The Leptonic CP Phases

Transcription

1 Shao-Feng Ge Max-Planck-Institut für Kernphysik, Heidelberg, Germany SFG, Duane A. Dicus, Wayne W. Repko, PLB 72, 22 (211) [arxiv:114.62] SFG, Duane A. Dicus, Wayne W. Repko, PRL 18, 4181 (212) [arxiv: ] Andrew D. Hanlon, SFG, Wayne W. Repko, PLB 729, (214) [arxiv: ] SFG [arxiv: ] Jarah Evslin, SFG, Kaoru Hagiwara, JHEP 162 (216) 137 [arxiv: ] SFG, Pedro Pasquini, M. Tortola, J. W. F. Valle, PRD 95 (217) No.3, 335 [arxiv: ] SFG, Alexei Smirnov, JHEP 161 (216) 138 [arxiv: ] SFG [arxiv: ] SFG, Manfred Lindner, PRD 95 (217) No.3, 333 [arxiv: ]

2 Why neutrino mass & oscillation? Higgs boson for electroweak symmetry breaking & mass. Chiral symmetry breaking for mass. The world seems not affected by the tiny neutrino mass! Neutrino mass Mixing 3 Neutrino possible CP violation CP violation Leptogenesis Leptogenesis Matter-Antimatter Asymmetry There is something left in the Universe. Baryogenesis from quark mixing is not enough.

3 ν Oscillation Data (for NH) 1σ Best Value +1σ m 2 s m 2 12 (1 5 ev 2 ) m 2 a m 2 13 (1 3 ev 2 ) sin 2 θ s (θ s θ 12 ).294 (32.81 ).36 (33.56 ).318 (34.33 ) sin 2 θ a (θ a θ 23 ).42 (4.4 ).441 (41.6 ).468 (43.1 ) sin 2 θ r (θ r θ 13 ).291 (8.41 ).2166 (8.46 ).2241 (8.61 ) δ D, δ Mi?,???,???,?? Esteban, Gonzalez-Garcia, Maltoni, Martinez-Soler & Schwetz, arxiv:

4 Evidence of µ τ Symmetry Two small deviations (1σ level): 3.5 < θ a 45 < < θ r < 9.2 with Best Fit Value: θ a 45 = 3.9 & θ r = 8.8. Zeroth Order Approximation: θ a 45, θ r. CP & µ τ Symmetric Mass Matrix: A B B M ν () = C D C Mohapatra & Nussinov [hep-ph/989415], Lam [hep-ph/14116]

5 Horizontal Symmetry [Lam, PRL11:12162(28), PRD78:7315(28)] Mass Matrix M ν invariant under Transformation: Diagonalization: Rephasing: G T ν M ν G ν = M ν V T ν M ν V ν = D ν D ν = d T ν D ν d ν with d 2 ν = I 3 d ν = diag(±, ±, ±). Together M ν = G T ν M ν G ν = G T ν V νd ν V νg ν = V νd ν V ν = V νd T ν D ν d ν V ν Consequence: V νg ν = d ν V ν G ν = V ν d ν V ν For Leptons: F l = V l d l V l with d l = diag(e iβ 1, e iβ 2, e iβ 3).

6 Symmetry v.s. Mixing [Lam, PRL11:12162(28), PRD78:7315(28)] Two Nontrivial Independent possibilities of d ν : d (1) ν = diag( 1, 1, 1), d (2) ν = diag(1, 1, 1), d (3) ν = d (1) ν d (2) ν. θ s parameterized in terms of k: tan θ s = 2/k V ν (k) = k 2+k k k k 2 k 1 2(2+k 2 ) 2 k 1 2(2+k 2 ) 2 k = 2 k = 3 2 k = 6 θ s = 35.3 [TBM] θ s = 33.7 θ s = 3. Two Independent Symmetry Transformations G i = V ν d (i) G 1 = 1 2 k 2 2k 2k 1 k 2 + k 2 2 2, G 3 = 1 1 Z s 2 ( Zs 2) Z µτ 2 G = {E, G 1, G 2 ( G 1 G 3 ), G 3 } k 2 ν V ν

7 Full v.s. Residual [Lam, PRL11:12162(28), PRD78:7315(28)] Full Symmetries: H G F G F S 4 Z s 2 Zµτ 2 Z 3 {I, F, F 2 } {G 1, G 3, F } G 1 (G 2 ), G 3 F diag (1, ω, ω 2 ) Bottom-Up Top-Down See also Smirnov et. al., , , Residual Symmetries: ν i : G Z s 2 (Zs 2) Z µτ 2 for d i ν = diag (±1, ±1, ±1) l i : F U(1) U(1) for d i l = diag (eiβ 1, e iβ 2, e iβ 3 )

8 Residual Symmetry as Effective Theory Full symmetry HAS TO be Broken! Fermion needs to acquire mass. Non-trivial mixing V PMNS = V l V ν If mixing is TRUELY determined by symmetry, it has to be residual symmetry VEVs Yukawa couplings Residual Symmetry as Custodial Symmetry Gauge symmetry has to be broken. Otherwise, no mixing. Weak mixing angle is a function of gauge couplings, which cannot be dictated by gauge symmetry (and VEV). Weak mixing angle is related to the physical observables, the gauge boson masses, by custodial symmetry.

9 Example Zee-A 4 Model L l = Lepton s Representation: e R 1 3, µ R 1, τ R 1 e L µ L τ L A 4 invariant Lagrangian: ϕ 1 ϕ 2 ϕ 3 3. L l = y 1 e R (1ϕ 1 e L + 1ϕ 2 τ L + 1ϕ 3 τ L) Mass term with ϕ i = v i : + y 2 µ R (ωϕ 1 e L + 1ϕ 2 τ L + ω 2 ϕ 3 τ L) + y 3 τ R (ω 2 ϕ 1 e L + 1ϕ 2 τ L + ωϕ 3 τ L). y e R µ R τ R y 2 ω 1 ω 2 y 3 1 v v 2 ω 2 1 ω v 1 = v 2 = v 3 = v U l,r = I, U l,l (ω), m l,i = y i v. y 1 = y 2 = y 3 = y U l,l = I, U l,r (ω), m l,i = yv i. v 3 hep-ph/58278 e L µ L τ L.

10 Prediction of Large δ D by Z s 2 and Zs 2 cos δ D = (s2 s c 2 s s 2 r )(c 2 a s 2 a ) 4c a s a c s s s s r cos δ D = (s2 s s 2 r c 2 s )(c 2 a s 2 a ) 4c a s a c s s s s r.3.25 Z s 2 Z s 2 NH IH dp( δ D )/d δ D o 2 o 4 o 6 o 8 o 1 o 12 o 14 o 16 o 18 o δ D 1σ Indication for δ D = 74 ( 11 ) [Schwetz et.al ]

11 Dirac CP Phase Measurement

12 CP Accelerator Exps T2K NOνA DUNE,T2KII/T2HK/T2KK/T2KO, MOMENT/ADS-CI, Super-PINGU

13 The Dirac CP Phase δ Accelerator Exp To leading order in α = δm2 21 3%, the oscillation probability δm 2 31 relevant to measuring δ T2(H)K, P νµ νe ν µ ν e 4s 2 ac 2 r s 2 r sin 2 φ 31 8c a s a c 2 r s r c s s s sin φ 21 sin φ 31 [cos δ D cos φ 31 ±sin δ D sin φ 31 ] for ν & ν, respectively. [φ ij δm2 ij L 4E ν ] ν µ ν µ Exps measure sin 2 (2θ a ) precisely, but not sin 2 θ a. Run both ν & ν first peak [φ 31 = π 2, φ 21 = α π 2 ], P νµ ν e + P νµ ν e = 2s 2 ac 2 r s 2 r, P νµ ν e P νµ ν e = απ sin(2θ s ) sin(2θ r ) sin(2θ a ) cos θ r sin δ D.

14 The Dirac CP Phase δ Accelerator Exp Accelerator experiment, such as T2(H)K, uses off-axis beam to compare ν e & ν e the oscillation maximum. Disadvantages: Efficiency: Proton accelerators produce ν more efficiently than ν (σ ν > σ ν). The ν mode needs more beam time [T ν : T ν = 2 : 1]. Undercut statistics Difficult to reduce the uncertainty. Degeneracy: Only sin δ D appears in P νµ ν e & P νµ ν e. Cannot distinguish δ D from π δ D. CP Uncertainty Pµe δ D cos δ D (δ D ) 1/ cos δ D. Solution: Measure ν mode with µ + rest (µdar)

15 µdar ν Oscillation Experiments A cyclotron produces 8 MeV proton fixed target. Produce π ± which stops & π is absorbed, π + rest: π + µ + + ν µ. µ + stops & rest: µ + e + + ν µ + ν e. e + ν µ ν e µdar Spectrum E ν [MeV] ν µ travel in all directions, oscillating as they go. A detector measures the ν e from ν µ ν e oscillation.

16 Accelerator + µdar Experiments Combining ν µ ν accelerator [narrow 55 MeV] & ν µ ν µdar [wide peak 45 MeV] solves the 2 problems: Efficiency: high intensity, µdar is plentiful enough. Accelerator Exps can devote all run time to the ν mode. With same run time, the statistical uncertainty drops by 3. Degeneracy: (decomposition in propagation basis [ ]) P (i) µe decomposition coefficients for cosδ and sinδ at T2(H)K [295 km] -.1 ν Mode: coeff of cosδ -.15 sinδ ν Mode: coeff of cosδ sinδ E ν, ν [MeV] P (i) µe or P (i) µe decomposition coefficients for cosδ and sinδ at µdarts near detector [1 km]: coeff of cosδ sinδ far detector [3 km]: coeff of cosδ sinδ E ν, ν [MeV]

17 New Proposals 1 µdar source + 2 detectors Advantages: Full (1%) duty factor! Lower intensity: 9mA [ 4 lower than DAEδALUS] Not far beyond the current state-of-art technology of cyclotron Paul Scherrer Institute] MUCH cheaper & technically easier. Only one cyclotron. Lower intensity. Disadvantage? A second detector! µdar with Two Scintillators (µdarts) [ ] Tokai N Toyama to(2) Kamioka (TNT2K) [ ]

18 TNT2K T2(H)K + µsk + µhk µdar is also useful for material, medicine industries in Toyama

19 Event TNT2K Evslin, Ge & Hagiwara [ ] µsk [6 years] (L = 15km) µhk [6 years] (L = 15+8km) NH - δ = o 9 o 18 o 27 o ν e - 16 O QE ν-e ES atmos invmu atmos (ν e + ν e ) µ - DAR Event Rate [MeV -1 ] Event Rate [MeV -1 ] E ν [MeV] E ν [MeV] Expected µdar IBD signal from 6 yrs of SK (15km) & HK (23km) with NH. Simulated by NuPro,

20 δ D TNT2K Evslin, Ge & Hagiwara [ ] 5 o 4 o δ = o 9 o 18 o -9 o NH T2Kν+µDAR (5%) 5 o 4 o IH Average (δ) 3 o 2 o Average (δ) 3 o 2 o 1 o 1 o o Baseline Length [km] o Baseline Length [km] Simulated by NuPro,

21 δ D TNT2K Evslin, Ge & Hagiwara [ ] NH T2Kν+T2HKν+µDAR (5%) IH 14 o 14 o 12 o 12 o 1 o 1 o Average (δ) 8 o 6 o Average (δ) 8 o 6 o 4 o 2 o δ = o 9 o 18 o 4 o 2 o -9 o o o Baseline to SK [km] Baseline to SK [km] Simulated by NuPro,

22 Majorana CP Phase Measurement

23 Preference of NH Non-Observation of ν2β? 7 6 Oscillation + CMB NH+IH NH IH 12 1 Oscillation + CMB + EUCLID NH+IH NH IH 5 8 Prior PDF Prior PDF m ee [mev] m ee [mev] 1 P( m ee < m upper ee ) [%] 1 1 Oscillation + CMB Oscillation + EUCLID m upper ee [mev]

24 Any chance of obtaining some information? Im Majorana Triangle I 1 O L 1 M1 Π L 2 L 3 M3 Re I 2 with m ee L 1 + L 2 + L 3, L1 m 1 Ue1 2 = m 1 cr 2 cs 2 e iδ M1, L2 m 2 Ue2 2 = m1 2 + m2 s cr 2 ss 2, L3 m 3 Ue3 2 = m1 2 + m2 asr 2 e iδ M3.

25 Determine 2 Majorana Phases Simultaneously L 1 L 3 L 2 L 1 + L 3. cos δ M1 = L2 1 + L2 2 L2 3 2L 1 L 2 cos δ M3 = + L2 1 L2 2 L2 3 2L 2 L 3 = m2 1 c4 r c 4 s + m 2 2 c4 r s 4 s m 2 3 s4 r 2m 1 m 2 c 4 r c 2 s s 2 s = + m2 1 c4 r c 4 s m 2 2 c4 r s 4 s m 2 3 s4 r 2m 2 m 3 c 2 r s 2 r s 2 s, M3 Degree m 1 6meV m 1 3meV m 1 4 mev m 1 5meV M1 Degree M1, M3 Degree M1 M3 b m 1 mev

26 Uncertainties from Oscillation Parameters 18 a 18 b M3 Degree Σ 3Σ m 1 4meV M3 Degree Σ 3Σ m 1 4meV m s 2 7.5± ev M1 Degree m a ± ev M1 Degree 18 c 18 d M3 Degree m 1 4meV 3Σ 3Σ M3 Degree Σ m 1 4meV 3Σ Θ s o ±.76 o M1 Degree Θ r 8.5 o ±.2 o M1 Degree

27 Uncertainties from Oscillation Parameters 18o 18o (a) (b) Prior 135o Posterior 135o m1 = 3meV m1 = 3meV 4meV 5meV 9o δm3 δm3 4meV 6meV Turning Point o o 45 o o o 19o 195o δm1 2o 25o o o 18 21o.4 (c) Posterior m1 = 3meV 4meV 5meV 6meV 19o o 19o Prior Distribution of Majorana CP δm3 Distribution of Majorana CP δm1 185o 195o δm1 2o 25o 21o.6 Prior 18o 6meV Turning Point meV 9o 195o δm1 2o 25o 21o (d) Posterior m1 = 3meV 4meV 5meV 6meV o 45o 9o δm3 135o 18o

28 Uncertainties from Oscillation Parameters 36 a 36 b M3 Degree M3 Degree m1 3meV M1 Degree 45 m1 4meV M1 Degree 36 c 36 d M3 Degree M3 Degree m1 5meV M1 Degree 45 m1 6meV M1 Degree

29 Majorana Pyramid Im Im I1 I 1 O L 1 L 3 L1 L3 L 2 E 1 E 2 Re O L2 E1 E2 Re I 2 I2 Majorana Trangle Size mev b B L 1 L 2 Peak L 1 L 3 L 1 L 3 B L 3 upper Sensitivity m ee mev a Peak ±5 o M1 Majorana Pyramid.2 ±5 o M3 B B

30 Prey of Leptonic CP Phases

31 Thank You!