Residual Flavor Symmetries in the Sector Probir Roy Centre for - PowerPoint PPT Presentation

Residual Flavor Symmetries in the ν µ ν τ Sector Probir Roy Centre for Astroparticle Physics and Space Science Bose Institute, Kolkata IMHEP 2019, IOPB Collaborators R. Sinha and A. Ghosal of SINP Probir Roy Residual Flavor Symmetries in the ν µ ν τ Sector

PLAN OF THE TALK INTRODUCTION NEUTRINO RESIDUAL FLAVOR SYMMETRIES NEUTRINO MIXING ANGLES AND PHASES NUMERICAL ANALYSIS NEUTRINOLESS DOUBLE BETA DECAY CP ASYMMETRY IN LONG-BASELINE OSCILLATIONS FLAVOR FLUX RATIOS AT NEUTRINO TELESCOPES CONCLUSIONS Probir Roy Residual Flavor Symmetries in the ν µ ν τ Sector

1. INTRODUCTION Regularities observed in neutrino mixing over the years: 1. Atmospheric mixing angle θ 23 is close to maximal value π/ 4. 2. Solar mixing angle θ 12 is not far from tribimaximal value sin − 1 ( 1 3 ) ∼ 35 . 26 ◦ . √ 3. Reactor mixing angle θ 12 not far from tribimaximal value 0 ◦ . 4. Dirac CP phase δ is close to the maximal value 3 π/ 2. Current best-fit values θ 12 = 33 . 82 ◦ , θ 23 = 49 . 6 ◦ ( NO ) , 49 . 8 ◦ ( IO ) , δ = 215 ◦ ( NO ) , 284 ◦ ( IO ) ⇒ Some kind of discrete symmetry in the flavor space of neutrinos. Probir Roy Residual Flavor Symmetries in the ν µ ν τ Sector

2. NEUTRINO RESIDUAL FLAVOR SYMMETRIES Work with Majorana neutrinos = 1 −L mass 2 ν C ℓ L ( M ν ) ℓ m ν m + h . c ., ( M ν ) ℓ m = ( M ν ) m ℓ ν U T M ν U = M d = diag ( m 1 , m 2 , m 3 ) , with m 1 , 2 , 3 assumed > 0 . Perhaps there is a residual symmetry G with G T M ν G =? RHS can be + M ν , − M ν , + M ∗ ν , − M ∗ ν . G is a discrete symmetry. Questions: 1. What is G ? 2. What are the characteristic phenomenological predictions of G ? 3. How do these predictions compare with current experiment? 4. Will distinctive predictions from G be testable in future set-ups? 5. Can G be embedded in a larger symmetry group which in turn comes from a GUT? Probir Roy Residual Flavor Symmetries in the ν µ ν τ Sector

We deal with exact symmetries: perturbations introduce too many parameters. 1. Historically, first µτ exchange symmetry ( µτ S ); Fukushima and Nishiura (1997), Review by King (2017) Invariance under ν L ℓ → G ℓ m ν Lm  − 1 0 0   and G T M ν G = M ν . Obtainable from S 4 G = 0 0 1  0 1 0 Altarelli and Feruglio (2010)   − a x a M µτ S  , x , a , c , y complex mass-dimensional = a y c ν  − a c y ⇒ θ 13 = 0 ruled out at 10 σ, θ 23 = π/ 4 (disfavored). No observable Dirac CP violation. Strong experimental hints to the contrary. Abandoned! Probir Roy Residual Flavor Symmetries in the ν µ ν τ Sector

2. Next, µτ exchange antisymmetry ( µτ A ). Grimus et al (2006) Same G but G T M ν G = − M ν . Obtainable from Z 4 Altarelli and Feruglio (2010), Joshipura (2015)   0 a a ⇒ M µτ S = a y 0 ν   0 − y a ⇒ θ 13 = 0 ruled out at 10 σ, θ 23 = π/ 4 (disfavored) . Same consequences as µτ S + one massless and two degenerate neutrinos (ruled out by ∆ m 2 21 � = 0 � = ∆ m 2 32 ). Proponents considered perturbations → too complicated. Abandoned! Probir Roy Residual Flavor Symmetries in the ν µ ν τ Sector

3. Now, CP extended µτ symmetry (CP µτ S ) Harrison and Scott (2002) Grimus & Lavoura (2004) Mohapatra & Nishi (2015) G T M ν G = M ∗ ν . Obtainable from S 4  − a  x 1 a ⇒ M CP µτ S = a y c 1 ν   a ∗ c 1 y ∗ Symmetry transformation: ν L ℓ → iG ℓ m γ 0 ν C Lm . Admits θ 13 � = 0, Majorana phases 0 or π . θ 23 = π/ 4 and Dirac phase δ either π/ 2 or 3 π/ 2 (both in tension with latest data). Probir Roy Residual Flavor Symmetries in the ν µ ν τ Sector

4. Next, CP extended µτ antisymmetry (CP µτ A ) Samanta, PR, Ghosal (2018) G T M ν G = − M ∗ ν . Obtainable from ν L ℓ → − G ℓ m γ 0 ν C Lm M CP µτ S = − iM CP µτ S ν ν Phenomenology identical to that of CP µτ S . Leptogenesis with minimal seesaw (two heavy RH neutrinos N 1 , N 2 ) worked out in detail by SRG. Probir Roy Residual Flavor Symmetries in the ν µ ν τ Sector

5. Mixed ( θ ) µτ exchange symmetry ( µτθ S ) Introduces one extra parameter: mixing angle θ . Now,   − 1 0 0 G θ =  and G T M ν G = M ν . 0 − cos θ sin θ  0 sin θ cos θ θ → π/ 2 lets µτθ S → µτ S .  − a 1 − c θ  x a s θ M µτθ S = a y c  .   ν  − a 1 − c θ y + 2 c c θ c s θ s θ Though θ 23 � = π/ 4 , θ 13 = 0. Excluded! A modification, proposed by Samanta, Sinha, Ghosal (2018) is still allowed. Probir Roy Residual Flavor Symmetries in the ν µ ν τ Sector

6. Mixed ( θ ) µτ exchange antisymmetry ( µτθ A ). Same G θ but G T M ν G = − M ν .  a 1+ c θ  x a s θ y c θ M µτθ A = a y  .   ν s θ  a 1+ c θ y c θ − y s θ s θ θ → π/ 2 lets µτθ A → µτ A . Once again, θ 13 = 0. Excluded! Probir Roy Residual Flavor Symmetries in the ν µ ν τ Sector

7. CP-transformed mixed µτ symmetry (CP µτθ S ). Chen et al (2016) Now, ( G θ ) T M ν G θ = M ∗ ν .  1 − c θ 1+ c θ  x 1 a 1 + ia 2 − a 1 + ia 2 s θ s θ c θ M CP µτθ S = a 1 + ia 2 y 1 + iy 2 c 1 + iy 2  .   ν s θ  1 − c θ 1+ c θ c θ c θ − a 1 + ia 2 c 1 + iy 2 − iy 2 + 2 c 1 s θ s θ s θ s θ with x , a 1 , 2 , y 1 , 2 and c 1 as real mass-dimensional parameters. ⇒ θ 13 � = 0 , θ 23 � = π/ 4 and δ not fixed: sin δ = ± sin θ . sin 2 θ 23 Note that, for θ → π/ 2, CP µτθ S → CP µτ S. Probir Roy Residual Flavor Symmetries in the ν µ ν τ Sector

8. CP-transformed mixed µτ antisymmetry (CP µτθ A ). Sinha, Roy, Ghosal (2018) Now, ( G θ ) T M ν G θ = − M ∗ ν . One obtains M CP µτθ A = iM CP µτ S . ν ν Phenomenology identical to that of M CP µτθ S . ν Implications of leptonic CP violation in long-baseline experiments, 0 νββ decay and flavor flux ratios at neutrino telescopes worked out in detail by SRG. Probir Roy Residual Flavor Symmetries in the ν µ ν τ Sector

3. NEUTRINO MIXING ANGLES AND PHASES Lam’s observation: Lam (2007) G θ U ∗ = U ˜ d = diag ( ˜ ˜ d 1 , ˜ d 2 , ˜ d , d 3 ) , d 1 , 2 , 3 = ± 1 . U = diag ( e i φ 1 , e i φ 2 , e i φ 3 ) U PMNS , s 13 e − i ( δ − β e i α  2 )  2 s 12 c 13 c 12 c 13 e i α c 13 s 23 e i β U PMNS = − s 12 c 23 − c 12 s 23 s 13 e i δ 2 ( c 12 c 23 − s 12 s 13 s 23 e i δ )  .   2  c 13 c 23 e i β e i α s 12 s 23 − c 12 s 13 c 23 e i δ 2 ( − c 12 s 23 − s 12 s 13 c 23 e i δ ) 2 Algebraic matching leads to e i α = ˜ d 2 , e 2 i ( δ − β 2 ) = ˜ d 1 ˜ d 1 ˜ d 3 ⇒ α = 0 or π, and β = 2 δ or (2 δ − π ) . Moreover, cot 2 θ 23 = cot θ cos( φ 2 − φ 3 ) , sin δ = ± sin θ/ sin 2 θ 23 , i . e . θ → π/ 2 ⇒ θ 23 → π 4 . In general, θ 23 � = π/ 4 and δ � = 0 or π. Probir Roy Residual Flavor Symmetries in the ν µ ν τ Sector

4.NUMERICAL ANALYSIS Input mixing angles and mass-squared differences from latest global analysis. Esteban et al (2017) Neutrino mass sum m 1 + m 2 + m 3 < 0 . 17 eV from Planck data. Aghanim et al (2016) Table: Input 3 σ ranges used in the analysis ∆ m 2 | ∆ m 2 Values θ 12 θ 23 θ 13 31 | 21 10 − 5 eV 2 10 − 3 ( eV 2 ) degrees degrees degrees NO 31 . 42 to 36 . 05 40 . 3 to 51 . 5 8 . 09 to 8 . 98 6 . 80 to 8 . 02 2 . 399 to 2 . 593 31 . 43 to 36 . 06 41 . 3 to 51 . 7 8 . 14 to 9 . 01 6 . 80 to 8 . 02 2 . 399 to 2 . 593 IO Table: Output values of the parameters of M ν 10 3 x 10 3 a 1 10 3 a 2 10 3 y 1 10 3 y 1 10 3 c θ ( ◦ ) Values NO -22 to 22 -45 to 45 − 32 to 32 -35 to 35 -45 to 45 -35 to 35 12 to 164 IO -25 to 25 -45 to 45 -4 to 4 -25 to 25 -35 to 35 -25 to 25 2 to 156 Probir Roy Residual Flavor Symmetries in the ν µ ν τ Sector

Table: Predictions on the light neutrino masses. Normal Ordering ( m 3 > m 2 ) Inverted Ordering ( m 3 < m 1 ) 10 3 m 1 ( eV ) 10 − 3 m 2 ( eV ) 10 3 m 3 ( eV ) 10 3 m 1 ( eV ) 10 3 m 2 ( eV ) 10 3 m 3 ( eV ) 8 . 4 × 10 − 2 − 49 4 . 4 × 10 − 2 − 42 9 − 51 50 − 71 48 − 64 49 − 66 Neutrino masses for normal (left) and inverted (right) ordering against the lightest mass eigenvalue. The red, green and blue bands refer to m 1 , m 2 and m 1 respectively. Probir Roy Residual Flavor Symmetries in the ν µ ν τ Sector

5. NEUTRINOLESS DOUBLE BETA DECAY ( A , Z ) → ( A , Z + 2) + 2 e − T 0 ν 1 / 2 = G 0 ν |M| 2 | M ee ν | 2 m − 2 Half-life e , G 0 ν = two-body phase space factor , M = nuclear matrix element , 13 m 2 e i α + s 2 M ee ν = c 2 12 c 2 13 m 1 + s 2 12 c 2 13 m 3 e i ( β − 2 δ ) Four cases in our model. (i) | M ee ν | = c 2 12 c 2 13 m 1 + s 2 12 c 2 13 m 2 + s 2 13 m 3 for α = 0 , β = 2 δ , ν | = c 2 12 c 2 13 m 1 + s 2 12 c 2 13 m 2 − s 2 (ii) | M ee 13 m 3 for α = 0 , β = 2 δ − π , ν | = c 2 12 c 2 13 m 1 − s 2 12 c 2 13 m 2 + s 2 (iii) | M ee 13 m 3 for α = π, β = 2 δ and (iv) | M ee ν | = c 2 12 c 2 13 m 1 − s 2 12 c 2 13 m 2 − s 2 13 m 3 for α = π, β = 2 δ − π . Probir Roy Residual Flavor Symmetries in the ν µ ν τ Sector

Plots of | M ee ν | versus the minimum neutrino mass m min The four plots correspond to four possible choices of α and β . Predicted signal below the reach of GERDA phase II but reachable by LEGEND-200, LEGEND-1K and nEXO. Failure of nEXO to see any signal would rule out our model for IO. Probir Roy Residual Flavor Symmetries in the ν µ ν τ Sector