Neutrino Mixing and Oscillations

Neutrino Mixing and Mass Matrix
* Basis and mixing: The weak eigenstates are | _j = _k U_jk |m_k, where |m_k are the mass eigenstates and U_jk is the MNS (Maki-Nakagawa-Sakata) matrix, a unitary matrix with three mixing angles ₁₂, ₂₃ and ₁₃, and three phases ₁, ₂ and ; This in the Dirac neutrino case, while in the Majorana neutrino case the phases reduce to just , which could be found from CP violation in the neutrino sector, if present.
* Status: 2007, Best values, from solar, atmospheric and reactor neutrinos, are

sin ₁₂ = 0.56+0.05–0.04 ,   sin ₂₃ = 0.67+0.12–0.07 ,   sin ₁₃ = 0.09+0.13–0.09 .

* Experiments: 2007, Mini-BooNE about to announce results; EXO (Enriched Xenon Observatory) being prepared.
@ Experiments: Schwarzschild PT(96)feb [neutrino beam plans]; news sr(07)apr, pw(07)apr [Mini-BooNE results].

Neutrino Oscillations > s.a. experimental particle physics; special relativity; torsion.
* Idea: Because weak eigenstates are linear combinations of mass eigenstates, they undergo analogs of beats; Effective masses depend on the medium; In vacuum, the transition probabilities are given by expressions like

P_{e → mu} = sin² 2 (1 – cos 2x/L),

where the characteristic length

L:= 4E (m₁² – m₂²) ;

Experiments with different x values can estimate values of both and m²; The latter can be used to study CP violations.
* In matter: The effect of coherent forward scattering must be taken into account when considering the oscillations of neutrinos travelling through matter (MSW effect); Used to solve the solar neutrino puzzle.
* Status: 1998, Direct evidence from Superkamiokande, with m_e-mu = 0.07 eV; 2002, Indirect evidence as solution to solar problem; Uncertainties narrowed considerably, estimate m_e-mu = 0.049 eV, sin² 2 = 1; 2004, KamLAND confirms results [@ news pw(04)nov]; 2007,

(m²)₁₂ = (7.9 0.7) 10^–5 eV² ;   (m²)₂₃ = (2.6 0.4) 10^–3 eV² ;

LSND has some evidence for a third, independent m², which would imply the existence of a 4th neutrino favor (sterile neutrino).

References
@ Status, reviews: news pw(98)jul; Giunti PS(03), & Laveder hp/03-in; Bilenky PRS(04); Valle NPPS(07).
@ General references: Athanassopoulos et al PRL(95); Kaneyuki & Scholberg AS(99) [experiment]; Ereditato & Migliozzi RNC(00) [accelerator]; De Santo IJMPA(01); King JPG(01)hp; Ahmad et al PRL(02), PRL(02) [SNO, evidence and parameters]; Giunti AJP(04) [Lorentz invariance].
@ In matter: Wolfenstein PRD(78); Mikheev & Smirnov SJNP(85); Benatti & Floreanini PRD(05)hp/04 [random fluctuations].
@ In massless neutrinos: Benatti & Floreanini PRD(01) [dynamical semigroups].
@ And gravity: Ahluwalia & Burgard GRG(96)gq, PRD(98)gq; Singh et al PLA(06)gq/05 [weak g fields]; > s.a. matter in quantum gravity.
@ And CP violation: Sarkar & Singh NPB(07).

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