Neutrino Mixing and Oscillations  

Neutrino Mixing and Mass Matrix
* Basis and mixing: The weak eigenstates are |νj\(\rangle\) = ∑k Ujk |mk\(\rangle\), where |mk\(\rangle\) are the mass eigenstates and Ujk is the MNS (Maki-Nakagawa-Sakata) matrix, a unitary matrix with three mixing angles θ12, θ23 and θ13, and three phases α1, α2 and δ; This in the Dirac neutrino case, while in the Majorana neutrino case the phases reduce to just δ, which could be found from CP violation in the neutrino sector, if present.
* 2007: The best values, from solar, atmospheric and reactor neutrinos, are

sin θ12 = 0.56+0.05−0.04 ,   sin θ23 = 0.67+0.12−0.07 ,   sin θ13 = 0.09+0.13−0.09 .

* 2012: New results for masurements of θ13 exclude the no-oscillation hypothesis at 6.3 standard deviations,

sin2 2θ13 = 0.092 ± 0.017 [Daya Bay Reactor Neutrino Experiment],   sin2 2θ13 = 0.103 ± 0.013 (stat) ± 0.011 (syst) [RENO].

* Experiments: 2007, MiniBooNE about to announce results; EXO (Enriched Xenon Observatory) being prepared; 2012, RENO results for θ13.
@ References: Kim + RENO PRL(12)-a1204, news int(12)mar [measurement of θ13]; Conrad Phy(12) [consequences of θ13 not being so small]; Meloni & Ohlsson PRD(12)-a1206 [determining δ and other parameters from neutrino flux ratios at neutrino telescopes]; Balantekin AIP(13)-a1211 [towards a very precise value of θ13].

Neutrino Oscillations > s.a. astrophysical neutrinos; experimental particle physics; Leggett-Garg Inequality; 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

Peμ = \(1\over2\)sin2 2θ (1 − cos 2π x/L) ,   where   L:= 4π E (m12m22)   is the characteristic length;

Experiments with different x values can estimate values of both θ and Δm2; 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 Δme-μ = 0.07 eV; 2002, Indirect evidence as solution to solar neutrino problem; Uncertainties narrowed considerably, estimate Δme-μ = 0.049 eV, sin2 2θ = 1; 2004, KamLAND confirms results [@ news pw(04)nov]; 2007,

m2)12 = (7.9 ± 0.7) × 10−5 eV2 ;   (Δm2)23 = (2.6 ± 0.4) × 10−3 eV2 ;

LSND has some evidence for a third, independent Δm2, which would imply the existence of a 4th neutrino favor (sterile neutrino).
@ Related topics: Balantekin a1710-proc [collective neutrino oscillations and nucleosynthesis]; Joshi PLB(20)-a2008 [mixed state geometric phase].

@ Reviews, status: Kaneyuki & Scholberg AS(99) [Superkamiokande experiment]; Ereditato & Migliozzi RNC(00) [accelerator studies]; De Santo IJMPA(01); King JPG(01)hp; Giunti & Laveder hp/03-in; Bilenky PRS(04); Valle NPPS(07); Fogli et al in(08)-a0809; Fogli et al PRD(12)-a1205; Kajita 16.
@ News, results: Athanassopoulos et al PRL(95) [LSND]; news pw(98)jul [evidence seen at Superkamiokande]; Ahmad et al PRL(02), PRL(02) [SNO, evidence and parameters]; news sr(07)apr, news pw(07)apr [MiniBooNE]; Habig MPLA(10) [MINOS]; Stefanski MPLA(11) [MiniBooNE]; Adamson et al PRL(11) + Louis Phy(11) [muon antineutrino disappearance at MINOS]; Parke Phy(11) [hints of muon neutrino to electron neutrino oscillation]; news msnbc(11)nov [Borexino results]; news disc(12)mar [Daya Bay]; news wired(15)jun [observation of \(\nu_\mu\)-\(\nu_\tau\) oscillations]; Aartsen et IceCube PRL(18) [observation at 6-56 GeV, atmospheric neutrinos].
@ Plans: Schwarzschild PT(96)feb [neutrino beam]; Fargion et al ApJ(12)-a1012 [beaming (anti)neutrinos across the Earth]; news nat(12)mar, ns(12)mar [funding issues for LBNE].
@ History: Bilenky PS(05)hp/04 [rev]; Dore & Zanello a0910 [contributions of Bruno Pontecorvo]; Rajasekaran a1206, Bilenky a1902-conf [history].

Theory > s.a. dirac fields; non-commutative field theory; wave-function collapse.
@ General references: Giunti PS(03) [phase, and finite coherence time]; Hecht TPT(03)mar, Waltham AJP(04)jun [pedagogical]; Giunti AJP(04)may [Lorentz invariance]; Goldman MPLA(10) [description based on relativistic quantum mechanics with four-momentum conservation]; Indurain PhD(09)-a1002 [as window to new physics]; Anastopoulos & Savvidou a1005 [measurement-theoretic approach]; Tureanu EPJC(20)-a1902 [universal definition of oscillating neutrino states]; Valle a2012-proc [and mass generation].
@ Quantum-field-theoretic treatment: Akhmedov & Kopp JHEP(10)-a1001 [vs quantum-mechanical]; Kobach et al PLB(18)-a1711.
@ And entanglement: Cohen et al PLB(09)-a0810; Blasone et al JPCS(10)-a1003; Wu et al IJMPA(11) [and coherence]; Blasone et al EPL(14)-a1401 [field-theoretic approach]; Blasone et al a2104 [wave-packet approach to correlations].
@ And new physics: Sprenger et al CQG(11)-a1101 [and minimal length]; Lipkin a1105.
@ 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]; Floyd FP(17)-a1607.
@ And gravity: Ahluwalia & Burgard GRG(96)gq, PRD(98)gq; Singh et al PLA(06)gq/05 [weak g fields]; Ren & Zhang CQG(10)-a1002 [in Kerr-Newman spacetime]; Visinelli GRG(15)-a1410, Capolupo et al PRD(20)-a2003 [in curved spacetime]; > s.a. equivalence principle and experiments.
@ In modified gravity theories: Chakraborty JCAP(15)-a1506; Buoninfante et al PRD(20)-a1906; > s.a. brane theory; lorentz violations and phenomenology; torsion-based theories.
@ Quantum gravity: Singh Koranga IJTP(12) [phase shift]; Singh Koranga & Narayan IJTP(13) =? IJTP(14); Miller & Pasechnik AHEP-a1305; > s.a. particle phenomenology in quantum gravity.
@ And CP violation: Sarkar & Singh NPB(07); Singh Koranga IJTP(11) [from Planck-scale effects]; Ahuja MPLA(11); > s.a. CPT violation.

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