Mass and Mixing, Global Analysis Carlo Giunti INFN, Torino, Italy - PowerPoint PPT Presentation

Mass and Mixing, Global Analysis Carlo Giunti INFN, Torino, Italy Rencontres du Vietnam 2017: Neutrinos Qui Nhon, Vietnam, 16-22 July 2017 C. Giunti − Mass and Mixing, Global Analysis − Rencontres du Vietnam 2017: Neutrinos − 17 July 2017 − 1/34

Fermion Mass Spectrum 10 12 t 10 11 b 10 10 c 10 9 τ s 10 8 ν τ µ d 10 7 u 10 6 ν µ e 10 5 m [eV] 10 4 10 3 10 2 10 ν e ν 1 ν 2 ν 3 1 10 − 1 10 − 2 10 − 3 10 − 4 C. Giunti − Mass and Mixing, Global Analysis − Rencontres du Vietnam 2017: Neutrinos − 17 July 2017 − 2/34

Neutrino Mixing Left-handed Flavor Neutrinos produced in Weak Interactions | ν e , −� | ν µ , −� | ν τ , −� H CC = g W ρ ( ν eL γ ρ e L + ν µ L γ ρ µ L + ν τ L γ ρ τ L ) + H.c. √ 2 � � U ∗ Fields ν α L = U α k ν kL = ⇒ | ν α , −� = α k | ν k , −� States k k | ν 1 , −� | ν 2 , −� | ν 3 , −� Left-handed Massive Neutrinos propagate from Source to Detector   U e 1 U e 2 U e 3 3 × 3 Unitary Mixing Matrix: U = U µ 1 U µ 2 U µ 3   U τ 1 U τ 2 U τ 3 C. Giunti − Mass and Mixing, Global Analysis − Rencontres du Vietnam 2017: Neutrinos − 17 July 2017 − 3/34

Neutrino Oscillations | ν ( t = 0) � = | ν α � = U ∗ α 1 | ν 1 � + U ∗ α 2 | ν 2 � + U ∗ α 3 | ν 3 � ν 1 ν α ν β ν 2 ν 3 L source detector α 1 e − iE 1 t | ν 1 � + U ∗ α 2 e − iE 2 t | ν 2 � + U ∗ α 3 e − iE 3 t | ν 3 � � = | ν α � | ν ( t > 0) � = U ∗ k = p 2 + m 2 E 2 t = L k � � ∆ m 2 kj L P ν α → ν β ( L ) = |� ν β | ν ( L ) �| 2 = � U β k U ∗ α k U ∗ β j U α j exp − i 2 E k , j the oscillation probabilities depend on U and ∆ m 2 kj ≡ m 2 k − m 2 j C. Giunti − Mass and Mixing, Global Analysis − Rencontres du Vietnam 2017: Neutrinos − 17 July 2017 − 4/34

� ∆ m 2 L � L osc = 4 π E P ν α → ν β = sin 2 2 ϑ sin 2 2 ν -mixing: = ⇒ ∆ m 2 4 E 1 0.8 sin 2 2 ϑ P ν α → ν β 0.6 0.4 0.2 0 L osc L Tiny neutrino masses lead to observable macroscopic oscillation distances! � km ∆ m 2 � 10 − 1 eV 2  m � 10 short-baseline experiments MeV GeV   � km ∆ m 2 � 10 − 3 eV 2  10 3 m � long-baseline experiments  L  MeV GeV E � ∆ m 2 � 10 − 4 eV 2 10 4 km atmospheric neutrino experiments  GeV  ∆ m 2 � 10 − 11 eV 2   10 11 m solar neutrino experiments  MeV Neutrino oscillations are the optimal tool to reveal tiny neutrino masses! C. Giunti − Mass and Mixing, Global Analysis − Rencontres du Vietnam 2017: Neutrinos − 17 July 2017 − 5/34

Three-Neutrino Mixing Paradigm Standard Parameterization of Mixing Matrix (as CKM)         0 s 13 e − i δ 13 1 0 0 c 13 c 12 s 12 0 1 0 0 U =         0 e i λ 21 0 0 1 0 − s 12 c 12 0 0 c 23 s 23                 − s 13 e i δ 13 0 e i λ 31 0 − s 23 c 23 c 13 0 0 1 0 0     s 13 e − i δ 13 c 12 c 13 s 12 c 13 1 0 0 =     − s 12 c 23 − c 12 s 23 s 13 e i δ 13 c 12 c 23 − s 12 s 23 s 13 e i δ 13 0 e i λ 21 0 s 23 c 13         s 12 s 23 − c 12 c 23 s 13 e i δ 13 − c 12 s 23 − s 12 c 23 s 13 e i δ 13 e i λ 31 c 23 c 13 0 0 0 ≤ ϑ ab ≤ π c ab ≡ cos ϑ ab s ab ≡ sin ϑ ab 0 ≤ δ 13 , λ 21 , λ 31 < 2 π 2  3 Mixing Angles: ϑ 12 , ϑ 23 , ϑ 13 OSCILLATION  1 CPV Dirac Phase: δ 13 PARAMETERS 2 independent ∆ m 2 kj ≡ m 2 k − m 2 j : ∆ m 2 21 , ∆ m 2  31 2 CPV Majorana Phases: λ 21 , λ 31 ⇐ ⇒ | ∆ L | = 2 processes C. Giunti − Mass and Mixing, Global Analysis − Rencontres du Vietnam 2017: Neutrinos − 17 July 2017 − 6/34

Three-Neutrino Mixing Ingredients         s 13 e − i δ 13 1 0 0 c 13 0 c 12 s 12 0 1 0 0 U =         e i λ 21 0 0 1 0 0 0 0 c 23 s 23 − s 12 c 12                 − s 13 e i δ 13 e i λ 31 0 − s 23 c 23 0 c 13 0 0 1 0 0    SNO, Borexino  Solar  Super-Kamiokande     21 ≃ 7 . 4 × 10 − 5 eV 2     ν e → ν µ , ν τ ∆ m 2 S = ∆ m 2  GALLEX/GNO, SAGE      → Homestake, Kamiokande sin 2 ϑ S = sin 2 ϑ 12 ≃ 0 . 30     VLBL Reactor    (KamLAND)  ¯ ν e disappearance  C. Giunti − Mass and Mixing, Global Analysis − Rencontres du Vietnam 2017: Neutrinos − 17 July 2017 − 7/34

Three-Neutrino Mixing Ingredients         s 13 e − i δ 13 1 0 0 c 13 0 c 12 s 12 0 1 0 0 U =         e i λ 21 0 0 1 0 0 0 0 c 23 s 23 − s 12 c 12                 − s 13 e i δ 13 e i λ 31 0 − s 23 c 23 0 c 13 0 0 1 0 0    Super-Kamiokande Atmospheric   Kamiokande, IMB    ν µ → ν τ    MACRO, Soudan-2        31 | ≃ 2 . 5 × 10 − 3 eV 2 ∆ m 2 A ≃ | ∆ m 2   � �   LBL Accelerator K2K, MINOS → sin 2 ϑ A = sin 2 ϑ 23 ≃ 0 . 50 ν µ disappearance T2K, NO ν A            LBL Accelerator    (OPERA)  ν µ → ν τ  C. Giunti − Mass and Mixing, Global Analysis − Rencontres du Vietnam 2017: Neutrinos − 17 July 2017 − 8/34

Three-Neutrino Mixing Ingredients         s 13 e − i δ 13 1 0 0 c 13 0 c 12 s 12 0 1 0 0 U =         e i λ 21 0 0 1 0 0 0 0 c 23 s 23 − s 12 c 12                 − s 13 e i δ 13 e i λ 31 0 − s 23 c 23 0 c 13 0 0 1 0 0 LBL Accelerator  (T2K, MINOS, NO ν A)  ν µ → ν e  31 | ≃ 2 . 5 × 10 − 3 eV 2   ∆ m 2 A ≃ | ∆ m 2     → sin 2 ϑ 13 ≃ 0 . 022   � � LBL Reactor  Daya Bay, RENO    ν e disappearance ¯  Double Chooz C. Giunti − Mass and Mixing, Global Analysis − Rencontres du Vietnam 2017: Neutrinos − 17 July 2017 − 9/34

Mass Ordering ν e ν µ ν τ m 2 m 2 ν 2 ν 3 ∆ m 2 SOL ν 1 ∆ m 2 ∆ m 2 ATM ATM ν 2 ∆ m 2 SOL ν 1 ν 3 Normal Ordering Inverted Ordering ∆ m 2 31 > ∆ m 2 ∆ m 2 32 < ∆ m 2 32 > 0 31 < 0 absolute scale is not determined by neutrino oscillation data C. Giunti − Mass and Mixing, Global Analysis − Rencontres du Vietnam 2017: Neutrinos − 17 July 2017 − 10/34

CP Transformation Right-handed antineutrinos are described by CP-conjugated states C − ⇀ Particle − Antiparticle ↽ P − ⇀ Left-Handed Helicity − Right-Handed Helicity ↽ CP � � − − ⇀ | ν α , −� = U ∗ α k | ν k , −� | ¯ ν α , + � = U α k | ¯ ν k , + � ↽ − − k k CP − − ⇀ In oscillation probabilities: Neutrino U U ∗ Antineutrino ↽ − − � � ∆ m 2 kj L � sin 2 � � P ν α → ν β = δ αβ − 4 Re U ∗ α k U β k U α j U ∗ ← CP Even β j 4 E k > j � � ∆ m 2 kj L � � � + 2 Im U ∗ α k U β k U α j U ∗ sin ← CP Odd β j 2 E k > j Survival probabilities: P ν α → ν α = P ¯ CPT ν α → ¯ ν α C. Giunti − Mass and Mixing, Global Analysis − Rencontres du Vietnam 2017: Neutrinos − 17 July 2017 − 11/34

CP Asymmetries A CP αβ = P ν α → ν β − P ¯ ν α → ¯ ν β � ∆ m 2 � ∆ m 2 � ∆ m 2 � � � 21 L 31 L 32 L = 16 J αβ sin sin sin 4 E 4 E 4 E � U ∗ α 1 U β 1 U α 2 U ∗ � J αβ = Im = ± J CP Jarlskog Invariant β 2 U ∗ µ 1 U e 1 U µ 2 U ∗ = c 12 s 12 c 23 s 23 c 2 � � J CP = Im 13 s 13 sin δ 13 e 2 J CP � = 0 ⇐ ⇒ ϑ 12 , ϑ 23 , ϑ 13 � = 0 , π/ 2 and δ 13 � = 0 , π Necessary conditions for observation of CP violation: ◮ Sensitivity to all mixing angles, including small ϑ 13 . ◮ Sensitivity to oscillations due to ∆ m 2 21 and ∆ m 2 31 . C. Giunti − Mass and Mixing, Global Analysis − Rencontres du Vietnam 2017: Neutrinos − 17 July 2017 − 12/34

LBL ν µ → ν e and ¯ ν µ → ¯ ν e ∆ = ∆ m 2 √ 31 L A = 2 EV V = 2 G F N e ∆ m 2 4 E 31 ∆ m 2 21 / ∆ m 2 sin θ 13 ≪ 1 31 ≪ 1 octant ↓ sin 2 [(1 − A )∆] ν µ → ν e ≃ sin 2 2 ϑ 13 P LBL sin 2 ϑ 23 (1 − A ) 2 +∆ m 2 )sin( A ∆) sin[(1 − A )∆] 21 sin 2 ϑ 13 sin 2 ϑ 12 sin 2 ϑ 23 cos(∆ + δ 13 ∆ m 2 1 − A A ↑ 31 � 2 � ∆ m 2 sin 2 ( A ∆) CPV sin 2 2 ϑ 12 cos 2 ϑ 23 21 + ∆ m 2 A 2 31 ∆ m 2 ∆ m 2 NO: 31 > 0 IO: 31 < 0 for antineutrinos: δ 13 → − δ 13 (CPV) and A → − A (Fake CPV!) [see: Mezzetto, Schwetz, JPG 37 (2010) 103001] C. Giunti − Mass and Mixing, Global Analysis − Rencontres du Vietnam 2017: Neutrinos − 17 July 2017 − 13/34