Phenomenology of Light Sterile Neutrinos Carlo Giunti INFN, Sezione - PowerPoint PPT Presentation

Phenomenology of Light Sterile Neutrinos Carlo Giunti INFN, Sezione di Torino, and Dipartimento di Fisica, Universit` a di Torino mailto://giunti@to.infn.it Neutrino Unbound: http://www.nu.to.infn.it Technische Universit¨ at M¨ unchen Garching, M¨ unchen, Germany 11 December 2013 C. Giunti − Phenomenology of Light Sterile Neutrinos − TUM − 11 Dec 2013 − 1/38

Fermion Mass Spectrum 10 12 t 10 11 10 10 b c τ 10 9 s 10 8 µ ν τ d 10 7 u m [eV] 10 6 ν µ e 10 5 10 4 10 3 10 2 10 ν e ν 1 , ν 2 , ν 3 1 10 − 1 C. Giunti − Phenomenology of Light Sterile Neutrinos − TUM − 11 Dec 2013 − 2/38

Neutrino Oscillations ◮ 1957: Bruno Pontecorvo proposed Neutrino Oscillations in analogy with K 0 ⇆ ¯ K 0 oscillations (Gell-Mann and Pais, 1955) ◮ Flavor Neutrinos: ν e , ν µ , ν τ produced in Weak Interactions ◮ Massive Neutrinos: ν 1 , ν 2 , ν 3 propagate from Source to Detector ◮ A Flavor Neutrino is a superposition of Massive Neutrinos | ν e � = U e 1 | ν 1 � + U e 2 | ν 2 � + U e 3 | ν 3 � | ν µ � = U µ 1 | ν 1 � + U µ 2 | ν 2 � + U µ 3 | ν 3 � | ν τ � = U τ 1 | ν 1 � + U τ 2 | ν 2 � + U τ 3 | ν 3 � ◮ U is the 3 × 3 Neutrino Mixing Matrix C. Giunti − Phenomenology of Light Sterile Neutrinos − TUM − 11 Dec 2013 − 3/38

| ν ( t = 0) � = | ν e � = U e 1 | ν 1 � + U e 2 | ν 2 � + U e 3 | ν 3 � ν 1 ν e ν µ ν 2 ν 3 propagation source detector | ν ( t > 0) � = U e 1 e − iE 1 t | ν 1 � + U e 2 e − iE 2 t | ν 2 � + U e 3 e − iE 3 t | ν 3 �� = | ν e � k = p 2 + m 2 E 2 k at the detector there is a probability > 0 to see the neutrino as a ν µ Neutrino Oscillations are Flavor Transitions ν e → ν µ ν e → ν τ ν µ → ν e ν µ → ν τ ¯ ν e → ¯ ν µ ¯ ν e → ¯ ν τ ν µ → ¯ ¯ ν e ν µ → ¯ ¯ ν τ transition probabilities depend on U and ∆ m 2 kj ≡ m 2 k − m 2 j C. Giunti − Phenomenology of Light Sterile Neutrinos − TUM − 11 Dec 2013 − 4/38

Two-Neutrino Mixing and Oscillations ν 2 ν µ 2 � | ν α � = U α k | ν k � ( α = e , µ ) ν e k =1 ϑ ν 1 � cos ϑ � sin ϑ | ν e � = cos ϑ | ν 1 � + sin ϑ | ν 2 � U = − sin ϑ cos ϑ | ν µ � = − sin ϑ | ν 1 � + cos ϑ | ν 2 � ∆ m 2 ≡ ∆ m 2 21 ≡ m 2 2 − m 2 1 � ∆ m 2 L � P ν e → ν µ = P ν µ → ν e = sin 2 2 ϑ sin 2 Transition Probability: 4 E Survival Probabilities: P ν e → ν e = P ν µ → ν µ = 1 − P ν e → ν µ C. Giunti − Phenomenology of Light Sterile Neutrinos − TUM − 11 Dec 2013 − 5/38

Experimental Evidences of Neutrino Oscillations    SNO, BOREXino   Solar Super-Kamiokande  S ≃ 7 . 6 × 10 − 5 eV 2     ∆ m 2     ν e → ν µ , ν τ GALLEX/GNO, SAGE     → sin 2 ϑ S ≃ 0 . 30 Homestake, Kamiokande    VLBL Reactor    (KamLAND)  ν e disappearance ¯     Super-Kamiokande Atmospheric   Kamiokande, IMB    ν µ → ν τ   A ≃ 2 . 4 × 10 − 3 eV 2   ∆ m 2 MACRO, Soudan-2     LBL Accelerator → (K2K, MINOS, T2K) sin 2 ϑ A ≃ 0 . 50 ν µ disappearance       LBL Accelerator   (Opera)   ν µ → ν τ LBL Accelerator   ∆ m 2 (T2K, MINOS)  ν µ → ν e  A   → � � sin 2 ϑ 13 ≃ 0 . 023 LBL Reactor Daya Bay, RENO    ν e disappearance ¯  Double Chooz C. Giunti − Phenomenology of Light Sterile Neutrinos − TUM − 11 Dec 2013 − 6/38

Three-Neutrino Mixing Paradigm ν e ν µ ν τ m 2 m 2 ν 3 ν 2 ∆ m 2 S ν 1 ∆ m 2 ∆ m 2 A A ν 2 ∆ m 2 S ν 1 ν 3 Normal Spectrum Inverted Spectrum 21 = 7 . 50 ± 0 . 20 × 10 − 5 eV 2 ∆ m 2 S = ∆ m 2 uncertainty ≃ 2 . 6% − 0 . 08 × 10 − 3 eV 2 ∆ m 2 A = | ∆ m 2 31 | ≃ | ∆ m 2 32 | = 2 . 32 +0 . 12 uncertainty ≃ 5% C. Giunti − Phenomenology of Light Sterile Neutrinos − TUM − 11 Dec 2013 − 7/38

    s 13 e − i δ 13 1 0 0 c 12 c 13 s 12 c 13 U =     − 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 2 s 23 c 13 0         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 3 0 0 c 23 c 13         1 0 0 0 s 13 e − i δ 13 c 13 c 12 s 12 0 1 0 0   =       0 e i λ 2 0 c 23 s 23 0 1 0 − s 12 c 12 0 0             0 − s 23 c 23 − s 13 e i δ 13 0 e i λ 3 c 13 0 0 1 0 0 ββ 0 ν ϑ 23 = ϑ A Chooz, Palo Verde ϑ 12 = ϑ S sin 2 ϑ 23 ≃ 0 . 4 − 0 . 6 sin 2 ϑ 12 = 0 . 30 ± 0 . 01 T2K, MINOS Daya Bay, RENO sin 2 ϑ 13 = 0 . 023 ± 0 . 002 δ sin 2 ϑ 23 δ sin 2 ϑ 13 δ sin 2 ϑ 12 ≃ 40% ≃ 10% ≃ 5% sin 2 ϑ 23 sin 2 ϑ 13 sin 2 ϑ 12 C. Giunti − Phenomenology of Light Sterile Neutrinos − TUM − 11 Dec 2013 − 8/38

Open Problems ◮ ϑ 23 ⋚ 45 ◦ ? ◮ Atmospheric ν , T2K, NO ν A, . . . . . . ◮ Mass Hierarchy ? ◮ NO ν A, Atmospheric ν , Day Bay II, RENO-50, Supernova ν , . . . ◮ CP violation ? ◮ NO ν A, LAGUNA-LBNO, LBNE (USA), HyperK, . . . ◮ Absolute Mass Scale ? ◮ β Decay, Neutrinoless Double- β Decay, Cosmology, . . . ◮ Dirac or Majorana ? ◮ Neutrinoless Double- β Decay, . . . ◮ Beyond Three-Neutrino Mixing ? Sterile Neutrinos ? C. Giunti − Phenomenology of Light Sterile Neutrinos − TUM − 11 Dec 2013 − 9/38

Absolute Scale of Neutrino Masses Normal Spectrum Inverted Spectrum Quasi−Degenerate Quasi−Degenerate m 3 m 2 1 1 m 1 m 2 m 1 m 3 m 1 , m 2 , m 3 [eV] m 3 , m 1 , m 2 [eV] 10 − 1 10 − 1 m 2 ∆ m A 2 ∆ m A 2 95% Cosmological Limit 95% KATRIN Sensitivity 95% Cosmological Limit 95% KATRIN Sensitivity m 3 m 1 95% Kinematical Limit 95% Kinematical Limit 10 − 2 10 − 2 ∆ m S 2 m 2 m 1 m 3 Normal Hierarchy Inverted Hierarchy 10 − 3 10 − 3 10 − 3 10 − 2 10 − 1 10 − 3 10 − 2 10 − 1 1 1 Lightest mass: m 1 [eV] Lightest mass: m 3 [eV] m 2 2 = m 2 1 + ∆ m 2 21 = m 2 1 + ∆ m 2 m 2 1 = m 2 3 − ∆ m 2 31 = m 2 3 + ∆ m 2 S A m 2 3 = m 2 1 + ∆ m 2 31 = m 2 1 + ∆ m 2 m 2 2 = m 2 1 + ∆ m 2 21 ≃ m 2 3 + ∆ m 2 A A � A ≃ 5 × 10 − 2 eV Quasi-Degenerate for m 1 ≃ m 2 ≃ m 3 ≃ m ν � ∆ m 2 95% Cosmological Limit: Planck + WMAP9 + highL + BAO [arXiv:1303.5076] C. Giunti − Phenomenology of Light Sterile Neutrinos − TUM − 11 Dec 2013 − 10/38

Effective Neutrino Mass in Beta-Decay β = | U e 1 | 2 m 2 1 + | U e 2 | 2 m 2 2 + | U e 3 | 2 m 2 m 2 3 10 ◮ Quasi-Degenerate: � k | U ek | 2 = m 2 Current 95% Bound m 2 β ≃ m 2 ν ν 1 ◮ Inverted Hierarchy: m 2 β ≃ (1 − s 2 13 )∆ m 2 A ≃ ∆ m 2 KATRIN 95% Sensitivity A m β [eV] 10 − 1 IS 95% Cosmological Limit ◮ Normal Hierarchy: ∆ m A 2 m 2 β ≃ s 2 12 c 2 13 ∆ m 2 S + s 2 13 ∆ m 2 A ≃ 2 × 10 − 5 + 6 × 10 − 5 eV 2 10 − 2 NS 1 σ ◮ m β � 4 × 10 − 2 eV 2 σ 3 σ ⇓ 10 − 3 10 − 3 10 − 2 10 − 1 1 10 Normal Spectrum m min [eV] C. Giunti − Phenomenology of Light Sterile Neutrinos − TUM − 11 Dec 2013 − 11/38

Majorana ν : Neutrinoless Double-Beta Decay Arsenic 1 / 2 ) − 1 = G 0 ν |M 0 ν | 2 m 2 ( T 0 ν ββ 76 β + 33 As Germanium β − Effective Majorana Mass 76 32 Ge � � � � 3 � � � β − β − U 2 m ββ = � ek m k � Selenium � � k =1 76 34 Se EXO + KamLAND-Zen 56 Ba + e − + e − 136 54 Xe → 136 d u W � [PRL 109 (2012) 032505; PRL 110 (2013) 062502] e U ek | m ββ | � 0 . 12 − 0 . 25 eV (90%C.L.) m � k k GERDA 34 Se + e − + e − 76 32 Ge → 76 U ek � e [arXiv:1307.4720] W | m ββ | � 0 . 2 − 0 . 6 eV (90%C.L.) d u C. Giunti − Phenomenology of Light Sterile Neutrinos − TUM − 11 Dec 2013 − 12/38

Effective Majorana Neutrino Mass m ββ = | U e 1 | 2 m 1 + | U e 2 | 2 e i α 2 m 2 + | U e 3 | 2 e i α 3 m 3 1 90% GERDA ◮ Quasi-Degenerate: � 90% EXO+KLZ 10 − 1 1 − s 2 2 ϑ 12 s 2 | m ββ | ≃ m ν α 2 IS ◮ Inverted Hierarchy: |m ββ | [eV] 95% Cosmological Limit � 10 − 2 ∆ m 2 A (1 − s 2 2 ϑ 12 s 2 | m ββ | ≃ α 2 ) ◮ Normal Hierarchy: NS 10 − 3 | m ββ | ≃ | s 2 S + e i α s 2 � ∆ m 2 � ∆ m 2 A | 12 13 ≃ | 2 . 7 + 1 . 2 e i α | × 10 − 3 eV 1 σ 2 σ m 1 � 10 − 3 eV ⇒ cancellation? 3 σ 10 − 4 10 − 4 10 − 3 10 − 2 10 − 1 1 m min [eV] | m ββ | � 10 − 2 eV = ⇒ Normal Spectrum C. Giunti − Phenomenology of Light Sterile Neutrinos − TUM − 11 Dec 2013 − 13/38

Beyond Three-Neutrino Mixing: Sterile Neutrinos · · · ν s 1 ν s 2 ν τ ν µ ν e · · · ν 1 ν 2 ν 3 ν 4 ν 5 m 2 m 2 m 2 m 2 m 2 log m 2 1 2 3 4 5 ∆ m 2 ∆ m 2 ∆ m 2 SOL ATM SBL 3 ν -mixing C. Giunti − Phenomenology of Light Sterile Neutrinos − TUM − 11 Dec 2013 − 14/38