Neutrino Physics Part II: Phenomenology of Massive Neutrinos Carlo - PowerPoint PPT Presentation

Neutrino Physics Part II: Phenomenology of Massive Neutrinos Carlo Giunti INFN, Torino, Italy giunti@to.infn.it MISP 2019 Moscow International School of Physics Voronovo, Moscow, Russia, 20-27 February 2019 C. Giunti − Neutrino Physics – II − MISP 2019 − Moscow − 20-23 Feb 2019 − 1/89

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 − Neutrino Physics – II − MISP 2019 − Moscow − 20-23 Feb 2019 − 2/89

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 − Neutrino Physics – II − MISP 2019 − Moscow − 20-23 Feb 2019 − 3/89

Effective Two-Neutrino Mixing Approximation ν j ν β | ν α � = cos ϑ | ν k � + sin ϑ | ν j � ν α | ν β � = − sin ϑ | ν k � + cos ϑ | ν j � ϑ ν k � cos ϑ � sin ϑ U = − sin ϑ cos ϑ ∆ m 2 ≡ ∆ m 2 kj ≡ m 2 k − m 2 j � ∆ m 2 L � P ν α → ν β = P ν β → ν α = sin 2 2 ϑ sin 2 Transition Probability: 4 E P ν α → ν α = P ν β → ν β = 1 − P ν α → ν β Survival Probabilities: C. Giunti − Neutrino Physics – II − MISP 2019 − Moscow − 20-23 Feb 2019 − 4/89

� ∆ 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 ◮ The effect of a tiny ∆ m 2 can be amplified by a large distance L . ◮ A tiny ∆ m 2 generates oscillations observable at macroscopic distances! ◮ Neutrino oscillations are the optimal tool to reveal tiny neutrino masses! C. Giunti − Neutrino Physics – II − MISP 2019 − Moscow − 20-23 Feb 2019 − 5/89

1 . 27 ∆ m 2 [eV 2 ] L [km] � � P ν α → ν β = sin 2 2 ϑ sin 2 2 ν -mixing: E [GeV] 1 0.8 sin 2 2 ϑ P ν α → ν β 0.6 0.4 0.2 0 L osc L � 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  E � MeV GeV ∆ 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 C. Giunti − Neutrino Physics – II − MISP 2019 − Moscow − 20-23 Feb 2019 − 6/89

Neutrinos and Antineutrinos Right-handed antineutrinos are described by CP-conjugated fields: α L = γ 0 C ν α LT ν CP Particle ⇆ Antiparticle C = ⇒ Left-Handed ⇆ Right-Handed P = ⇒ � v � v ν ν ¯ � � S S CP mirror left-handed neutrino right-handed antineutrino C. Giunti − Neutrino Physics – II − MISP 2019 − Moscow − 20-23 Feb 2019 − 7/89

CP � → ν CP � U ∗ α k ν CP Fields: ν α L = U α k ν kL − − α L = kL k k CP � � U ∗ States: | ν α � = α k | ν k � − − → | ¯ ν α � = U α k | ¯ ν k � k k ⇆ U ∗ NEUTRINOS ANTINEUTRINOS U � ∆ m 2 � kj L � U ∗ α k U β k U α j U ∗ P ν α → ν β ( L , E ) = β j exp − i 2 E k , j � ∆ m 2 � kj L � U α k U ∗ β k U ∗ P ¯ ν β ( L , E ) = α j U β j exp − i ν α → ¯ 2 E k , j C. Giunti − Neutrino Physics – II − MISP 2019 − Moscow − 20-23 Feb 2019 − 8/89

CPT Symmetry CPT − − − → P ν α → ν β P ¯ ν β → ¯ ν α A CPT CPT Asymmetries: = P ν α → ν β − P ¯ ν β → ¯ ν α αβ A CPT ⇒ Local Quantum Field Theory = = 0 CPT Symmetry αβ � ∆ m 2 � kj L � U ∗ α k U β k U α j U ∗ − i P ν α → ν β ( L , E ) = β j exp 2 E k , j U ∗ ⇆ ⇆ is invariant under CPT: α β U P ν α → ν β = P ¯ ν β → ¯ ν α P ν α → ν α = P ¯ (solar ν e , reactor ¯ ν e , accelerator ν µ ) ν α → ¯ ν α C. Giunti − Neutrino Physics – II − MISP 2019 − Moscow − 20-23 Feb 2019 − 9/89

CP Symmetry CP − − → P ν α → ν β P ¯ ν α → ¯ ν β CP Asymmetries: A CP αβ = P ν α → ν β − P ¯ ν α → ¯ ν β � ∆ m 2 � kj L � A CP U ∗ α k U β k U α j U ∗ � � αβ ( L , E ) = 4 Im sin β j 2 E k > j U ∗ α k U β k U α j U ∗ � � Jarlskog rephasing invariant: Im = ± J β j J = c 12 s 12 c 23 s 23 c 2 13 s 13 sin δ 13 J � = 0 ⇐ ⇒ ϑ 12 , ϑ 23 , ϑ 13 � = 0 , π/ 2 δ 13 � = 0 , π C. Giunti − Neutrino Physics – II − MISP 2019 − Moscow − 20-23 Feb 2019 − 10/89

0 = A CPT CPT = ⇒ αβ = P ν α → ν β − P ¯ ν β → ¯ ν α ν β ← A CP = P ν α → ν β − P ¯ ν α → ¯ αβ ν β − P ν β → ν α ← − A CPT + P ¯ = 0 ν α → ¯ βα ν α ← A CP + P ν β → ν α − P ¯ ν β → ¯ βα = A CP αβ + A CP A CP αβ = − A CP = ⇒ βα βα C. Giunti − Neutrino Physics – II − MISP 2019 − Moscow − 20-23 Feb 2019 − 11/89

T Symmetry T P ν α → ν β − → P ν β → ν α A T T Asymmetries: αβ = P ν α → ν β − P ν β → ν α 0 = A CPT CPT = ⇒ αβ = P ν α → ν β − P ¯ ν β → ¯ ν α = P ν α → ν β − P ν β → ν α ← A T αβ ν α ← A CP + P ν β → ν α − P ¯ ν β → ¯ βα = A T αβ + A CP βα = A T αβ − A CP A T αβ = A CP = ⇒ αβ αβ C. Giunti − Neutrino Physics – II − MISP 2019 − Moscow − 20-23 Feb 2019 − 12/89

Average over Energy Resolution of the Detector � ∆ m 2 L � ∆ m 2 L � � �� = 1 P ν α → ν β ( L , E ) = sin 2 2 ϑ sin 2 2 sin 2 2 ϑ 1 − cos 4 E 2 E ⇓ � ∆ m 2 L � P ν α → ν β ( L , E ) � = 1 � � � � 2 sin 2 2 ϑ 1 − ( α � = β ) cos φ ( E ) d E 2 E 1 ∆ m 2 = 10 − 3 eV sin 2 2 ϑ = 0 . 8 � E � = 1 GeV σ E = 0 . 1 GeV 0 . 8 0 . 6 P ν α → ν β 0 . 4 0 . 2 0 10 2 10 3 10 4 10 5 [km] L C. Giunti − Neutrino Physics – II − MISP 2019 − Moscow − 20-23 Feb 2019 − 13/89

1.0 0.8 0.6 P ν α →ν β 0.4 0.2 0.0 10 − 2 10 − 1 1 10 E [GeV] ∆ m 2 = 10 − 3 eV sin 2 2 ϑ = 0 . 8 L = 10 3 km σ E = 0 . 01 GeV � ∆ m 2 L � P ν α → ν β ( L , E ) � = 1 � � � � 2 sin 2 2 ϑ 1 − cos φ ( E ) d E ( α � = β ) 2 E C. Giunti − Neutrino Physics – II − MISP 2019 − Moscow − 20-23 Feb 2019 − 14/89

A Brief History of Neutrino Oscillations ◮ 1957: Pontecorvo proposed Neutrino Oscillations in analogy with K 0 ⇆ ¯ K 0 oscillations (Gell-Mann and Pais, 1955) ν ⇆ ¯ = ⇒ ν ◮ In 1957 only one neutrino type ν = ν e was known! The possible existence of ν µ was discussed by several authors. Maybe the first have been Sakata and Inoue in 1946 and Konopinski and Mahmoud in 1953. Maybe Pontecorvo did not know. He discussed the possibility to distinguish ν µ from ν e in 1959. ◮ 1962: Maki, Nakagava, Sakata proposed a model with ν e and ν µ and Neutrino Mixing: “weak neutrinos are not stable due to the occurrence of a virtual transmutation ν e ⇆ ν µ ” ◮ 1962: Lederman, Schwartz and Steinberger discover ν µ ◮ 1967: Pontecorvo: intuitive ν e ⇆ ν µ oscillations with maximal mixing. Applications to reactor and solar neutrinos (“prediction” of the solar neutrino problem). ◮ 1969: Gribov and Pontecorvo: ν e − ν µ mixing and oscillations. But no clear derivation of oscillations with a factor of 2 mistake in the phase (misprint?). C. Giunti − Neutrino Physics – II − MISP 2019 − Moscow − 20-23 Feb 2019 − 15/89

◮ 1975-76: Start of the “Modern Era” of Neutrino Oscillations with a general theory of neutrino mixing and a rigorous derivation of the oscillation probability by Eliezer and Swift, Fritzsch and Minkowski, and Bilenky and Pontecorvo. [Bilenky, Pontecorvo, Phys. Rep. (1978) 225] ◮ 1978: Wolfenstein discovers the effect on neutrino oscillations of the matter potential (“Matter Effect”) ◮ 1985: Mikheev and Smirnov discover the resonant amplification of solar ν e → ν µ oscillations due to the Matter Effect (“MSW Effect”) ◮ 1998: the Super-Kamiokande experiment observed in a model-independent way the Vacuum Oscillations of atmospheric neutrinos ( ν µ → ν τ ). ◮ 2002: the SNO experiment observed in a model-independent way the flavor transitions of solar neutrinos ( ν e → ν µ , ν τ ), mainly due to adiabatic MSW transitions. [see: Smirnov, arXiv:1609.02386] ◮ 2015: Takaaki Kajita (Super-Kamiokande) and Arthur B. McDonald (SNO) received the Physics Nobel Prize “for the discovery of neutrino oscillations, which shows that neutrinos have mass”. C. Giunti − Neutrino Physics – II − MISP 2019 − Moscow − 20-23 Feb 2019 − 16/89