a 24: 10143: 9881: 9530: 8729: 8135:Cohen, Glashow & Ligeti (2009) 8056:Oscillations in the early universe 7369: 6032: 6029: 6026: 6015: 6012: 5996: 5992: 5963: 5817: 5546: 5494: 5442: 5220: 5216: 5146: 5044: 5040: 4814: 4811: 4808: 4799: 4796: 4777: 4774: 4748: 4726: 4723: 4720: 4711: 4708: 4689: 4686: 4660: 4634: 4631: 4623: 4620: 4617: 4549: 4432: 4360: 4258: 4254: 4177: 4068: 4064: 25: 10570: 10559:Physics beyond the Standard Model 10082: 8424:Webb, Jonathan (6 October 2015). 6427:{\displaystyle {\sqrt {k/m\;}}\,} 6343:{\displaystyle {\sqrt {g/L\;}}\,} 6312:is the mass of the pendulum, and 5382:the CP asymmetry is expressed as 4644: 4596: 3377:we can approximate the energy as 3070: 1392:is a neutrino with definite mass 598:Neutrino oscillation is of great 10515: 10504: 10503: 10248: 9511:. Wolfram Demonstrations Project 8030: 6187: 6173: 6159: 6145: 740:Atmospheric neutrino oscillation 223:Mathematical universe hypothesis 9754: 9695: 9521:These images were created with 9367: 9323: 9283: 9254:Progress of Theoretical Physics 9240: 9187: 9134: 9083: 9032: 8971: 8381:The European Physical Journal C 8160: 8140: 8116: 6308:is the length of the pendulum, 6240:of a single pendulum system is 6166:Time evolution of the pendulums 5848: 919:announced the observation of a 633: 10431:Causal dynamical triangulation 9605:10.1088/0954-3899/37/7a/075021 9468:10.1016/j.physletb.2004.06.001 9440:. Review of Particle Physics. 9143:Journal of High Energy Physics 9076:10.1016/j.physletb.2009.06.020 8957:10.1016/j.physletb.2010.06.022 8892:10.1103/PhysRevLett.108.191802 8823:10.1103/physrevlett.108.171803 8762:10.1103/PhysRevLett.108.131801 8411:10.1140/epjc/s10052-019-7209-2 8346:Il Nuovo Cimento A (1971-1996) 8201:. Princeton University Press. 7234:of the matrix. The variables x 6580: 6553: 6434:. With two pendulums (labeled 6035: 6023: 6018: 6009: 6005: 5989: 5934: 5925: 5889: 5793: 5784: 5748: 5416: 5407: 5010: 4998: 4988: 4976: 4966: 4957: 4944: 4931: 4920: 4911: 4578: 4561: 4007: 3828: 3822: 3764: 3705: 3699: 3612: 3606: 3319: 3277: 3251:{\displaystyle {\vec {p}}_{j}} 3236: 3080: 3054: 3012: 3006: 2976: 2955: 2900: 2894: 2799:neutrinoless double beta decay 624:Sudbury Neutrino Observatories 428:Causal dynamical triangulation 13: 1: 10270:Spontaneous symmetry breaking 9888:Gonzalez-Garcia; Nir (2003). 9173:10.1088/1126-6708/2007/09/116 8595:10.1103/physrevlett.87.071301 8496:10.1016/j.physrep.2007.12.004 8306:reproduced and translated in 8239:reproduced and translated in 8173: 8023:through a mechanism known as 7914:and the typical energies are 6875:. That is, there is an angle 1554:). It is the analogue of the 1109:relating the flavor and mass 677:is the distance traveled and 626:was recognized with the 2015 115:Cosmological constant problem 10089:Review Articles on arxiv.org 9578:"Review of Particle Physics" 9361:10.1016/0370-2693(69)90525-5 8237:(2): 549–551. February 1957. 8226:"Mesonium and anti-mesonium" 8099:Neutral particle oscillation 7631: . This corresponds to 7386:Three neutrino probabilities 6194:Higher frequency normal mode 6107:is a mix (superposition) of 3044:quantities are expressed in 2821:Propagation and interference 1531:{\displaystyle U_{\alpha i}} 775:Reactor neutrino oscillation 723:Sudbury Neutrino Observatory 620:Super-Kamiokande Observatory 148:Cosmic censorship hypothesis 7: 9317:10.1103/PhysRevLett.20.1205 9196:American Journal of Physics 8656:10.1103/PhysRevLett.81.1562 8539:10.1103/PhysRevLett.20.1205 8246:"Mesonium and Antimesonium" 8072: 6396:is the spring constant and 6180:Lower frequency normal mode 10: 10575: 10108:Indian Academy of Sciences 10067:10.1103/PhysRevD.86.073012 10020:10.1103/PhysRevD.86.013012 9740:10.1088/1742-6596/53/1/031 9117:10.1103/PhysRevD.97.072009 9010:10.1103/PhysRevD.88.032002 7998: 3286:{\displaystyle {\vec {x}}} 1562:. If this matrix were the 1550:, or sometimes simply the 1470:the superscript asterisk ( 1421:{\displaystyle \ m_{i}\ ,} 1087: 690:Solar neutrino oscillation 10499: 10458: 10436:Canonical quantum gravity 10406: 10373: 10342: 10299: 10288: 10257: 10246: 10151: 9971:10.1088/1367-2630/6/1/122 9924:10.1103/RevModPhys.75.345 9894:Reviews of Modern Physics 9673:10.1038/s41586-020-2177-0 3258:is the three-dimensional 957: 869:Beam neutrino oscillation 443:Canonical quantum gravity 268:Black hole thermodynamics 253:Doubly special relativity 36:Beyond the Standard Model 10441:Superfluid vacuum theory 9854:10.1103/PhysRevD.49.1740 9785:10.1103/PhysRevD.34.1642 9410:10.1103/PhysRevD.22.2227 8679:Physics of Atomic Nuclei 8198:The Physics of Neutrinos 8109: 7956:Origins of neutrino mass 6152:Spring-coupled pendulums 1461:{\displaystyle i=1,2,3,} 557:created with a specific 453:Superfluid vacuum theory 303:Gauge gravitation theory 10223:Quantum electrodynamics 10213:Electroweak interaction 9509:"Neutrino Oscillations" 9296:Physical Review Letters 8862:Physical Review Letters 8793:Physical Review Letters 8732:Physical Review Letters 8626:Physical Review Letters 8565:Physical Review Letters 8519:Physical Review Letters 7862:The last mixing angle, 7756:(normal mass hierarchy) 7504:Normal mass hierarchy: 6879:such that if we define 4860:Oscillation distances, 3299:ultrarelativistic limit 3178:of the mass-eigenstate 853:with a significance of 791:-neutrinos produced in 628:Nobel Prize for Physics 608:Einstein-Cartan torsion 10201:Quantum chromodynamics 9941:New Journal of Physics 9557:Cite journal requires 9480:Revised September 2005 9096:Physical Review D 9045:Physics Letters B 8561:+ d → p + p + e 7794:are currently unknown. 7457: 7447: 7435: 7425: 7413: 7403: 7374: 7300: 7268: 7207: 7039: 6853: 6601: 6428: 6386: 6344: 6290: 6056: 5858: 5721: 5620: 5373: 5191: 4850:The mass differences, 4833: 4529: 4528:{\displaystyle \hbar } 4503: 4415: 3976: 3724: 3541: 3371: 3287: 3252: 3214: 3192: 3168: 3140: 3093: 3031: 2868:solutions of the form 2858: 2730: 1532: 1490: 1462: 1422: 1386: 1327: 1280: 1197: 1113:and can be written as 1107:unitary transformation 843:experiment found that 829:experiment found that 825:In December 2011, the 784: 715:solar neutrino problem 640:Nobel Prize in Physics 593:solar neutrino problem 553:phenomenon in which a 433:Causal fermion systems 423:Loop quantum cosmology 368:Large extra dimensions 358:Supersymmetry breaking 263:Causal fermion systems 10317:Cosmological constant 7932:From atmospheric and 7921:The mixing parameter 7455: 7445: 7433: 7423: 7411: 7401: 7373: 7301: 7269: 7208: 7040: 6854: 6602: 6429: 6387: 6345: 6291: 6057: 5859: 5722: 5621: 5374: 5192: 4834: 4530: 4504: 4416: 3977: 3725: 3542: 3372: 3288: 3253: 3215: 3193: 3169: 3167:{\displaystyle E_{j}} 3141: 3094: 3032: 2859: 2731: 1533: 1491: 1463: 1423: 1387: 1328: 1281: 1198: 782: 448:Semiclassical gravity 243:Twistor string theory 233:Randall–Sundrum model 50:Large Hadron Collider 18:Neutrino oscillations 10426:Loop quantum gravity 10365:Theory of everything 10360:Grand Unified Theory 10334:Neutrino oscillation 10181:Quantum field theory 9583:Journal of Physics G 8290:Zh. Eksp. Teor. Fiz. 8231:Zh. Eksp. Teor. Fiz. 7335:is analogous to the 7278: 7246: 7055: 6886: 6639: 6449: 6404: 6354: 6320: 6244: 6203:harmonic oscillators 5878: 5737: 5642: 5389: 5210: 4893: 4542: 4519: 4428: 3992: 3753: 3587: 3384: 3305: 3268: 3226: 3204: 3182: 3151: 3103: 3051: 2875: 2829: 1580: 1548:lepton mixing matrix 1512: 1489:{\displaystyle ^{*}} 1474: 1431: 1396: 1355: 1296: 1208: 1120: 950:in a neutrino beam. 878:particle accelerator 707:Standard Solar Model 699:Homestake experiment 547:Neutrino oscillation 413:Loop quantum gravity 308:Gauge theory gravity 173:Grand Unified Theory 168:Unified field theory 163:Theory of everything 125:Neutrino oscillation 10393:Split supersymmetry 10355:Kaluza–Klein theory 10228:Fermi's interaction 10059:2012PhRvD..86g3012F 10012:2012PhRvD..86a3012F 9963:2004NJPh....6..122M 9916:2003RvMP...75..345G 9846:1994PhRvD..49.1740K 9777:1986PhRvD..34.1642M 9732:2006JPhCS..53..473V 9665:2020Natur.580..339T 9596:2010JPhG...37g5021N 9460:2004PhLB..592....1P 9425:Particle Data Group 9402:1980PhRvD..22.2227S 9374:Schechter, Joseph; 9353:1969PhLB...28..493G 9309:1968PhRvL..20.1205D 9267:1962PThPh..28..870M 9218:2004AmJPh..72..742W 9165:2007JHEP...09..116A 9108:2018PhRvD..97g2009A 9067:2009PhLB..678..191C 9002:2013PhRvD..88c2002A 8949:2010PhLB..691..138A 8884:2012PhRvL.108s1802A 8815:2012PhRvL.108q1803A 8754:2012PhRvL.108m1801A 8701:2000PAN....63.1002M 8648:1998PhRvL..81.1562F 8587:2001PhRvL..87g1301A 8531:1968PhRvL..20.1205D 8478:2008PhR...460....1G 8403:2019EPJC...79..697C 8358:1981NCimA..65..479S 8331:1968JETP...26..984P 8302:1968JETP...26..984P 8264:1958JETP....6..429P 8089:Neutral kaon mixing 7358:Theory, graphically 6539: 6504: 5420: 5300: 5253: 5124: 5077: 4924: 4870:Neutrino energies, 4492: 4474: 4338: 4291: 4148: 4101: 3936: 3892: 3658: 3517: 3471: 3435: 3417: 2779:The phase factors 1171: 1100:neutral kaon mixing 1071:The case of (real) 839:Then, in 2012, the 587:First predicted by 183:Kaluza–Klein theory 10554:Electroweak theory 10421:Superstring theory 10191:Strong interaction 10104:Ganesan Srinivasan 9705:Journal of Physics 9427:) (15 July 2004). 9276:10.1143/PTP.28.870 8366:10.1007/BF02902051 8104:Neutrino astronomy 7981:Majorana mass term 7458: 7448: 7436: 7426: 7414: 7404: 7375: 7296: 7264: 7203: 7197: 7157: 7107: 7035: 7029: 6989: 6923: 6849: 6840: 6800: 6690: 6597: 6525: 6490: 6424: 6382: 6367: 6340: 6286: 6274: 6257: 6052: 5854: 5717: 5708: 5616: 5598: 5392: 5369: 5329: 5283: 5236: 5202:Jarlskog invariant 5187: 5107: 5060: 5035: 4896: 4829: 4525: 4499: 4478: 4460: 4411: 4409: 4321: 4274: 4249: 4131: 4084: 4059: 3972: 3922: 3875: 3873: 3720: 3644: 3537: 3503: 3457: 3421: 3403: 3367: 3283: 3248: 3210: 3188: 3164: 3136: 3089: 3027: 2854: 2795:Majorana particles 2726: 2724: 2713: 2600: 2178: 2065: 1971: 1848: 1744: 1528: 1486: 1458: 1418: 1382: 1323: 1276: 1241: 1193: 1154: 1153: 785: 648:Arthur B. McDonald 564:("lepton flavor": 551:quantum mechanical 343:Superstring theory 273:Unparticle physics 213:Superstring theory 143:Brans–Dicke theory 10531: 10530: 10454: 10453: 10329:Strong CP problem 10307:Hierarchy problem 10037:Physical Review D 9989:Physical Review D 9764:Physical Review D 9710:Conference Series 9649:(7803): 339–344. 9507:Meszéna, Balázs. 9437:Physics Letters B 9389:Physical Review D 9376:Valle, José W. F. 9340:Physics Letters B 9303:(21): 1205–1209. 9291:Raymond Davis Jr. 9226:10.1119/1.1646132 8980:Physical Review D 8927:Physics Letters B 8525:(21): 1205–1209. 8244:(February 1957). 8208:978-0-691-12853-5 7462: 7461: 7294: 7262: 7094: 7072: 6796: 6783: 6764: 6747: 6732: 6719: 6656: 6551: 6523: 6488: 6466: 6421: 6366: 6337: 6273: 6256: 6048: 6039: 5983: 5852: 5842: 5630:Two-neutrino case 5589: 5578: 5526: 5474: 5365: 5314: 5181: 5020: 5001: 4979: 4825: 4821: 4803: 4788: 4733: 4715: 4700: 4651: 4607: 4495: 4456: 4403: 4395: 4234: 4212: 4044: 3968: 3950: 3864: 3716: 3674: 3533: 3529: 3490: 3437: 3363: 3322: 3280: 3239: 3213:{\displaystyle t} 3191:{\displaystyle j} 3132: 3108: 3085: 3023: 2979: 2958: 1571:sterile neutrinos 1542:(also called the 1498:complex conjugate 1414: 1401: 1381: 1360: 1322: 1301: 1232: 1144: 1001:coherence lengths 544: 543: 418:Quantum cosmology 198:Quantum cosmology 120:Strong CP problem 80:Hierarchy problem 16:(Redirected from 10566: 10519: 10518: 10507: 10506: 10297: 10296: 10252: 10251: 10233:Weak hypercharge 10218:Weak interaction 10159:Particle physics 10138: 10131: 10124: 10115: 10114: 10102: 10078: 10052: 10031: 10005: 9982: 9956: 9935: 9909: 9876: 9875: 9865: 9840:(4): 1740–1757. 9829: 9817:Kostelecký, Alan 9813: 9807: 9806: 9796: 9771:(5): 1642–1645. 9758: 9752: 9751: 9725: 9699: 9693: 9692: 9658: 9634: 9628: 9627: 9617: 9607: 9573: 9567: 9566: 9560: 9555: 9553: 9545: 9541: 9528: 9527: 9518: 9516: 9504: 9483: 9482: 9453: 9451:astro-ph/0406663 9433: 9420: 9414: 9413: 9396:(9): 2227–2235. 9385: 9383: 9371: 9365: 9364: 9327: 9321: 9320: 9287: 9281: 9280: 9278: 9244: 9238: 9237: 9211: 9191: 9185: 9184: 9158: 9138: 9132: 9131: 9129: 9119: 9087: 9081: 9080: 9078: 9060: 9036: 9030: 9029: 8995: 8975: 8969: 8968: 8942: 8918: 8912: 8911: 8877: 8857: 8851: 8850: 8808: 8788: 8782: 8781: 8747: 8727: 8721: 8720: 8709:10.1134/1.855739 8694: 8674: 8668: 8667: 8641: 8632:(8): 1562–1567. 8621: 8615: 8614: 8580: 8562: 8557: 8549: 8543: 8542: 8514: 8508: 8507: 8489: 8471: 8449: 8443: 8442: 8440: 8438: 8421: 8415: 8414: 8396: 8376: 8370: 8369: 8341: 8335: 8334: 8305: 8277: 8268: 8267: 8238: 8222: 8213: 8212: 8192: 8167: 8164: 8158: 8156: 8144: 8138: 8120: 8007:seesaw mechanism 8001:Seesaw mechanism 7995:Seesaw mechanism 7924: 7917: 7913: 7912: 7910: 7905: 7894: 7892: 7865: 7861: 7856: 7848: 7847: 7840: 7832:Super-Kamiokande 7829: 7824: 7816: 7815: 7808: 7793: 7792: 7785: 7779:and the sign of 7778: 7755: 7753: 7749: 7744: 7742: 7741: 7713: 7711: 7707: 7702: 7700: 7699: 7677: 7675: 7670: 7653: 7650: 7630: 7628: 7623: 7606: 7604: 7599: 7580: 7578: 7572: 7571: 7560: 7559: 7546: 7544: 7538: 7537: 7394: 7393: 7305: 7303: 7302: 7297: 7295: 7292: 7291: 7282: 7273: 7271: 7270: 7265: 7263: 7260: 7259: 7250: 7212: 7210: 7209: 7204: 7202: 7201: 7194: 7193: 7180: 7179: 7162: 7161: 7154: 7153: 7130: 7129: 7112: 7111: 7104: 7103: 7092: 7091: 7090: 7073: 7065: 7044: 7042: 7041: 7036: 7034: 7033: 7026: 7025: 7012: 7011: 6994: 6993: 6928: 6927: 6920: 6919: 6906: 6905: 6864:spectral theorem 6858: 6856: 6855: 6850: 6845: 6844: 6837: 6836: 6823: 6822: 6805: 6804: 6797: 6789: 6784: 6782: 6781: 6769: 6765: 6757: 6748: 6740: 6733: 6725: 6720: 6718: 6717: 6705: 6695: 6694: 6687: 6686: 6675: 6674: 6657: 6649: 6606: 6604: 6603: 6598: 6593: 6589: 6588: 6587: 6578: 6577: 6565: 6564: 6552: 6544: 6538: 6533: 6524: 6522: 6521: 6509: 6503: 6498: 6489: 6487: 6486: 6474: 6467: 6459: 6433: 6431: 6430: 6425: 6422: 6416: 6408: 6391: 6389: 6388: 6383: 6381: 6380: 6368: 6359: 6349: 6347: 6346: 6341: 6338: 6332: 6324: 6302:standard gravity 6295: 6293: 6292: 6287: 6285: 6284: 6275: 6269: 6261: 6258: 6249: 6238:potential energy 6191: 6177: 6163: 6149: 6129: 6125: 6115: 6106: 6097: 6080: 6061: 6059: 6058: 6053: 6046: 6045: 6041: 6040: 6038: 6021: 6004: 6003: 5987: 5984: 5979: 5975: 5974: 5961: 5947: 5946: 5921: 5920: 5908: 5907: 5863: 5861: 5860: 5855: 5853: 5850: 5847: 5843: 5841: 5833: 5829: 5828: 5815: 5806: 5805: 5780: 5779: 5767: 5766: 5726: 5724: 5723: 5718: 5713: 5712: 5625: 5623: 5622: 5617: 5615: 5614: 5597: 5583: 5579: 5577: 5569: 5564: 5563: 5554: 5553: 5543: 5531: 5527: 5525: 5517: 5512: 5511: 5502: 5501: 5491: 5479: 5475: 5473: 5465: 5460: 5459: 5450: 5449: 5439: 5419: 5405: 5404: 5378: 5376: 5375: 5370: 5363: 5362: 5361: 5345: 5344: 5328: 5306: 5302: 5299: 5294: 5281: 5280: 5267: 5266: 5252: 5247: 5226: 5225: 5224: 5223: 5196: 5194: 5193: 5188: 5186: 5182: 5180: 5172: 5167: 5166: 5157: 5156: 5143: 5130: 5126: 5123: 5118: 5105: 5104: 5091: 5090: 5076: 5071: 5050: 5049: 5048: 5047: 5034: 5009: 5008: 5003: 5002: 4994: 4987: 4986: 4981: 4980: 4972: 4956: 4955: 4943: 4942: 4923: 4909: 4908: 4885: 4873: 4863: 4856: 4838: 4836: 4835: 4830: 4823: 4822: 4817: 4806: 4804: 4802: 4791: 4789: 4787: 4786: 4781: 4780: 4770: 4769: 4768: 4759: 4758: 4745: 4734: 4729: 4718: 4716: 4714: 4703: 4701: 4699: 4698: 4693: 4692: 4682: 4681: 4680: 4671: 4670: 4657: 4652: 4650: 4639: 4638: 4637: 4627: 4626: 4613: 4608: 4606: 4591: 4586: 4585: 4576: 4575: 4560: 4559: 4546: 4534: 4532: 4531: 4526: 4514: 4508: 4506: 4505: 4500: 4493: 4491: 4486: 4473: 4468: 4454: 4453: 4452: 4443: 4442: 4420: 4418: 4417: 4412: 4410: 4401: 4400: 4396: 4394: 4386: 4381: 4380: 4371: 4370: 4357: 4344: 4340: 4337: 4332: 4319: 4318: 4305: 4304: 4290: 4285: 4264: 4263: 4262: 4261: 4248: 4226: 4221: 4217: 4213: 4211: 4203: 4198: 4197: 4188: 4187: 4174: 4165: 4164: 4154: 4150: 4147: 4142: 4129: 4128: 4115: 4114: 4100: 4095: 4074: 4073: 4072: 4071: 4058: 4036: 4030: 4029: 4014: 4013: 3981: 3979: 3978: 3973: 3966: 3965: 3964: 3959: 3955: 3953: 3952: 3951: 3949: 3941: 3935: 3930: 3920: 3906: 3905: 3891: 3886: 3872: 3851: 3850: 3845: 3844: 3836: 3832: 3821: 3820: 3810: 3806: 3804: 3803: 3783: 3782: 3771: 3770: 3745: 3741: 3729: 3727: 3726: 3721: 3714: 3713: 3709: 3698: 3697: 3681: 3680: 3679: 3675: 3673: 3664: 3657: 3652: 3641: 3620: 3616: 3605: 3604: 3579: 3575: 3564: 3553: 3546: 3544: 3543: 3538: 3531: 3530: 3528: 3516: 3511: 3502: 3491: 3489: 3487: 3486: 3470: 3465: 3456: 3451: 3450: 3438: 3434: 3429: 3416: 3411: 3401: 3396: 3395: 3376: 3374: 3373: 3368: 3361: 3360: 3359: 3347: 3346: 3334: 3330: 3329: 3324: 3323: 3315: 3292: 3290: 3289: 3284: 3282: 3281: 3273: 3257: 3255: 3254: 3249: 3247: 3246: 3241: 3240: 3232: 3219: 3217: 3216: 3211: 3197: 3195: 3194: 3189: 3173: 3171: 3170: 3165: 3163: 3162: 3145: 3143: 3142: 3137: 3130: 3118: 3117: 3106: 3098: 3096: 3095: 3090: 3083: 3036: 3034: 3033: 3028: 3021: 3020: 3016: 3005: 3004: 2989: 2988: 2987: 2983: 2981: 2980: 2972: 2966: 2965: 2960: 2959: 2951: 2939: 2938: 2908: 2904: 2893: 2892: 2863: 2861: 2860: 2855: 2853: 2849: 2847: 2846: 2815:sterile neutrino 2804: 2789: 2782: 2778: 2776: 2769: 2766: 2758: 2756: 2749: 2746: 2735: 2733: 2732: 2727: 2725: 2718: 2717: 2688: 2687: 2683: 2678: 2677: 2641: 2640: 2636: 2631: 2630: 2605: 2604: 2597: 2596: 2587: 2586: 2575: 2574: 2562: 2561: 2552: 2551: 2542: 2541: 2529: 2528: 2519: 2518: 2504: 2503: 2491: 2490: 2481: 2480: 2471: 2470: 2458: 2457: 2448: 2447: 2434: 2433: 2424: 2423: 2412: 2411: 2399: 2398: 2389: 2388: 2379: 2378: 2366: 2365: 2356: 2355: 2344: 2343: 2331: 2330: 2321: 2320: 2311: 2310: 2298: 2297: 2288: 2287: 2271: 2270: 2255: 2254: 2243: 2242: 2233: 2232: 2221: 2220: 2211: 2210: 2187: 2183: 2182: 2153: 2152: 2148: 2143: 2142: 2106: 2105: 2101: 2096: 2095: 2070: 2069: 2040: 2039: 2028: 2027: 2006: 2005: 1994: 1993: 1976: 1975: 1968: 1967: 1951: 1950: 1938: 1937: 1904: 1903: 1888: 1887: 1871: 1870: 1853: 1852: 1845: 1844: 1833: 1832: 1811: 1810: 1799: 1798: 1753: 1749: 1748: 1741: 1740: 1726: 1725: 1711: 1710: 1694: 1693: 1679: 1678: 1664: 1663: 1647: 1646: 1632: 1631: 1617: 1616: 1537: 1535: 1534: 1529: 1527: 1526: 1495: 1493: 1492: 1487: 1485: 1484: 1467: 1465: 1464: 1459: 1427: 1425: 1424: 1419: 1412: 1411: 1410: 1399: 1391: 1389: 1388: 1383: 1379: 1378: 1374: 1373: 1358: 1348: 1344: 1340: 1336: 1332: 1330: 1329: 1324: 1320: 1319: 1315: 1314: 1299: 1285: 1283: 1282: 1277: 1272: 1268: 1267: 1254: 1253: 1240: 1228: 1224: 1223: 1202: 1200: 1199: 1194: 1189: 1185: 1184: 1170: 1165: 1152: 1140: 1136: 1135: 1096:Bruno Pontecorvo 1066: 1064: 1062: 1061: 1060: 1053: 1050: 1049: 1038: 1036: 1034: 1033: 1032: 1025: 1024: 945: 906:sterile neutrino 860: 858: 852: 847: 838: 833: 817: 808: 799: 793:nuclear reactors 765:Super-Kamiokande 680: 676: 672: 671: 670: 668: 667: 664: 661: 616:particle physics 589:Bruno Pontecorvo 536: 529: 522: 408:Quantum geometry 363:Extra dimensions 46: 32: 31: 21: 10574: 10573: 10569: 10568: 10567: 10565: 10564: 10563: 10534: 10533: 10532: 10527: 10495: 10450: 10408:Quantum gravity 10402: 10369: 10338: 10291: 10284: 10275:Higgs mechanism 10253: 10249: 10244: 10147: 10142: 10093: 10085: 9884: 9882:Further reading 9879: 9827: 9814: 9810: 9759: 9755: 9700: 9696: 9635: 9631: 9574: 9570: 9558: 9556: 9547: 9546: 9542: 9531: 9514: 9512: 9505: 9486: 9444:(1–4): 1–1109. 9431: 9421: 9417: 9381: 9379: 9372: 9368: 9328: 9324: 9288: 9284: 9245: 9241: 9209:physics/0303116 9192: 9188: 9139: 9135: 9088: 9084: 9037: 9033: 8976: 8972: 8924: 8919: 8915: 8858: 8854: 8789: 8785: 8728: 8724: 8675: 8671: 8622: 8618: 8578:nucl-ex/0106015 8560: 8555: 8553: 8550: 8546: 8515: 8511: 8487:10.1.1.312.3412 8455:Physics Reports 8450: 8446: 8436: 8434: 8422: 8418: 8377: 8373: 8342: 8338: 8318:Sov. Phys. JETP 8278: 8271: 8251:Sov. Phys. JETP 8224: 8223: 8216: 8209: 8193: 8180: 8176: 8171: 8170: 8165: 8161: 8155: 8151: 8147: 8145: 8141: 8121: 8117: 8112: 8075: 8058: 8033: 8003: 7997: 7958: 7927: 7922: 7915: 7908: 7906: 7899: 7898: 7890: 7883: 7882: 7868: 7863: 7859: 7851: 7850: 7846: 7843: 7842: 7841: 7835: 7827: 7819: 7818: 7814: 7811: 7810: 7809: 7803: 7791: 7788: 7787: 7786: 7780: 7776: 7769: 7759: 7751: 7747: 7745: 7740: 7737: 7736: 7735: 7727: 7720: 7716: 7709: 7705: 7703: 7698: 7695: 7694: 7693: 7685: 7681: 7673: 7671: 7668: 7661: 7655: 7651: 7648: 7641: 7637: 7626: 7624: 7621: 7614: 7602: 7600: 7597: 7590: 7587: 7576: 7574: 7570: 7567: 7566: 7565: 7558: 7555: 7554: 7553: 7542: 7540: 7536: 7533: 7532: 7531: 7524: 7517: 7510: 7494: 7484: 7474: 7388: 7365: 7360: 7323: 7314: 7287: 7283: 7281: 7279: 7276: 7275: 7255: 7251: 7249: 7247: 7244: 7243: 7241: 7237: 7229: 7222: 7196: 7195: 7189: 7185: 7182: 7181: 7175: 7171: 7164: 7163: 7156: 7155: 7149: 7145: 7143: 7137: 7136: 7131: 7125: 7121: 7114: 7113: 7106: 7105: 7099: 7095: 7086: 7082: 7075: 7074: 7064: 7056: 7053: 7052: 7028: 7027: 7021: 7017: 7014: 7013: 7007: 7003: 6996: 6995: 6988: 6987: 6976: 6961: 6960: 6949: 6933: 6932: 6922: 6921: 6915: 6911: 6908: 6907: 6901: 6897: 6890: 6889: 6887: 6884: 6883: 6839: 6838: 6832: 6828: 6825: 6824: 6818: 6814: 6807: 6806: 6799: 6798: 6788: 6777: 6773: 6768: 6766: 6756: 6750: 6749: 6739: 6734: 6724: 6713: 6709: 6704: 6697: 6696: 6689: 6688: 6682: 6678: 6676: 6670: 6666: 6659: 6658: 6648: 6640: 6637: 6636: 6631: 6622: 6583: 6579: 6573: 6569: 6560: 6556: 6543: 6534: 6529: 6517: 6513: 6508: 6499: 6494: 6482: 6478: 6473: 6472: 6468: 6458: 6450: 6447: 6446: 6412: 6407: 6405: 6402: 6401: 6376: 6372: 6357: 6355: 6352: 6351: 6328: 6323: 6321: 6318: 6317: 6280: 6276: 6262: 6259: 6247: 6245: 6242: 6241: 6211:spring constant 6199: 6198: 6197: 6196: 6195: 6192: 6183: 6182: 6181: 6178: 6169: 6168: 6167: 6164: 6155: 6154: 6153: 6150: 6139: 6132: 6127: 6123: 6117: 6114: 6108: 6105: 6099: 6095: 6088: 6082: 6079: 6072: 6066: 6022: 5999: 5995: 5988: 5986: 5970: 5966: 5962: 5960: 5955: 5951: 5942: 5938: 5916: 5912: 5885: 5881: 5879: 5876: 5875: 5849: 5834: 5824: 5820: 5816: 5814: 5810: 5801: 5797: 5775: 5771: 5744: 5740: 5738: 5735: 5734: 5707: 5706: 5695: 5680: 5679: 5668: 5652: 5651: 5643: 5640: 5639: 5632: 5604: 5600: 5593: 5570: 5559: 5555: 5549: 5545: 5544: 5542: 5538: 5518: 5507: 5503: 5497: 5493: 5492: 5490: 5486: 5466: 5455: 5451: 5445: 5441: 5440: 5438: 5434: 5406: 5397: 5396: 5390: 5387: 5386: 5351: 5347: 5334: 5330: 5318: 5295: 5287: 5273: 5269: 5259: 5255: 5248: 5240: 5234: 5230: 5219: 5215: 5214: 5213: 5211: 5208: 5207: 5173: 5162: 5158: 5149: 5145: 5144: 5142: 5138: 5119: 5111: 5097: 5093: 5083: 5079: 5072: 5064: 5058: 5054: 5043: 5039: 5038: 5037: 5024: 5004: 4993: 4992: 4991: 4982: 4971: 4970: 4969: 4951: 4947: 4938: 4934: 4910: 4901: 4900: 4894: 4891: 4890: 4883: 4878:If there is no 4871: 4861: 4851: 4807: 4805: 4795: 4790: 4782: 4773: 4772: 4771: 4764: 4760: 4751: 4747: 4746: 4744: 4719: 4717: 4707: 4702: 4694: 4685: 4684: 4683: 4676: 4672: 4663: 4659: 4658: 4656: 4640: 4630: 4629: 4616: 4615: 4614: 4612: 4592: 4581: 4577: 4571: 4567: 4552: 4548: 4547: 4545: 4543: 4540: 4539: 4520: 4517: 4516: 4512: 4487: 4482: 4469: 4464: 4448: 4444: 4435: 4431: 4429: 4426: 4425: 4408: 4407: 4387: 4376: 4372: 4363: 4359: 4358: 4356: 4352: 4333: 4325: 4311: 4307: 4297: 4293: 4286: 4278: 4272: 4268: 4257: 4253: 4252: 4251: 4238: 4225: 4219: 4218: 4204: 4193: 4189: 4180: 4176: 4175: 4173: 4169: 4160: 4156: 4143: 4135: 4121: 4117: 4107: 4103: 4096: 4088: 4082: 4078: 4067: 4063: 4062: 4061: 4048: 4035: 4031: 4022: 4018: 4003: 3999: 3995: 3993: 3990: 3989: 3960: 3942: 3931: 3926: 3921: 3919: 3912: 3908: 3898: 3894: 3887: 3879: 3868: 3862: 3858: 3857: 3846: 3840: 3839: 3838: 3816: 3812: 3799: 3795: 3794: 3791: 3789: 3785: 3778: 3777: 3760: 3756: 3754: 3751: 3750: 3743: 3739: 3693: 3689: 3687: 3683: 3665: 3653: 3648: 3642: 3640: 3636: 3628: 3624: 3600: 3596: 3594: 3590: 3588: 3585: 3584: 3577: 3566: 3562: 3551: 3518: 3512: 3507: 3501: 3482: 3478: 3472: 3466: 3461: 3455: 3446: 3442: 3430: 3425: 3412: 3407: 3400: 3391: 3387: 3385: 3382: 3381: 3355: 3351: 3342: 3338: 3325: 3314: 3313: 3312: 3308: 3306: 3303: 3302: 3272: 3271: 3269: 3266: 3265: 3242: 3231: 3230: 3229: 3227: 3224: 3223: 3205: 3202: 3201: 3183: 3180: 3179: 3158: 3154: 3152: 3149: 3148: 3113: 3109: 3104: 3101: 3100: 3052: 3049: 3048: 3000: 2996: 2994: 2990: 2971: 2970: 2961: 2950: 2949: 2948: 2934: 2930: 2928: 2924: 2916: 2912: 2888: 2884: 2882: 2878: 2876: 2873: 2872: 2842: 2838: 2836: 2832: 2830: 2827: 2826: 2823: 2802: 2792: 2787: 2785: 2780: 2775: 2771: 2767: 2765: 2761: 2760: 2755: 2751: 2747: 2745: 2741: 2740: 2723: 2722: 2712: 2711: 2706: 2701: 2695: 2694: 2689: 2679: 2673: 2669: 2665: 2661: 2659: 2653: 2652: 2647: 2642: 2632: 2626: 2622: 2618: 2614: 2607: 2606: 2599: 2598: 2592: 2588: 2582: 2578: 2576: 2567: 2563: 2557: 2553: 2547: 2543: 2537: 2533: 2524: 2520: 2514: 2510: 2505: 2496: 2492: 2486: 2482: 2476: 2472: 2466: 2462: 2453: 2449: 2443: 2439: 2436: 2435: 2429: 2425: 2419: 2415: 2413: 2404: 2400: 2394: 2390: 2384: 2380: 2374: 2370: 2361: 2357: 2351: 2347: 2345: 2336: 2332: 2326: 2322: 2316: 2312: 2306: 2302: 2293: 2289: 2283: 2279: 2273: 2272: 2260: 2256: 2250: 2246: 2244: 2238: 2234: 2228: 2224: 2222: 2216: 2212: 2206: 2202: 2195: 2194: 2185: 2184: 2177: 2176: 2171: 2166: 2160: 2159: 2154: 2144: 2138: 2134: 2130: 2126: 2124: 2118: 2117: 2112: 2107: 2097: 2091: 2087: 2083: 2079: 2072: 2071: 2064: 2063: 2058: 2053: 2047: 2046: 2041: 2035: 2031: 2029: 2023: 2019: 2013: 2012: 2007: 2001: 1997: 1995: 1989: 1985: 1978: 1977: 1970: 1969: 1963: 1959: 1957: 1952: 1943: 1939: 1933: 1929: 1923: 1922: 1917: 1912: 1906: 1905: 1893: 1889: 1883: 1879: 1877: 1872: 1866: 1862: 1855: 1854: 1847: 1846: 1840: 1836: 1834: 1828: 1824: 1819: 1813: 1812: 1806: 1802: 1800: 1794: 1790: 1788: 1782: 1781: 1776: 1771: 1761: 1760: 1751: 1750: 1743: 1742: 1733: 1729: 1727: 1718: 1714: 1712: 1703: 1699: 1696: 1695: 1686: 1682: 1680: 1671: 1667: 1665: 1656: 1652: 1649: 1648: 1639: 1635: 1633: 1624: 1620: 1618: 1609: 1605: 1598: 1597: 1590: 1583: 1581: 1578: 1577: 1564:identity matrix 1538:represents the 1519: 1515: 1513: 1510: 1509: 1496:) represents a 1480: 1477: 1475: 1472: 1471: 1432: 1429: 1428: 1406: 1402: 1397: 1394: 1393: 1369: 1365: 1361: 1356: 1353: 1352: 1346: 1342: 1338: 1334: 1310: 1306: 1302: 1297: 1294: 1293: 1263: 1259: 1255: 1246: 1242: 1236: 1219: 1215: 1211: 1209: 1206: 1205: 1180: 1176: 1172: 1166: 1158: 1148: 1131: 1127: 1123: 1121: 1118: 1117: 1092: 1086: 1059: 1056: 1055: 1054: 1051: 1048: 1046: 1045: 1044: 1043: 1041: 1040: 1031: 1029: 1028: 1027: 1023: 1021: 1020: 1019: 1018: 1016: 1015: 960: 948: 943: 898:LSND experiment 871: 856: 854: 850: 845: 844: 836: 831: 830: 820: 815: 811: 806: 802: 797: 777: 742: 692: 678: 674: 665: 662: 659: 658: 656: 655: 654: 636: 576:) can later be 540: 511: 510: 466: 458: 457: 383: 381:Quantum gravity 373: 372: 328: 318: 317: 298:Massive gravity 203:Brane cosmology 138: 130: 129: 75: 60: 28: 23: 22: 15: 12: 11: 5: 10572: 10562: 10561: 10556: 10551: 10549:Standard Model 10546: 10529: 10528: 10526: 10525: 10513: 10500: 10497: 10496: 10494: 10493: 10488: 10483: 10478: 10473: 10468: 10462: 10460: 10456: 10455: 10452: 10451: 10449: 10448: 10446:Twistor theory 10443: 10438: 10433: 10428: 10423: 10418: 10412: 10410: 10404: 10403: 10401: 10400: 10395: 10390: 10385: 10379: 10377: 10371: 10370: 10368: 10367: 10362: 10357: 10352: 10346: 10344: 10340: 10339: 10337: 10336: 10331: 10326: 10325: 10324: 10314: 10309: 10303: 10301: 10294: 10292:Standard Model 10286: 10285: 10283: 10282: 10277: 10272: 10267: 10261: 10259: 10255: 10254: 10247: 10245: 10243: 10242: 10241: 10240: 10235: 10230: 10225: 10220: 10210: 10209: 10208: 10203: 10198: 10188: 10183: 10178: 10177: 10176: 10171: 10166: 10155: 10153: 10149: 10148: 10145:Standard Model 10141: 10140: 10133: 10126: 10118: 10112: 10111: 10091: 10084: 10083:External links 10081: 10080: 10079: 10032: 9983: 9954:hep-ph/0405172 9936: 9907:hep-ph/0202058 9900:(2): 345–402. 9883: 9880: 9878: 9877: 9823:(March 1994). 9821:Samuel, Stuart 9808: 9753: 9723:hep-ph/0608101 9716:(1): 473–505. 9694: 9629: 9568: 9559:|journal= 9529: 9484: 9415: 9366: 9347:(7): 493–496. 9335:Pontecorvo, B. 9322: 9282: 9239: 9202:(6): 742–752. 9186: 9133: 9082: 9051:(2): 191–196. 9031: 8970: 8933:(3): 138–145. 8922: 8913: 8868:(19): 191802. 8852: 8799:(17): 171803. 8783: 8738:(19): 131801. 8722: 8692:hep-ex/9908047 8669: 8639:hep-ex/9807003 8616: 8558: 8544: 8509: 8462:(1–3): 1–129. 8444: 8416: 8371: 8352:(4): 479–500. 8336: 8269: 8258:(2): 429–431. 8214: 8207: 8177: 8175: 8172: 8169: 8168: 8159: 8153: 8149: 8139: 8128:density matrix 8114: 8113: 8111: 8108: 8107: 8106: 8101: 8096: 8091: 8086: 8081: 8074: 8071: 8062:early universe 8057: 8054: 8032: 8029: 7999:Main article: 7996: 7993: 7957: 7954: 7939:T2K experiment 7934:solar neutrino 7925: 7888: 7866: 7857: 7844: 7825: 7812: 7796: 7795: 7789: 7774: 7767: 7757: 7738: 7725: 7718: 7714: 7696: 7683: 7679: 7666: 7659: 7646: 7639: 7635: 7619: 7612: 7595: 7586: 7583: 7582: 7581: 7568: 7556: 7547: 7534: 7525: 7522: 7515: 7508: 7502: 7496: 7492: 7486: 7482: 7476: 7472: 7460: 7459: 7449: 7438: 7437: 7427: 7416: 7415: 7405: 7387: 7384: 7364: 7361: 7359: 7356: 7319: 7310: 7290: 7286: 7258: 7254: 7239: 7235: 7227: 7220: 7214: 7213: 7200: 7192: 7188: 7184: 7183: 7178: 7174: 7170: 7169: 7167: 7160: 7152: 7148: 7144: 7142: 7139: 7138: 7135: 7132: 7128: 7124: 7120: 7119: 7117: 7110: 7102: 7098: 7089: 7085: 7081: 7080: 7078: 7071: 7068: 7063: 7060: 7046: 7045: 7032: 7024: 7020: 7016: 7015: 7010: 7006: 7002: 7001: 6999: 6992: 6986: 6983: 6980: 6977: 6975: 6972: 6969: 6966: 6963: 6962: 6959: 6956: 6953: 6950: 6948: 6945: 6942: 6939: 6938: 6936: 6931: 6926: 6918: 6914: 6910: 6909: 6904: 6900: 6896: 6895: 6893: 6872:diagonalizable 6860: 6859: 6848: 6843: 6835: 6831: 6827: 6826: 6821: 6817: 6813: 6812: 6810: 6803: 6795: 6792: 6787: 6780: 6776: 6772: 6767: 6763: 6760: 6755: 6752: 6751: 6746: 6743: 6738: 6735: 6731: 6728: 6723: 6716: 6712: 6708: 6703: 6702: 6700: 6693: 6685: 6681: 6677: 6673: 6669: 6665: 6664: 6662: 6655: 6652: 6647: 6644: 6627: 6618: 6612:quadratic form 6608: 6607: 6596: 6592: 6586: 6582: 6576: 6572: 6568: 6563: 6559: 6555: 6550: 6547: 6542: 6537: 6532: 6528: 6520: 6516: 6512: 6507: 6502: 6497: 6493: 6485: 6481: 6477: 6471: 6465: 6462: 6457: 6454: 6419: 6415: 6411: 6379: 6375: 6371: 6365: 6362: 6335: 6331: 6327: 6283: 6279: 6272: 6268: 6265: 6255: 6252: 6193: 6186: 6185: 6184: 6179: 6172: 6171: 6170: 6165: 6158: 6157: 6156: 6151: 6144: 6143: 6142: 6141: 6140: 6138: 6135: 6130: 6121: 6112: 6103: 6093: 6086: 6077: 6070: 6063: 6062: 6051: 6044: 6037: 6034: 6031: 6028: 6025: 6020: 6017: 6014: 6011: 6007: 6002: 5998: 5994: 5991: 5982: 5978: 5973: 5969: 5965: 5958: 5954: 5950: 5945: 5941: 5936: 5933: 5930: 5927: 5924: 5919: 5915: 5911: 5906: 5903: 5900: 5897: 5894: 5891: 5888: 5884: 5865: 5864: 5846: 5840: 5837: 5832: 5827: 5823: 5819: 5813: 5809: 5804: 5800: 5795: 5792: 5789: 5786: 5783: 5778: 5774: 5770: 5765: 5762: 5759: 5756: 5753: 5750: 5747: 5743: 5728: 5727: 5716: 5711: 5705: 5702: 5699: 5696: 5694: 5691: 5688: 5685: 5682: 5681: 5678: 5675: 5672: 5669: 5667: 5664: 5661: 5658: 5657: 5655: 5650: 5647: 5631: 5628: 5627: 5626: 5613: 5610: 5607: 5603: 5596: 5592: 5587: 5582: 5576: 5573: 5568: 5562: 5558: 5552: 5548: 5541: 5537: 5534: 5530: 5524: 5521: 5516: 5510: 5506: 5500: 5496: 5489: 5485: 5482: 5478: 5472: 5469: 5464: 5458: 5454: 5448: 5444: 5437: 5433: 5430: 5426: 5423: 5418: 5415: 5412: 5409: 5403: 5400: 5395: 5380: 5379: 5368: 5360: 5357: 5354: 5350: 5343: 5340: 5337: 5333: 5327: 5324: 5321: 5317: 5312: 5309: 5305: 5298: 5293: 5290: 5286: 5279: 5276: 5272: 5265: 5262: 5258: 5251: 5246: 5243: 5239: 5233: 5229: 5222: 5218: 5198: 5197: 5185: 5179: 5176: 5171: 5165: 5161: 5155: 5152: 5148: 5141: 5137: 5134: 5129: 5122: 5117: 5114: 5110: 5103: 5100: 5096: 5089: 5086: 5082: 5075: 5070: 5067: 5063: 5057: 5053: 5046: 5042: 5033: 5030: 5027: 5023: 5018: 5015: 5012: 5007: 5000: 4997: 4990: 4985: 4978: 4975: 4968: 4965: 4962: 4959: 4954: 4950: 4946: 4941: 4937: 4933: 4930: 4927: 4922: 4919: 4916: 4913: 4907: 4904: 4899: 4876: 4875: 4868: 4858: 4842:where 1.27 is 4840: 4839: 4828: 4820: 4816: 4813: 4810: 4801: 4798: 4794: 4785: 4779: 4776: 4767: 4763: 4757: 4754: 4750: 4743: 4740: 4737: 4732: 4728: 4725: 4722: 4713: 4710: 4706: 4697: 4691: 4688: 4679: 4675: 4669: 4666: 4662: 4655: 4649: 4646: 4643: 4636: 4633: 4625: 4622: 4619: 4611: 4605: 4601: 4598: 4595: 4590: 4584: 4580: 4574: 4570: 4566: 4563: 4558: 4555: 4551: 4524: 4498: 4490: 4485: 4481: 4477: 4472: 4467: 4463: 4459: 4451: 4447: 4441: 4438: 4434: 4422: 4421: 4406: 4399: 4393: 4390: 4385: 4379: 4375: 4369: 4366: 4362: 4355: 4351: 4348: 4343: 4336: 4331: 4328: 4324: 4317: 4314: 4310: 4303: 4300: 4296: 4289: 4284: 4281: 4277: 4271: 4267: 4260: 4256: 4247: 4244: 4241: 4237: 4232: 4229: 4224: 4222: 4220: 4216: 4210: 4207: 4202: 4196: 4192: 4186: 4183: 4179: 4172: 4168: 4163: 4159: 4153: 4146: 4141: 4138: 4134: 4127: 4124: 4120: 4113: 4110: 4106: 4099: 4094: 4091: 4087: 4081: 4077: 4070: 4066: 4057: 4054: 4051: 4047: 4042: 4039: 4034: 4032: 4028: 4025: 4021: 4017: 4012: 4009: 4006: 4002: 3998: 3997: 3983: 3982: 3971: 3963: 3958: 3948: 3945: 3940: 3934: 3929: 3925: 3918: 3915: 3911: 3904: 3901: 3897: 3890: 3885: 3882: 3878: 3871: 3867: 3861: 3855: 3849: 3843: 3835: 3830: 3827: 3824: 3819: 3815: 3809: 3802: 3798: 3793: 3788: 3781: 3775: 3769: 3766: 3763: 3759: 3731: 3730: 3719: 3712: 3707: 3704: 3701: 3696: 3692: 3686: 3678: 3672: 3668: 3662: 3656: 3651: 3647: 3639: 3634: 3631: 3627: 3623: 3619: 3614: 3611: 3608: 3603: 3599: 3593: 3559:Lorentz factor 3548: 3547: 3536: 3526: 3522: 3515: 3510: 3506: 3500: 3497: 3494: 3485: 3481: 3476: 3469: 3464: 3460: 3454: 3449: 3445: 3441: 3433: 3428: 3424: 3420: 3415: 3410: 3406: 3399: 3394: 3390: 3366: 3358: 3354: 3350: 3345: 3341: 3337: 3333: 3328: 3321: 3318: 3311: 3295: 3294: 3279: 3276: 3263: 3245: 3238: 3235: 3221: 3209: 3199: 3187: 3161: 3157: 3146: 3135: 3129: 3126: 3122: 3116: 3112: 3088: 3082: 3078: 3075: 3072: 3069: 3066: 3063: 3060: 3056: 3038: 3037: 3026: 3019: 3014: 3011: 3008: 3003: 2999: 2993: 2986: 2978: 2975: 2969: 2964: 2957: 2954: 2946: 2942: 2937: 2933: 2927: 2922: 2919: 2915: 2911: 2907: 2902: 2899: 2896: 2891: 2887: 2881: 2852: 2845: 2841: 2835: 2822: 2819: 2790: 2783: 2773: 2763: 2753: 2743: 2737: 2736: 2721: 2716: 2710: 2707: 2705: 2702: 2700: 2697: 2696: 2693: 2690: 2686: 2682: 2676: 2672: 2668: 2664: 2660: 2658: 2655: 2654: 2651: 2648: 2646: 2643: 2639: 2635: 2629: 2625: 2621: 2617: 2613: 2612: 2610: 2603: 2595: 2591: 2585: 2581: 2577: 2573: 2570: 2566: 2560: 2556: 2550: 2546: 2540: 2536: 2532: 2527: 2523: 2517: 2513: 2509: 2506: 2502: 2499: 2495: 2489: 2485: 2479: 2475: 2469: 2465: 2461: 2456: 2452: 2446: 2442: 2438: 2437: 2432: 2428: 2422: 2418: 2414: 2410: 2407: 2403: 2397: 2393: 2387: 2383: 2377: 2373: 2369: 2364: 2360: 2354: 2350: 2346: 2342: 2339: 2335: 2329: 2325: 2319: 2315: 2309: 2305: 2301: 2296: 2292: 2286: 2282: 2278: 2275: 2274: 2269: 2266: 2263: 2259: 2253: 2249: 2245: 2241: 2237: 2231: 2227: 2223: 2219: 2215: 2209: 2205: 2201: 2200: 2198: 2193: 2190: 2188: 2186: 2181: 2175: 2172: 2170: 2167: 2165: 2162: 2161: 2158: 2155: 2151: 2147: 2141: 2137: 2133: 2129: 2125: 2123: 2120: 2119: 2116: 2113: 2111: 2108: 2104: 2100: 2094: 2090: 2086: 2082: 2078: 2077: 2075: 2068: 2062: 2059: 2057: 2054: 2052: 2049: 2048: 2045: 2042: 2038: 2034: 2030: 2026: 2022: 2018: 2015: 2014: 2011: 2008: 2004: 2000: 1996: 1992: 1988: 1984: 1983: 1981: 1974: 1966: 1962: 1958: 1956: 1953: 1949: 1946: 1942: 1936: 1932: 1928: 1925: 1924: 1921: 1918: 1916: 1913: 1911: 1908: 1907: 1902: 1899: 1896: 1892: 1886: 1882: 1878: 1876: 1873: 1869: 1865: 1861: 1860: 1858: 1851: 1843: 1839: 1835: 1831: 1827: 1823: 1820: 1818: 1815: 1814: 1809: 1805: 1801: 1797: 1793: 1789: 1787: 1784: 1783: 1780: 1777: 1775: 1772: 1770: 1767: 1766: 1764: 1759: 1756: 1754: 1752: 1747: 1739: 1736: 1732: 1728: 1724: 1721: 1717: 1713: 1709: 1706: 1702: 1698: 1697: 1692: 1689: 1685: 1681: 1677: 1674: 1670: 1666: 1662: 1659: 1655: 1651: 1650: 1645: 1642: 1638: 1634: 1630: 1627: 1623: 1619: 1615: 1612: 1608: 1604: 1603: 1601: 1596: 1593: 1591: 1589: 1586: 1585: 1525: 1522: 1518: 1506: 1505: 1483: 1479: 1468: 1457: 1454: 1451: 1448: 1445: 1442: 1439: 1436: 1417: 1409: 1405: 1377: 1372: 1368: 1364: 1350: 1318: 1313: 1309: 1305: 1287: 1286: 1275: 1271: 1266: 1262: 1258: 1252: 1249: 1245: 1239: 1235: 1231: 1227: 1222: 1218: 1214: 1203: 1192: 1188: 1183: 1179: 1175: 1169: 1164: 1161: 1157: 1151: 1147: 1143: 1139: 1134: 1130: 1126: 1088:Main article: 1085: 1082: 1057: 1047: 1030: 1022: 959: 956: 946: 925:OPERA detector 896:Data from the 876:produced at a 874:Neutrino beams 870: 867: 848: 834: 818: 809: 800: 776: 773: 741: 738: 691: 688: 644:Takaaki Kajita 642:was shared by 635: 632: 612:Standard Model 542: 541: 539: 538: 531: 524: 516: 513: 512: 509: 508: 503: 498: 493: 488: 483: 478: 473: 467: 464: 463: 460: 459: 456: 455: 450: 445: 440: 435: 430: 425: 420: 415: 410: 405: 400: 395: 390: 384: 379: 378: 375: 374: 371: 370: 365: 360: 355: 350: 345: 340: 335: 329: 324: 323: 320: 319: 316: 315: 310: 305: 300: 295: 290: 285: 280: 275: 270: 265: 260: 255: 250: 245: 240: 235: 230: 225: 220: 215: 210: 205: 200: 195: 190: 185: 180: 175: 170: 165: 160: 155: 150: 145: 139: 136: 135: 132: 131: 128: 127: 122: 117: 112: 107: 105:Dark radiation 102: 100:Phantom energy 97: 92: 87: 82: 76: 73: 72: 69: 68: 66:Standard Model 62: 61: 47: 39: 38: 26: 9: 6: 4: 3: 2: 10571: 10560: 10557: 10555: 10552: 10550: 10547: 10545: 10542: 10541: 10539: 10524: 10523: 10514: 10512: 10511: 10502: 10501: 10498: 10492: 10489: 10487: 10484: 10482: 10479: 10477: 10474: 10472: 10469: 10467: 10464: 10463: 10461: 10457: 10447: 10444: 10442: 10439: 10437: 10434: 10432: 10429: 10427: 10424: 10422: 10419: 10417: 10416:String theory 10414: 10413: 10411: 10409: 10405: 10399: 10396: 10394: 10391: 10389: 10386: 10384: 10381: 10380: 10378: 10376: 10375:Supersymmetry 10372: 10366: 10363: 10361: 10358: 10356: 10353: 10351: 10348: 10347: 10345: 10341: 10335: 10332: 10330: 10327: 10323: 10320: 10319: 10318: 10315: 10313: 10310: 10308: 10305: 10304: 10302: 10298: 10295: 10293: 10287: 10281: 10278: 10276: 10273: 10271: 10268: 10266: 10263: 10262: 10260: 10256: 10239: 10236: 10234: 10231: 10229: 10226: 10224: 10221: 10219: 10216: 10215: 10214: 10211: 10207: 10204: 10202: 10199: 10197: 10194: 10193: 10192: 10189: 10187: 10184: 10182: 10179: 10175: 10172: 10170: 10167: 10165: 10162: 10161: 10160: 10157: 10156: 10154: 10150: 10146: 10139: 10134: 10132: 10127: 10125: 10120: 10119: 10116: 10109: 10105: 10100: 10096: 10092: 10090: 10087: 10086: 10076: 10072: 10068: 10064: 10060: 10056: 10051: 10046: 10043:(7): 073012. 10042: 10038: 10033: 10029: 10025: 10021: 10017: 10013: 10009: 10004: 9999: 9996:(1): 013012. 9995: 9991: 9990: 9984: 9980: 9976: 9972: 9968: 9964: 9960: 9955: 9950: 9946: 9942: 9937: 9933: 9929: 9925: 9921: 9917: 9913: 9908: 9903: 9899: 9895: 9891: 9886: 9885: 9873: 9869: 9864: 9859: 9855: 9851: 9847: 9843: 9839: 9835: 9834: 9826: 9822: 9818: 9812: 9804: 9800: 9795: 9790: 9786: 9782: 9778: 9774: 9770: 9766: 9765: 9757: 9749: 9745: 9741: 9737: 9733: 9729: 9724: 9719: 9715: 9711: 9707: 9706: 9698: 9690: 9686: 9682: 9678: 9674: 9670: 9666: 9662: 9657: 9652: 9648: 9644: 9640: 9633: 9625: 9621: 9616: 9611: 9606: 9601: 9597: 9593: 9590:(7A): 1–708. 9589: 9585: 9584: 9579: 9572: 9564: 9551: 9540: 9538: 9536: 9534: 9526: 9524: 9510: 9503: 9501: 9499: 9497: 9495: 9493: 9491: 9489: 9481: 9477: 9473: 9469: 9465: 9461: 9457: 9452: 9447: 9443: 9439: 9438: 9430: 9426: 9419: 9411: 9407: 9403: 9399: 9395: 9391: 9390: 9377: 9370: 9362: 9358: 9354: 9350: 9346: 9342: 9341: 9336: 9332: 9326: 9318: 9314: 9310: 9306: 9302: 9298: 9297: 9292: 9286: 9277: 9272: 9268: 9264: 9260: 9256: 9255: 9250: 9243: 9235: 9231: 9227: 9223: 9219: 9215: 9210: 9205: 9201: 9197: 9190: 9182: 9178: 9174: 9170: 9166: 9162: 9157: 9152: 9148: 9144: 9137: 9128: 9123: 9118: 9113: 9109: 9105: 9102:(7): 072009. 9101: 9097: 9093: 9086: 9077: 9072: 9068: 9064: 9059: 9054: 9050: 9046: 9042: 9035: 9027: 9023: 9019: 9015: 9011: 9007: 9003: 8999: 8994: 8989: 8986:(3): 032002. 8985: 8981: 8974: 8966: 8962: 8958: 8954: 8950: 8946: 8941: 8936: 8932: 8928: 8917: 8909: 8905: 8901: 8897: 8893: 8889: 8885: 8881: 8876: 8871: 8867: 8863: 8856: 8848: 8844: 8840: 8836: 8832: 8828: 8824: 8820: 8816: 8812: 8807: 8802: 8798: 8794: 8787: 8779: 8775: 8771: 8767: 8763: 8759: 8755: 8751: 8746: 8741: 8737: 8733: 8726: 8718: 8714: 8710: 8706: 8702: 8698: 8693: 8688: 8684: 8680: 8673: 8665: 8661: 8657: 8653: 8649: 8645: 8640: 8635: 8631: 8627: 8620: 8612: 8608: 8604: 8600: 8596: 8592: 8588: 8584: 8579: 8574: 8571:(7): 071301. 8570: 8566: 8548: 8540: 8536: 8532: 8528: 8524: 8520: 8513: 8505: 8501: 8497: 8493: 8488: 8483: 8479: 8475: 8470: 8465: 8461: 8457: 8456: 8448: 8433: 8432: 8427: 8420: 8412: 8408: 8404: 8400: 8395: 8390: 8386: 8382: 8375: 8367: 8363: 8359: 8355: 8351: 8347: 8340: 8332: 8328: 8324: 8320: 8319: 8314: 8310: 8309:B. Pontecorvo 8303: 8299: 8296:: 1717–1725. 8295: 8292: 8291: 8286: 8282: 8281:B. Pontecorvo 8276: 8274: 8265: 8261: 8257: 8253: 8252: 8247: 8243: 8242:B. Pontecorvo 8236: 8233: 8232: 8227: 8221: 8219: 8210: 8204: 8200: 8199: 8191: 8189: 8187: 8185: 8183: 8178: 8163: 8143: 8136: 8133: 8129: 8125: 8119: 8115: 8105: 8102: 8100: 8097: 8095: 8092: 8090: 8087: 8085: 8082: 8080: 8077: 8076: 8070: 8068: 8063: 8053: 8051: 8047: 8043: 8039: 8031:Other sources 8028: 8026: 8020: 8017: 8015: 8010: 8008: 8002: 7992: 7988: 7984: 7982: 7977: 7975: 7974: 7969: 7968: 7963: 7953: 7949: 7947: 7942: 7940: 7935: 7930: 7919: 7903: 7895: 7887: 7880: 7876: 7872: 7855: 7839: 7833: 7823: 7807: 7801: 7784: 7773: 7766: 7762: 7758: 7734: 7730: 7723: 7715: 7692: 7688: 7680: 7678:(atmospheric) 7665: 7658: 7645: 7640: 7634: 7618: 7613: 7610: 7594: 7589: 7588: 7564: 7552: 7548: 7530: 7526: 7521: 7514: 7507: 7503: 7500: 7497: 7491: 7487: 7481: 7477: 7471: 7467: 7466: 7465: 7454: 7450: 7444: 7440: 7439: 7432: 7428: 7422: 7418: 7417: 7410: 7406: 7400: 7396: 7395: 7392: 7383: 7381: 7372: 7368: 7355: 7353: 7349: 7345: 7340: 7338: 7337:Cabibbo angle 7334: 7329: 7327: 7322: 7318: 7313: 7309: 7288: 7284: 7256: 7252: 7233: 7226: 7219: 7198: 7190: 7186: 7176: 7172: 7165: 7158: 7150: 7146: 7140: 7133: 7126: 7122: 7115: 7108: 7100: 7096: 7087: 7083: 7076: 7069: 7066: 7061: 7058: 7051: 7050: 7049: 7030: 7022: 7018: 7008: 7004: 6997: 6990: 6984: 6981: 6978: 6973: 6970: 6967: 6964: 6957: 6954: 6951: 6946: 6943: 6940: 6934: 6929: 6924: 6916: 6912: 6902: 6898: 6891: 6882: 6881: 6880: 6878: 6874: 6873: 6870: 6865: 6846: 6841: 6833: 6829: 6819: 6815: 6808: 6801: 6793: 6790: 6785: 6778: 6774: 6770: 6761: 6758: 6753: 6744: 6741: 6736: 6729: 6726: 6721: 6714: 6710: 6706: 6698: 6691: 6683: 6679: 6671: 6667: 6660: 6653: 6650: 6645: 6642: 6635: 6634: 6633: 6630: 6626: 6621: 6617: 6613: 6594: 6590: 6584: 6574: 6570: 6566: 6561: 6557: 6548: 6545: 6540: 6535: 6530: 6526: 6518: 6514: 6510: 6505: 6500: 6495: 6491: 6483: 6479: 6475: 6469: 6463: 6460: 6455: 6452: 6445: 6444: 6443: 6441: 6437: 6417: 6413: 6409: 6399: 6395: 6377: 6373: 6369: 6363: 6360: 6333: 6329: 6325: 6315: 6311: 6307: 6303: 6299: 6281: 6277: 6270: 6266: 6263: 6253: 6250: 6239: 6234: 6232: 6226: 6223: 6218: 6216: 6212: 6208: 6204: 6190: 6176: 6162: 6148: 6134: 6120: 6111: 6102: 6092: 6085: 6076: 6069: 6049: 6042: 6000: 5980: 5976: 5971: 5967: 5956: 5952: 5948: 5943: 5939: 5931: 5928: 5922: 5917: 5913: 5909: 5904: 5901: 5898: 5895: 5892: 5886: 5882: 5874: 5873: 5872: 5870: 5844: 5838: 5835: 5830: 5825: 5821: 5811: 5807: 5802: 5798: 5790: 5787: 5781: 5776: 5772: 5768: 5763: 5760: 5757: 5754: 5751: 5745: 5741: 5733: 5732: 5731: 5714: 5709: 5703: 5700: 5697: 5692: 5689: 5686: 5683: 5676: 5673: 5670: 5665: 5662: 5659: 5653: 5648: 5645: 5638: 5637: 5636: 5611: 5608: 5605: 5601: 5594: 5590: 5585: 5580: 5574: 5571: 5566: 5560: 5556: 5550: 5539: 5535: 5532: 5528: 5522: 5519: 5514: 5508: 5504: 5498: 5487: 5483: 5480: 5476: 5470: 5467: 5462: 5456: 5452: 5446: 5435: 5431: 5428: 5424: 5421: 5413: 5410: 5393: 5385: 5384: 5383: 5366: 5358: 5355: 5352: 5348: 5341: 5338: 5335: 5331: 5325: 5322: 5319: 5315: 5310: 5307: 5303: 5296: 5291: 5288: 5284: 5277: 5274: 5270: 5263: 5260: 5256: 5249: 5244: 5241: 5237: 5231: 5227: 5206: 5205: 5204: 5203: 5183: 5177: 5174: 5169: 5163: 5159: 5153: 5150: 5139: 5135: 5132: 5127: 5120: 5115: 5112: 5108: 5101: 5098: 5094: 5087: 5084: 5080: 5073: 5068: 5065: 5061: 5055: 5051: 5031: 5028: 5025: 5021: 5016: 5013: 5005: 4995: 4983: 4973: 4963: 4960: 4952: 4948: 4939: 4935: 4928: 4925: 4917: 4914: 4897: 4889: 4888: 4887: 4881: 4869: 4867: 4859: 4855: 4849: 4848: 4847: 4845: 4826: 4818: 4792: 4783: 4765: 4761: 4755: 4752: 4741: 4738: 4735: 4730: 4704: 4695: 4677: 4673: 4667: 4664: 4653: 4647: 4641: 4609: 4603: 4599: 4593: 4588: 4582: 4572: 4568: 4564: 4556: 4553: 4538: 4537: 4536: 4522: 4509: 4496: 4488: 4483: 4479: 4475: 4470: 4465: 4461: 4457: 4449: 4445: 4439: 4436: 4404: 4397: 4391: 4388: 4383: 4377: 4373: 4367: 4364: 4353: 4349: 4346: 4341: 4334: 4329: 4326: 4322: 4315: 4312: 4308: 4301: 4298: 4294: 4287: 4282: 4279: 4275: 4269: 4265: 4245: 4242: 4239: 4235: 4230: 4227: 4223: 4214: 4208: 4205: 4200: 4194: 4190: 4184: 4181: 4170: 4166: 4161: 4157: 4151: 4144: 4139: 4136: 4132: 4125: 4122: 4118: 4111: 4108: 4104: 4097: 4092: 4089: 4085: 4079: 4075: 4055: 4052: 4049: 4045: 4040: 4037: 4033: 4026: 4023: 4019: 4015: 4010: 4004: 4000: 3988: 3987: 3986: 3969: 3961: 3956: 3946: 3943: 3938: 3932: 3927: 3923: 3916: 3913: 3909: 3902: 3899: 3895: 3888: 3883: 3880: 3876: 3869: 3865: 3859: 3853: 3847: 3833: 3825: 3817: 3813: 3807: 3800: 3796: 3786: 3773: 3767: 3761: 3757: 3749: 3748: 3747: 3737: 3717: 3710: 3702: 3694: 3690: 3684: 3676: 3670: 3666: 3660: 3654: 3649: 3645: 3637: 3632: 3629: 3625: 3621: 3617: 3609: 3601: 3597: 3591: 3583: 3582: 3581: 3573: 3569: 3560: 3555: 3534: 3524: 3520: 3513: 3508: 3504: 3498: 3495: 3492: 3483: 3479: 3474: 3467: 3462: 3458: 3452: 3447: 3443: 3439: 3431: 3426: 3422: 3418: 3413: 3408: 3404: 3397: 3392: 3388: 3380: 3379: 3378: 3364: 3356: 3352: 3348: 3343: 3339: 3335: 3331: 3326: 3316: 3309: 3300: 3274: 3264: 3261: 3243: 3233: 3222: 3207: 3200: 3185: 3177: 3159: 3155: 3147: 3133: 3127: 3124: 3120: 3114: 3110: 3086: 3076: 3073: 3067: 3064: 3061: 3058: 3047: 3046:natural units 3043: 3042: 3041: 3024: 3017: 3009: 3001: 2997: 2991: 2984: 2973: 2967: 2962: 2952: 2944: 2940: 2935: 2931: 2925: 2920: 2917: 2913: 2909: 2905: 2897: 2889: 2885: 2879: 2871: 2870: 2869: 2867: 2850: 2843: 2839: 2833: 2818: 2816: 2812: 2808: 2800: 2796: 2719: 2714: 2708: 2703: 2698: 2691: 2684: 2680: 2674: 2670: 2666: 2662: 2656: 2649: 2644: 2637: 2633: 2627: 2623: 2619: 2615: 2608: 2601: 2593: 2589: 2583: 2579: 2571: 2568: 2564: 2558: 2554: 2548: 2544: 2538: 2534: 2530: 2525: 2521: 2515: 2511: 2507: 2500: 2497: 2493: 2487: 2483: 2477: 2473: 2467: 2463: 2459: 2454: 2450: 2444: 2440: 2430: 2426: 2420: 2416: 2408: 2405: 2401: 2395: 2391: 2385: 2381: 2375: 2371: 2367: 2362: 2358: 2352: 2348: 2340: 2337: 2333: 2327: 2323: 2317: 2313: 2307: 2303: 2299: 2294: 2290: 2284: 2280: 2276: 2267: 2264: 2261: 2257: 2251: 2247: 2239: 2235: 2229: 2225: 2217: 2213: 2207: 2203: 2196: 2191: 2189: 2179: 2173: 2168: 2163: 2156: 2149: 2145: 2139: 2135: 2131: 2127: 2121: 2114: 2109: 2102: 2098: 2092: 2088: 2084: 2080: 2073: 2066: 2060: 2055: 2050: 2043: 2036: 2032: 2024: 2020: 2016: 2009: 2002: 1998: 1990: 1986: 1979: 1972: 1964: 1960: 1954: 1947: 1944: 1940: 1934: 1930: 1926: 1919: 1914: 1909: 1900: 1897: 1894: 1890: 1884: 1880: 1874: 1867: 1863: 1856: 1849: 1841: 1837: 1829: 1825: 1821: 1816: 1807: 1803: 1795: 1791: 1785: 1778: 1773: 1768: 1762: 1757: 1755: 1745: 1737: 1734: 1730: 1722: 1719: 1715: 1707: 1704: 1700: 1690: 1687: 1683: 1675: 1672: 1668: 1660: 1657: 1653: 1643: 1640: 1636: 1628: 1625: 1621: 1613: 1610: 1606: 1599: 1594: 1592: 1587: 1576: 1575: 1574: 1572: 1567: 1565: 1561: 1557: 1553: 1549: 1545: 1541: 1523: 1520: 1516: 1503: 1502:antineutrinos 1499: 1481: 1478: 1469: 1455: 1452: 1449: 1446: 1443: 1440: 1437: 1434: 1415: 1407: 1403: 1375: 1370: 1366: 1362: 1351: 1316: 1311: 1307: 1303: 1292: 1291: 1290: 1273: 1269: 1264: 1260: 1256: 1250: 1247: 1243: 1237: 1233: 1229: 1225: 1220: 1216: 1212: 1204: 1190: 1186: 1181: 1177: 1173: 1167: 1162: 1159: 1155: 1149: 1145: 1141: 1137: 1132: 1128: 1124: 1116: 1115: 1114: 1112: 1108: 1103: 1101: 1097: 1091: 1081: 1079: 1074: 1069: 1013: 1009: 1004: 1002: 998: 993: 989: 984: 979: 977: 973: 969: 968:superposition 965: 955: 953: 949: 940: 936: 934: 930: 926: 922: 918: 914: 911:In 2010, the 909: 907: 903: 899: 894: 892: 888: 884: 879: 875: 866: 864: 842: 828: 823: 821: 812: 803: 794: 790: 781: 772: 770: 766: 762: 761: 756: 755:Kamiokande II 752: 748: 737: 735: 731: 726: 724: 720: 716: 712: 708: 704: 700: 697: 687: 684: 651: 649: 645: 641: 631: 629: 625: 621: 617: 613: 609: 605: 601: 596: 594: 590: 585: 583: 579: 575: 571: 567: 563: 562:family number 560: 556: 552: 548: 537: 532: 530: 525: 523: 518: 517: 515: 514: 507: 504: 502: 499: 497: 494: 492: 489: 487: 484: 482: 479: 477: 474: 472: 469: 468: 462: 461: 454: 451: 449: 446: 444: 441: 439: 436: 434: 431: 429: 426: 424: 421: 419: 416: 414: 411: 409: 406: 404: 401: 399: 396: 394: 393:String theory 391: 389: 386: 385: 382: 377: 376: 369: 366: 364: 361: 359: 356: 354: 351: 349: 346: 344: 341: 339: 336: 334: 331: 330: 327: 326:Supersymmetry 322: 321: 314: 311: 309: 306: 304: 301: 299: 296: 294: 291: 289: 286: 284: 281: 279: 276: 274: 271: 269: 266: 264: 261: 259: 256: 254: 251: 249: 246: 244: 241: 239: 236: 234: 231: 229: 228:Mirror matter 226: 224: 221: 219: 216: 214: 211: 209: 208:String theory 206: 204: 201: 199: 196: 194: 191: 189: 186: 184: 181: 179: 176: 174: 171: 169: 166: 164: 161: 159: 156: 154: 151: 149: 146: 144: 141: 140: 134: 133: 126: 123: 121: 118: 116: 113: 111: 108: 106: 103: 101: 98: 96: 93: 91: 88: 86: 83: 81: 78: 77: 71: 70: 67: 64: 63: 58: 54: 51: 45: 41: 40: 37: 34: 33: 30: 19: 10520: 10508: 10398:Supergravity 10333: 10258:Constituents 10238:Weak isospin 10196:Color charge 10186:Gauge theory 10098: 10040: 10036: 9993: 9987: 9944: 9940: 9897: 9893: 9837: 9833:Phys. Rev. D 9831: 9811: 9768: 9762: 9756: 9713: 9703: 9697: 9646: 9642: 9632: 9587: 9581: 9571: 9550:cite journal 9520: 9513:. Retrieved 9479: 9441: 9435: 9418: 9393: 9387: 9369: 9344: 9338: 9325: 9300: 9294: 9285: 9258: 9252: 9242: 9199: 9195: 9189: 9146: 9142: 9136: 9099: 9095: 9085: 9048: 9044: 9034: 8983: 8979: 8973: 8930: 8926: 8916: 8865: 8861: 8855: 8796: 8792: 8786: 8735: 8731: 8725: 8682: 8678: 8672: 8629: 8625: 8619: 8568: 8564: 8547: 8522: 8518: 8512: 8459: 8453: 8447: 8435:. Retrieved 8429: 8419: 8384: 8380: 8374: 8349: 8345: 8339: 8322: 8316: 8311:(May 1968). 8293: 8288: 8283:(May 1968). 8255: 8249: 8234: 8229: 8197: 8162: 8142: 8131: 8118: 8059: 8050:proton decay 8034: 8025:leptogenesis 8021: 8018: 8011: 8006: 8004: 7989: 7985: 7978: 7971: 7965: 7959: 7950: 7943: 7931: 7920: 7901: 7896: 7885: 7875:Double Chooz 7853: 7837: 7821: 7805: 7797: 7782: 7771: 7764: 7760: 7732: 7728: 7721: 7690: 7686: 7663: 7656: 7643: 7632: 7616: 7592: 7562: 7550: 7528: 7519: 7512: 7505: 7498: 7489: 7479: 7469: 7463: 7389: 7379: 7376: 7366: 7352:CP violation 7344:Euler angles 7341: 7332: 7330: 7325: 7320: 7316: 7311: 7307: 7224: 7217: 7215: 7047: 6876: 6869:orthogonally 6867: 6861: 6628: 6624: 6619: 6615: 6609: 6439: 6435: 6397: 6393: 6313: 6309: 6305: 6297: 6235: 6227: 6222:normal modes 6219: 6200: 6118: 6109: 6100: 6090: 6083: 6074: 6067: 6064: 5866: 5729: 5633: 5381: 5200:In terms of 5199: 4880:CP-violation 4877: 4853: 4841: 4510: 4423: 3984: 3736:interference 3732: 3571: 3567: 3556: 3549: 3296: 3039: 2824: 2738: 1568: 1551: 1547: 1543: 1539: 1507: 1341:(electron), 1288: 1104: 1093: 1070: 1005: 980: 961: 937: 910: 895: 872: 827:Double Chooz 824: 786: 758: 743: 727: 693: 652: 637: 634:Observations 604:experimental 597: 586: 546: 545: 403:Quantum foam 388:False vacuum 353:Supergravity 313:CPT symmetry 124: 95:Quintessence 29: 10459:Experiments 10350:Technicolor 10312:Dark matter 10206:Quark model 10174:Higgs boson 10169:Gauge boson 9794:10550/47211 9615:10481/34593 9523:Mathematica 9386:theories". 9127:2440/112089 8685:(6): 1002. 8325:: 984–988. 8060:During the 7967:Higgs boson 7916:≈1 GeV 7232:eigenvalues 2807:CP symmetry 1544:PMNS matrix 1508:The symbol 1010:decay, and 976:eigenstates 964:eigenstates 927:located at 600:theoretical 465:Experiments 438:Causal sets 283:Graviscalar 278:Graviphoton 178:Technicolor 153:Fifth force 110:Dark photon 90:Dark energy 85:Dark matter 57:Higgs boson 10538:Categories 10466:Gran Sasso 10290:Beyond the 10265:CKM matrix 10152:Background 9947:(1): 122. 9863:2022/18663 9656:1910.03887 9331:Gribov, V. 9261:(5): 870. 9149:(9): 116. 8394:1904.06036 8387:(8): 697. 8174:References 8079:MSW effect 7911:10 eV 7754:10 eV 7712:10 eV 7579:10 eV 7545:10 eV 7331:The angle 6610:This is a 5867:Or, using 4866:kilometers 4535:restored) 2866:plane wave 1556:CKM matrix 1552:MNS matrix 1345:(muon) or 1111:eigenbasis 1076:(0.1 929:Gran Sasso 760:muon decay 734:MSW effect 709:, using a 696:Ray Davis' 476:Gran Sasso 248:Dark fluid 48:Simulated 10544:Neutrinos 10050:1205.4018 10028:119107183 10003:1205.5254 9979:119459743 9932:119501801 9689:203951445 9515:8 October 9476:118588567 9156:0706.1216 9058:0810.4602 9018:1550-7998 8993:1304.0841 8965:119256958 8940:1006.1623 8875:1204.0626 8831:0031-9007 8806:1203.1669 8745:1112.6353 8603:0031-9007 8504:119651816 8482:CiteSeerX 8469:0704.1800 8437:6 October 8157:breaking. 8124:entangled 8014:GUT scale 7973:chirality 7495:) = 0.861 7285:λ 7253:λ 7147:λ 7123:λ 6985:θ 6982:⁡ 6974:θ 6971:⁡ 6965:− 6958:θ 6955:⁡ 6947:θ 6944:⁡ 6754:− 6737:− 6567:− 6207:pendulums 5964:Δ 5949:⁡ 5932:θ 5923:⁡ 5905:β 5902:≠ 5899:α 5893:β 5890:→ 5887:α 5818:Δ 5808:⁡ 5791:θ 5782:⁡ 5764:β 5761:≠ 5758:α 5752:β 5749:→ 5746:α 5704:θ 5701:⁡ 5693:θ 5690:⁡ 5684:− 5677:θ 5674:⁡ 5666:θ 5663:⁡ 5612:γ 5609:β 5606:α 5602:ε 5595:γ 5591:∑ 5547:Δ 5536:⁡ 5495:Δ 5484:⁡ 5443:Δ 5432:⁡ 5414:β 5411:α 5359:ℓ 5349:ε 5342:γ 5339:β 5336:α 5332:ε 5326:ℓ 5320:γ 5316:∑ 5297:∗ 5289:β 5275:α 5261:β 5250:∗ 5242:α 5228:⁡ 5147:Δ 5136:⁡ 5121:∗ 5113:β 5099:α 5085:β 5074:∗ 5066:α 5052:⁡ 5022:∑ 5006:β 4999:¯ 4996:ν 4989:→ 4984:α 4977:¯ 4974:ν 4961:− 4953:β 4949:ν 4945:→ 4940:α 4936:ν 4918:β 4915:α 4749:Δ 4742:× 4736:≈ 4661:Δ 4654:× 4645:ℏ 4597:ℏ 4550:Δ 4523:ℏ 4476:− 4458:≡ 4433:Δ 4361:Δ 4350:⁡ 4335:∗ 4327:β 4313:α 4299:β 4288:∗ 4280:α 4266:⁡ 4236:∑ 4178:Δ 4167:⁡ 4145:∗ 4137:β 4123:α 4109:β 4098:∗ 4090:α 4076:⁡ 4046:∑ 4038:− 4027:β 4024:α 4020:δ 4011:β 4008:→ 4005:α 3914:− 3900:β 3889:∗ 3881:α 3866:∑ 3818:α 3814:ν 3801:β 3797:ν 3768:β 3765:→ 3762:α 3691:ν 3630:− 3598:ν 3493:≈ 3440:≃ 3349:≫ 3320:→ 3278:→ 3237:→ 3125:− 3121:≡ 3071:ℏ 2998:ν 2977:→ 2968:⋅ 2956:→ 2945:− 2918:− 2886:ν 2840:ν 2671:α 2624:α 2572:δ 2531:− 2508:− 2501:δ 2460:− 2409:δ 2368:− 2341:δ 2300:− 2277:− 2268:δ 2262:− 2136:α 2089:α 2017:− 1948:δ 1927:− 1901:δ 1895:− 1822:− 1735:τ 1720:τ 1705:τ 1688:μ 1673:μ 1658:μ 1521:α 1482:∗ 1367:ν 1312:α 1308:ν 1261:ν 1248:α 1234:∑ 1221:α 1217:ν 1182:α 1178:ν 1168:∗ 1160:α 1150:α 1146:∑ 1129:ν 1042: | 1017: | 997:coherence 902:MiniBooNE 719:Cherenkov 398:Spin foam 293:Gravitino 10510:Category 10491:Tevatron 10343:Theories 10300:Evidence 10164:Fermions 10075:53708945 9872:10017160 9681:32296192 9624:10020536 9234:14205602 9181:13895776 9026:53322828 8908:33056442 8900:23003027 8847:16580300 8839:22680853 8778:19008791 8770:22540693 8717:15221390 8611:11497878 8431:BBC News 8073:See also 8046:sleptons 8038:R parity 7962:fermions 7946:Majorana 7871:Daya Bay 7649:″) > 7607: . 7485:) = 0.97 7328:is 45°. 7230:are the 6866:) it is 6296:, where 6215:friction 5869:SI units 5851: . 4844:unitless 3834:⟩ 3787:⟨ 3711:⟩ 3618:⟩ 3260:momentum 3018:⟩ 2906:⟩ 2851:⟩ 1376:⟩ 1349:(tauon), 1317:⟩ 1270:⟩ 1226:⟩ 1187:⟩ 1138:⟩ 841:Daya Bay 711:chlorine 673:, where 622:and the 578:measured 566:electron 555:neutrino 501:Tevatron 348:M-theory 288:Graviton 218:M-theory 158:F-theory 137:Theories 74:Evidence 10522:Commons 10486:Super-K 10322:problem 10099:YouTube 10055:Bibcode 10008:Bibcode 9959:Bibcode 9912:Bibcode 9842:Bibcode 9803:9957332 9773:Bibcode 9748:2094005 9728:Bibcode 9661:Bibcode 9592:Bibcode 9456:Bibcode 9398:Bibcode 9349:Bibcode 9305:Bibcode 9263:Bibcode 9214:Bibcode 9161:Bibcode 9104:Bibcode 9063:Bibcode 8998:Bibcode 8945:Bibcode 8880:Bibcode 8811:Bibcode 8750:Bibcode 8697:Bibcode 8664:7102535 8644:Bibcode 8583:Bibcode 8554: 8527:Bibcode 8474:Bibcode 8399:Bibcode 8354:Bibcode 8327:Bibcode 8298:Bibcode 8260:Bibcode 8084:Majoron 8042:squarks 7800:KamLAND 7348:complex 6300:is the 6231:W boson 3297:In the 3174:is the 2811:unitary 1073:W boson 891:Super-K 859: ; 763:). The 669:⁠ 657:⁠ 496:Super-K 10073: 10026: 9977: 9930: 9870: 9801: 9746: 9687: 9679: 9643:Nature 9622: 9474: 9380:SU(2) 9232: 9179: 9024: 9016: 8963: 8906: 8898: 8845: 8837: 8829: 8776: 8768: 8715: 8662: 8609: 8601: 8502: 8484: 8205: 8152:× U(1) 7884:sin(2 7724:| ≈ |Δ 7708:0.018) 7704:(0.753 7642:sin(2 7615:sin(2 7591:sin(2 7216:where 7093: 6392:where 6098:where 6047: 5364: 4824: 4494: 4455: 4424:where 4402: 3967: 3715: 3576:where 3550:where 3532: 3362: 3176:energy 3131: 3107: 3084: 3040:where 3022: 2825:Since 2739:where 1560:quarks 1500:; for 1413: 1400: 1380: 1359: 1321: 1300: 1289:where 1052:ν 990:, and 983:phases 958:Theory 933:Geneva 889:, and 753:, and 582:flavor 559:lepton 10388:NMSSM 10071:S2CID 10045:arXiv 10024:S2CID 9998:arXiv 9975:S2CID 9949:arXiv 9928:S2CID 9902:arXiv 9828:(PDF) 9744:S2CID 9718:arXiv 9685:S2CID 9651:arXiv 9472:S2CID 9446:arXiv 9432:(PDF) 9230:S2CID 9204:arXiv 9177:S2CID 9151:arXiv 9053:arXiv 9022:S2CID 8988:arXiv 8961:S2CID 8935:arXiv 8904:S2CID 8870:arXiv 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Neutrino oscillation

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