Nonunitary mixing: current constraints and new ambiguity

Transcription

1 Nonunitary mixing: current constraints and new ambiguity Omar Miranda Cinvestav September 7, 2016 Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

2 Outline 1 Theoretical motivation 2 The main formalism 3 Constraints from non universality 4 Oscillations 5 The CP phase Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

3 Seesaw schemes [ ] ML D D T M R 0 D 0 D 0 M 0 M T µ n(n 1) 2 mixing angles (n 1)(n 2) 2 phases Minkowski 1977, Gell-Mann Ramond Slanski 1979, Yanagida 1979, Mohapatra Senjanovic 80, Schechter Valle Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

4 Mixing matrix U n n = ω n 1 n ω n 2 n... ω 1 n ω n 2 n 1 ω n 3 n 1... ω 1 n 1... ω 2 3 ω 1 3 ω 1 2, c ij 0 η ij..... ω ij = η ij 0 c ij Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

5 Mixing matrix U NP = ω n 1 n ω n 2 n... ω 2 n ω 1 n ω n 2 n 1... ω 2 n 1 ω 1 n 1... ω 3 4 ω 2 4 ω 1 4, U 3 3 = ω 2 3 ω 1 3 ω 1 2. ω 13 = c 13 0 e iφ 13 s e iφ 13 s 13 0 c with s ij = sin θ ij, c ij = cos θ ij, η ij = e iφ ij sin θ ij, and η ij = e iφ ij sin θ ij Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

6 Mixing matrix ( U n n N S αi = V T ) NN + SS = I, N N + V V = I. Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

7 Mixing matrix N = N NP U 3 3 = α α 21 α 22 0 α 31 α 32 α 33 U 3 3 α 11 = c 1 n c 1n 1 c 1 n 2... c 14, α 22 = c 2 n c 2n 1 c 2 n 2... c 24, α 33 = c 3 n c 3n 1 c 3 n 2... c 34, Escrihuela, Forero, OGM, Tortola, Valle PRD (2015) Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

8 Mixing matrix α 21 = c 2 n c 2n 1... c 2 5 η 24 η 14 + c 2 n... c 2 6 η 25 η 15 c η 2n η 1n c 1n 1 c 1n 2... c 14 α 32 = c 3 n c 3n 1... c 3 5 η 34 η 24 + c 3 n... c 3 6 η 35 η 25 c η 3n η 2n c 2n 1 c 2n 2... c 24 η ij = e iφ ij sin θ ij η ij = e iφ ij sin θ ij Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

9 Mixing matrix NN = α11 2 α 11 α21 α 11 α31 α 11 α 21 α 11 α 31 α α 21 2 α 22 α 32 + α 31 α21 α 22 α32 + α 21α31 α α α 32 2 Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

10 Mixing matrix N = N NP U 3 3 = α α 21 α 22 0 α 31 α 32 α 33 U 3 3 α 11 = c 1 n c 1n 1 c 1 n 2... c 14, α 22 = c 2 n c 2n 1 c 2 n 2... c 24, α 33 = c 3 n c 3n 1 c 3 n 2... c 34, Escrihuela, Forero, OGM, Tortola, Valle PRD (2015) Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

11 Current constraints beta decay [ ē L γ µ N1i ν il ] (1) G β = G F (NN ) 11 = G F α Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

12 Current constraints muon decay [ N 2j ν jl γ µ µ L ] [ēl γ µ N1i ν il ] (2) G µ = G F (NN ) 11 (NN ) 22 = G F α 2 11 (α α 21 2 ), Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

13 Current constraints 3 V ui 2 = i=1 ( Gβ G µ 3 V ui 2 = i=1 ) 2 = ( G F (NN ) 11 G F (NN ) 11 (NN ) 22 ) 2 = 1 α α = ± , (NN ) 22, PDG Chin.Phys. C38 (2014) Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

14 Current constraints r π = R π R SM π R π = Γ(π+ e + ν) Γ(π + µ + ν). = (NN ) 11 (NN ) 22 = r π = ± α 2 11 α α 21 2 PDG Chin.Phys. C38 (2014) Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

15 Oscillation probabilities P µe = 3 NµiN ei N µj Nej 4 i,j Re [ ( ) NµjN ej N µi Nei ] sin 2 m 2 ji L 4E 3 Im [ ( ) NµjN ej N µi Nei ] m 2 ji L sin. 2E j>i j>i Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

16 Oscillation probabilities P µe = (α 11 α 22 ) 2 P 3 3 µe + α 2 11α 22 α 21 P I µe + α 2 11 α 21 2, [ Pµe I = 2 sin(2θ 13 ) sin θ 23 sin ( m 2 31 L 4E ν ( m 2 cos θ 13 cos θ 23 sin(2θ 12 ) sin 21 L 2E ν ) ( m 2 sin 31 L 4E ν ) sin(φ), with δ CP = φ 12 φ 13 + φ 23 and φ = I NP = φ 12 Arg(α 21 ). + φ + δ CP ) ] Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

17 Oscillation probabilities P µe = α 2 11 α 21 2 = 1 2 [ sin 2 (2θ µe ) ] eff m 2 (ev 2 ) 10 3 LSND reactors NuTeV CCFR NOMAD 10-1 KARMEN sin 2 2Θ NOMAD Coll. PLB 570 (2003) 19 Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

18 Current constraints P. Astier et al. Search for nu(mu) nu(e) oscillations in the NOMAD experiment. Phys. Lett., B570:19 31, α Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

19 Current constraints K.A. Olive et al. Review of Particle Physics. Chin.Phys., C38:090001, A. Abada, A.M. Teixeira, A. Vicente, and C. Weiland. JHEP, 1402:091, G. Czapek et al. Phys. Rev. Lett., 70:17 20, P. Astier et al. Search for nu(mu) nu(e) oscillations in the NOMAD experiment. Phys. Lett., B570:19 31, α , α , α Limits at 90 % CL Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

20 Oscillation probabilities P µe = (α 11 α 22 ) 2 P 3 3 µe + α 2 11α 22 α 21 P I µe + α 2 11 α 21 2, [ Pµe I = 2 sin(2θ 13 ) sin θ 23 sin ( m 2 31 L 4E ν ( m 2 cos θ 13 cos θ 23 sin(2θ 12 ) sin 21 L 2E ν ) ( m 2 sin 31 L 4E ν ) sin(φ), with δ CP = φ 12 φ 13 + φ 23 and φ = I NP = φ 12 Arg(α 21 ). + φ + δ CP ) ] Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

21 CP-phase ambiguity 0.08 P µe δ CP = π/2 δ CP = 0 δ CP = 3π/ P µe OGM, Tortola, Valle, PRL 117 (2016) Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

22 CP-phase ambiguity χ L/E = 500 km/gev α 21 = 2.5x10-2 α 21 = 2.5x10-3 unitary rec δ CP /π OGM, Tortola, Valle, PRL 117 (2016) Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

23 On the positive side matter effects may also contribute to the signal Non-standard interactions may also contribute to the matter potential making the phenomenology more interesting Forero, Huber PRL 117 (2016) Forero, Huang Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

24 The drawbacks Any improvement in the restriction of α 21 leads to a diminish in the effect of the new phase (at least in vacuum). If we consider specific models for extra heavy neutral isosinglets, such as the seesaw, α 21 gets more restricted. Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

25 Conclusions We have shown a parametrization that is useful from the phenomenological point of view and it is general for any number of extra neutral heavy leptons. The parametrization incorporates naturally the right number of parameters for a non unitary mixing matrix. Non unitarity will introduce new phases and their effect in the conversion probability have been shown. In the case of big values of the non diagonal α parameters a signal might be hinted if both neutrino chanels are measured. Otherwise, LBLN experiments could give complementary constraints on these parameters in future. Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

26 Thanks Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27

27 CP-phase ambiguity P µe x3 P µe with δcp = 0 δ CP = 7π/4, φ = 5π/3 δ CP = 3π/2, φ = π δ CP = 4π/3, φ = 6π/ L/E (km/gev) OGM, Tortola, Valle, PRL 117 (2016) Omar Miranda (Cinvestav ) Non unitary neutrino mixing September 7, / 27