Lecture III: Leptonic Mixing Neutrinos in cosmology Summer School - PowerPoint PPT Presentation

Lecture III: Leptonic Mixing Neutrinos in cosmology Summer School on Particle Physics ICTP , Trieste 6-7 June 2017 Silvia Pascoli IPPP - Durham U. mass 1 @Silvia Pascoli

What will you learn from this lecture? ● The problem of leptonic mixing - Current status - Prospects to discover leptonic CPV and measure with precision the oscillation parameters - How to explain the observed mixing structure and Flavour symmetry models ● Neutrinos in cosmology - neutrinos in the Early Universe - sterile neutrinos as WDM - Leptogenesis and the baryon asymmetry 2

Plan of lecture III ● The problem of leptonic mixing - Current status - Prospects to discover leptonic CPV and measure with precision the oscillation parameters - How to explain the observed mixing structure and Flavour symmetry models ● Neutrinos in cosmology - neutrinos in the Early Universe - sterile neutrinos as WDM - Leptogenesis and the baryon asymmetry 3

Recap of neutrino mixing 360 2.8 8.5 31 2.6 2 2 ] ∆ m ★ 270 8 2 ] 2.4 ★ -5 eV -3 eV 2.2 21 [10 7.5 ★ -2.2 32 [10 180 2 ∆ m -2.4 δ CP 7 2 ∆ m -2.6 90 6.5 0.2 0.25 0.3 0.35 0.4 -2.8 2 θ 12 0.3 0.4 0.5 0.6 0.7 sin 2 θ 23 sin 0 Important aspects: 0.01 0.02 0.03 0.04 2 θ 13 sin - maximal or close to maximal θ 23 NuFit 3.0: M. C. Gonzalez- Garcia et al., 1611.01514 - significantly different from maximal θ 12 See also F. Capozzi et al., - quite large. This poses some θ 13 1703.04471 challenges for understanding the origin of the flavour structure - Mixings very different from quark sector 4 @Silvia Pascoli

Hints of CP-violation Neutrino 2014 Daya Bay results Neutrino 2014 RENO results 2 2.0 NO NO 2.0 300 Normal Hierarchy 2016 results 1.8 1.5 1.5 1 σ 1.6 250 ★ 2 σ 1.4 δ / π 3 σ 200 1.0 1 1.2 1.0 150 0.8 0.5 0.5 100 360 0.6 NO 0.4 50 0.0 0.2 0 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0 0.02 0.04 0.06 270 0.0 0 2 sin 0.01 0.02 0.03 0.04 0.05 0.06 θ ★ 2 θ 13 13 sin 2.0 2.0 D. V. Forero et al., 1405.7540 2 1.8 180 IO Inverted Hierarchy 300 There is a slight 1.6 1.5 δ CP 1.4 250 preference for CP- 1.2 90 1.0 200 1.0 violation, which is 0.8 150 0.6 mainly due to the 0.5 0 0.4 0.01 0.02 0.03 0.04 100 2 θ 13 combination of T2K 0.2 sin 50 0.0 0.0 NuFit 3.0: M. C. Gonzalez- 0.01 0.02 0.03 0.04 0.05 0.06 0.00 0.01 0.02 0.03 0.04 0.05 0.06 a n d r e a c t o r Garcia et al., 1611.01514 2 0 sin θ 13 neutrino data. F. Capozzi et al., 1312.2878 5

1. Different flavour models can lead to specific predictions for the value of the delta phase: sin θ 23 − 1 ● Sum rules: 2 = a 0 + λ sin θ 13 cos δ + higher orders √ ● discrete symmetries models ● charged lepton corrections to : U PMNS = U † U ν e U ν e.g. M.-C. Chen and Mahanthappa; Girardi et al.; Petcov; Alonso, Gavela, Isidori, Maiani; Ding et al.; Ma; Hernandez, Smirnov; Feruglio et al.; Mohapatra, Nishi; Holthausen, Lindner, Schmidt; and others 2. In order to generate dynamically a baryon asymmetry, the Sakharov’s conditions need to be satisfied: Neutrinoless double beta decay - B (or L) violation; LBL - C, CP violation; Expansion of the Universe - departure from thermal equilibrium. Leptogenesis in models of neutrino masses 6

CP-violation in LBL experiments CP-violation will manifest itself in neutrino oscillations, due to the delta phase. The CP-asymmetry: � � P ( ν µ → ν e ; t ) − P (¯ ν µ → ¯ ν e ; t ) = − → · · · ⇥ ∆ m 2 ⇥ ∆ m 2 ⇥ ∆ m 2 ⌅ ⇤ ⇤ ⇤⇧ 21 L 23 L 31 L = 4 s 12 c 12 s 13 c 2 13 s 23 c 23 sin δ sin + sin + sin 2 E 2 E 2 E ● CP-violation requires all angles to be nonzero. ● It is proportional to the sin of the delta phase. ● If one can neglects , the asymmetry goes to zero: ∆ m 2 21 effective 2-neutrino probabilities are CP-symmetric. 7

CPV needs to be searched for in long baseline neutrino experiments which have access to 3-neutrino oscillations. A. Cervera et al., hep-ph/0002108; (1 � r A ) 2 sin 2 (1 � r A ) ∆ 31 L 1 K. Asano, H. Minakata, 1103.4387; P µe ' 4 c 2 23 s 2 13 S. K. Agarwalla et al., 1302.6773... 4 E sin (1 � r A ) ∆ 31 L ✓ ◆ ∆ 21 L δ � ∆ 31 L + sin 2 θ 12 sin 2 θ 23 s 13 cos 2 E 4 E 4 E ∆ 2 21 L 2 13 sin 2 (1 � r A ) ∆ 31 L 23 sin 2 2 θ 12 + s 2 16 E 2 � 4 c 2 23 s 4 4 E ● The CP asymmetry peaks for 6 � 10 � 2 sin^2 2 theta13 ~0.001. Large 10 3 4 � 10 � 2 Atmospheric Solar theta13 makes its searches 10 3 2 � 10 � 2 Solar Atmospheric 0 P 0 possible but not ideal. 10 3 � 2 � 10 � 2 1˚ Interference Θ 13 � 10˚ CP Interference ● Crucial to know mass ordering. 10 3 � 4 � 10 � 2 ● CPV effects more pronounced at 10 3 � 6 � 10 � 2 0 500 1000 1500 0 500 1000 1500 2000 low energy. L � E � km � GeV � P . Coloma, E. Fernandez-Martinez, JHEP1204 8 ●

CPV Searches Category Experiment Status Oscillation parameters Accelerator MINOS+ [74] Data-taking MH/CP/octant Accelerator T2K [21] Data-taking MH/CP/octant Near future: T2K Accelerator NOvA [108] Commissioning MH/CP/octant and NOvA. Some Accelerator RADAR [76] Design/ R&D MH/CP/octant Accelerator CHIPS [75] Design/ R&D MH/CP/octant sensitivity to CPV Accelerator LBNE [87] Design/ R&D MH/CP/octant Accelerator Hyper-K [97] Design/ R&D MH/CP/octant Accelerator LBNO [109] Design/ R&D MH/CP/octant Accelerator ESS ν SB [110] Design/ R&D MH/CP/octant Accelerator DAE δ ALUS [111] Design/ R&D CP T2K WG Report: Neutrinos, de Gouvea (Convener) et al., 1310.4340 60 CP Violation at 95% C.L. Coverage “NOvAplus” 50 CP � Percent NOvA 40 12 12 30 T2K(3+2) T2K(3+2)+NO ν A(3+3) T2K(5+0) T2K(5+0)+NO ν A(3+3) True NH, θ µµ = 39 o True NH, θ µµ = 39 o 10 10 T2K 20 8 8 M. Gosh et al., Normal hierarchy χ 2 χ 2 6 6 Inverted Hierarchy 1401.7243; see 10 also Machado 4 4 et al.; Huber et 2 2 0 al. 0 1 2 3 4 5 NOvA Exposure / Baseline 0 0 -180 -120 -60 0 60 120 180 -180 -120 -60 0 60 120 180 NOvA Coll., 1308.0106 9 δ CP (True) δ CP (True)

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Plan of lecture III ● The problem of leptonic mixing - Current status - Prospects to discover leptonic CPV and measure with precision the oscillation parameters - How to explain the observed mixing structure and Flavour symmetry models ● Neutrinos in cosmology - neutrinos in the Early Universe - sterile neutrinos as WDM - Leptogenesis and the baryon asymmetry 11

Masses and mixing from the mass matrix Neutrino masses and the mixing matrix arises from the diagonalisation of the mass matrix M M = ( U † ) T m diag U † n L = U † ν L Experiments Theory Example . In the diagonal basis for the leptons ✓ a ◆ b M ν = b c 2 b the angle is tan 2 θ = a � c � 1 for a ⇠ c and, or a, c ⌧ b m 1 , 2 ' a + c ± 2 b and masses 2 12

In a model of flavour, both the mass matrix for leptons and neutrinos will be predicted and need to be diagonalised:     e 0 ν eL R ν c ν c ν c e 0 µ 0 τ 0 (¯ eL , ¯ µL , ¯ τ L ) M ν (¯ L , ¯ L , ¯ L ) M ` µ 0 ν µL     R τ 0 ν τ L R     e 0 ν eL R L ) V L V † L M ` V R V † ν c ν c ν c ν U T ν M ν U ν U † e 0 µ 0 τ 0 (¯ L , ¯ L , ¯ µ 0 (¯ eL , ¯ µL , ¯ τ L ) U ∗ ν µL     R R ν τ 0 ν τ L R     ν 1 L e R ν c ν c ν c (¯ 1 L , ¯ 2 L , ¯ 3 L ) M diag , ν (¯ e L , ¯ µ L , ¯ τ L ) M diag ν 2 L µ R     ν 3 L τ R 13 @Silvia Pascoli

In a model of flavour, both the mass matrix for leptons and neutrinos will be predicted and need to be diagonalised:     e 0 ν eL R ν c ν c ν c e 0 µ 0 τ 0 (¯ eL , ¯ µL , ¯ τ L ) M ν (¯ L , ¯ L , ¯ L ) M ` µ 0 ν µL     R τ 0 ν τ L R     e 0 ν eL R L ) V L V † L M ` V R V † ν c ν c ν c ν U T ν M ν U ν U † e 0 µ 0 τ 0 (¯ L , ¯ L , ¯ µ 0 (¯ eL , ¯ µL , ¯ τ L ) U ∗ ν µL     R R ν τ 0 ν τ L R     ν 1 L e R ν c ν c ν c (¯ 1 L , ¯ 2 L , ¯ 3 L ) M diag , ν (¯ e L , ¯ µ L , ¯ τ L ) M diag ν 2 L µ R     ν 3 L τ R in the CC interactions (and oscillations):     ν 1 L ν eL g g τ L ) γ µ U osc  W µ L ) γ µ  W µ ⇒ e 0 µ 0 τ 0 2(¯ e L , ¯ µ L , ¯ L CC = 2(¯ L , ¯ L , ¯ √ ν µL ν 2 L   √ ν τ L ν 3 L U osc = V † L U ν 14 @Silvia Pascoli

Phenomenological approaches Various strategies and ideas can be employed to understand the observed pattern (many many models!). - Mixing related to mass ratios θ 12 , 23 , 13 = function( m e , . . . , m 1 ) m µ m 2 too small - Flavour symmetries - Complementarity between quarks and leptons θ 12 + θ C ' 45 o - Anarchy (all elements of the matrix of the same order). 15 @Silvia Pascoli