Right-handed Currents in Single and Double Beta Decay v Werner - PowerPoint PPT Presentation

Right-handed Currents in Single and Double Beta Decay v Werner Rodejohann m v = m L - m D M -1 m D T R NDM 2015 MANITOP 03/06/15 Massive Neutrinos: Investigating their Theoretical Origin and Phenomenology 1

Left-right Symmetry very simple extension of SM gauge group to SU (2) L × SU (2) R × U (1) B − L usual particle content:      ν ′  ν R L L Li = ∼ ( 2 , 1 , − 1 ) , L Ri = ∼ ( 1 , 2 , − 1 )   ℓ L ℓ R i i      u L  u R ∼ ( 2 , 1 , 1 ∼ ( 1 , 2 , 1 Q Li = 3 ) , Q Ri = 3 )   d L d R i i for symmetry breaking: √ √      δ + δ ++  δ + δ ++ L / 2 R / 2 L R  ∼ ( 3 , 1 , 2 ) ,  ∼ ( 1 , 3 , 2 ) ∆ L ≡ ∆ R ≡ √ √ − δ + − δ + δ 0 δ 0 L / 2 R / 2 L R   φ +  φ 0 1 2  ∼ ( 2 , 2 , 0 ) φ ≡ φ − φ 0 1 2 2

Left-right Symmetry • very rich Higgs sector (13 extra scalars) • rich gauge boson sector ( Z ′ , M W ± R ) with � 1 − tan 2 θ W M W R ≃ 1 . 7 M W R > 2 M Z ′ = ∼ 4 . 3 TeV • ’sterile’ neutrinos ν R • type I + type II seesaw for neutrino mass � 2 � � 2 � g R m W • right-handed currents with strength G F g L M WR • m ν ∝ 1 /M W R : maximal parity violation ↔ smallness of neutrino mass (Note: in case of modified symmetry breaking gL � = gR and MZ ′ < MWR possible . . . ) 3

Left-right Symmetry L and mass states n L = ( ν L , N c R ) T 6 neutrinos with flavor states n ′          ν ′  K L  U S  ν L L  =  n L = n ′ L =   ν Rc N c K R T V R Right-handed currents: g L lep ℓ L γ µ K L n L ( W − 1 µ + ξe iα W − 2 µ ) + ℓ R γ µ K R n c L ( − ξe − iα W − 1 µ + W − � � CC = √ 2 µ ) 2 ( K L and K R are 3 × 6 mixing matrices) plus: gauge boson mixing        W ±  W ± sin ξ e iα cos ξ 1 L  =    W ± W ± − sin ξ e − iα cos ξ 2 R 4

Connection to Neutrinos Majorana mass matrices M L = f L v L from � ∆ L � and M R = f R v R from � ∆ R � (with f L = f R = f )     c  ν ′  M L M D � c � L L ν  ⇒ m ν = M L − M D M − 1 R M T mass = − 1 ν ′ L ν ′  D 2 R M T ν ′ M R D R useful special cases (i) type I dominance: m ν = M D M − 1 D = M D f − 1 R M T R /v R M T D (ii) type II dominance: m ν = f L v L for case (i): mixing of light neutrinos with heavy neutrinos of order � 1 / 2 � m ν � TeV < | S αi | ≃ | T T ∼ 10 − 7 αi | ≃ M i M i small (or enhanced up to 10 − 2 by cancellations) 5

Right-handed Currents in Double Beta Decay ( A, Z ) → ( A, Z + 2) + 2 e − 3 g L lep � e L γ µ ( U ei ν Li + S ei N c Ri )( W − 1 µ + ξe iα W − � CC = √ 2 µ ) 2 i =1 + e R γ µ ( T ∗ ei ν c Li + V ∗ ei N Ri )( − ξe − iα W − 1 µ + W − � 2 µ ) ′ c ′ c L ℓ L iσ 2 ∆ L f L L ′ R iσ 2 ∆ R f R L ′ Y = − L L − L R classify diagrams: • mass dependent diagrams (same helicity of electrons) • triplet exchange diagrams (same helicity of electrons) • momentum dependent diagrams (different helicity of electrons) 6

Mass Dependent Diagrams electrons either both left- or right-handed: � U 2 − S 2 � ei m i A LL ≃ G 2 1 + 2 tan ξ + tan 2 ξ � � � ei F i q 2 M i � � � m 4 m 2 T ∗ − V ∗ � 2 m i 2 � WR tan ξ + tan 2 ξ A RR ≃ G 2 WL WL WR + 2 ei ei F i M 4 M 2 q 2 M i leading diagrams: d L u L d R u R W R W U ei e − e − L R ν i q N Ri ν i e − e − L R U ei W R W u L u R d L d R � m WL � 4 � F m ee V ∗ 2 A ν ≃ G 2 A R N R ≃ G 2 ei F q 2 i M WR M i ∝ L 2 ∝ L 4 R R 5 7

Triplet Exchange Diagrams leading diagrams: d L u L d R u R e − e − L R W L W R √ √ 2 g 2 v L h ee 2 g 2 v R h ee δ −− δ −− L R W L W R e − e − L R u L u R d L d R � m WL � 4 � V 2 ei M i h ee v L A δ L ≃ G 2 A δ R ≃ G 2 F m 2 F i m 2 M WR δL δR ∝ L 4 (negligible) R 5 8

Momentum Dependent Diagrams electrons with opposite helicity � m 2 + tan ξ + m 2 � � � � 1 q W L W L A LR ≃ G 2 tan ξ + tan 2 ξ U ei T ∗ q − S ei V ∗ F ei ei M 2 M 2 M 2 W R W R i i leading diagrams (long range): u L u L d L d L W L W L e − e − L L ν L ν L N R N R N R N R e − e − R R W R W R W L u R u L d R d L � m WL � 2 � 1 1 A λ ≃ G 2 i U ei T ∗ A η ≃ G 2 i U ei T ∗ F tan ξ � F ei ei M WR q q L 3 L 3 ∝ ∝ R 3 q R 3 q 9

Limits Γ 0 ν = G x ( Q, Z ) |M x ( A, Z ) η x | 2 Xe-limit is stronger than Ge-limit when: 2 � � G Ge M Ge � � T Xe > T Ge yrs � � G Xe M Xe � � 26 10 IBM (M-S) QRPA (CCM) Ge Combined 76 Ge] (yrs) GERDA HM 25 10 T 1/2 [ KamLAND-Zen Xe Combined EXO 24 10 24 25 26 10 10 10 136 Xe] (yrs) T 1/2 [ Barry , W . R ., JHEP 1309 GERDA 10

Current Limits on | m ee | 76 Ge 136 Xe NME GERDA comb KLZ comb EDF(U) 0.32 0.27 0.13 – ISM(U) 0.52 0.44 0.24 – IBM-2 0.27 0.23 0.16 – pnQRPA(U) 0.28 0.24 0.17 – SRQRPA-A 0.31 0.26 0.23 – QRPA-A 0.28 0.24 0.25 – SkM-HFB-QRPA 0.29 0.24 0.28 – GERDA Bhupal Dev, Goswami, Mitra, W.R., Phys. Rev. D88 11

mechanism amplitude current limit G 2 F � � � U 2 light neutrino exchange ( A ν ) 0.3 eV ei m i � q 2 S 2 � � 7 . 4 × 10 − 9 GeV − 1 ei heavy neutrino exchange ( A L G 2 � � N R ) � � F M i � � � � 2 V ∗ � � 1 . 7 × 10 − 16 GeV − 5 ei heavy neutrino exchange ( A R G 2 F m 4 N R ) � � W L M i M 4 � � W R � � � � V 2 ei M i � � 1 . 7 × 10 − 16 GeV − 5 G 2 F m 4 Higgs triplet exchange ( A δ R ) � � W L m 2 δ R M 4 � � W R � � � � m 2 U ei T ∗ � � 8 . 8 × 10 − 11 GeV − 2 W L ei G 2 λ -mechanism ( A λ ) � � F q M 2 � � W R � � 1 G 2 � � 3 . 0 × 10 − 9 � tan ξ � η -mechanism ( A η ) i U ei T ∗ � F ei q 12

Type II dominance ( Senjanovic et al. , 1011.3522 ) D = v L f − v 2 Y D f − 1 Y T ∗ m ν = M L − M D M − 1 R M T − → v L f D v R ⇒ m ν fixes M R = fv R and exchange of N R with W R fixed in terms of PMNS: � m W � 4 � V 2 � U 2 ⇒ A N R ≃ G 2 ei ei ∝ F M W R M i m i ∗ (for leptogenesis: Joshipura, Paschos, W.R., JHEP 0108 ) 13

Constraints from Lepton Flavor Violation e + d R u R R e − h eµ µ − R W R R √ 2 g 2 v R h ee δ −− R δ −− R e − W R R e − R h ee e − u R d R R 14

Constraints from Lepton Flavor Violation e + d R u R R e − µ − h eµ R W R R √ 2 g 2 v R h ee δ −− R δ −− R e − W R R e − R h ee e − u R d R R m δ R = 3.5 TeV Normal Inverted Normal Inverted m δ R = 3.5 TeV m δ R = 2 TeV 30 10 32 m δ R = 2 TeV 10 m δ R = 1 TeV m δ R = 1 TeV 30 10 [T 1/2 ] N R (yrs) 28 [T 1/2 ] ν (yrs) 10 GERDA 1T 28 10 GERDA 1T GERDA 40kg 26 10 GERDA 40kg 26 10 Excluded by KamLAND-Zen Excluded by KamLAND-Zen 0.0001 0.001 0.01 0.1 0.0001 0.001 0.01 0.1 0.0001 0.001 0.01 0.1 0.0001 0.001 0.01 0.1 m light (eV) m light (eV) Barry, W.R., JHEP 1309 15

Adding diagrams d R u R d L u L W R W U ei e − e − R L ν i q N Ri ν i e − e − R L U ei W R W u R u L d R d L ⇒ lower bound on m (lightest) > ∼ meV Bhupal Dev, Goswami, Mitra, W.R., PR D88 16

LHC Tests d R u R W R e − − e R R e − d R u R ¯ R N Ri e − N Ri W R W R R W R u R d R ¯ u R d R Senjanovic, Keung, 1983 17

d R u R W R − e − e R e − R R d R u R ¯ N Ri e − R N Ri W R W R W R u R ¯ d R u R d R Bhupal Dev, Goswami, Mitra, W.R., PR D88 18

Type I Dominance: Mixed Diagrams can dominate u L d L d R u R W L W R e − L ν L e − R N R N Ri e − N R R e − R W R W R u R u R d R d R � m W � m W � 2 U T � 4 V 2 A λ ∼ A N R ∼ M W R q M W R M R M R ∼ 10 − 7 (or huge enhancements up to 10 − 2 ) � m ν with T ≃ � 2 ⇒ A λ ≃ M R � M W R T ≃ 10 5 ( → 3) T A N R q m W Barry, W.R., JHEP 1309 19

Type I Dominance: Mixed Diagrams can dominate d L u L d R u R W L W R e − L ν L e − R N R N Ri N R e − R e − R W R W R u R u R d R d R Normal Inverted N R (L) / ν λ/ν 1000 [T 1/2 ] k / [T 1/2 ] ν 1 0.001 1e-06 0.001 0.01 0.001 0.01 m light (eV) Barry, W.R., JHEP 1309 (tests with SuperNEMO and e − e − colliders) 20

KATRIN and right-handed currents u R u L u R u L W − W − R L W − e − e − e − W − R e − L L R R W − W − L L R d R d L d R d L U ei ν ′ ν ′ ν ′ ν Li L R R • left-handed contribution • right-handed contribution • interference contribution Neutrino masses up to m = 18 . 6 keV testable 21

] Imprint of keV neutrinos on ß-spectrum � � � � � � � � � � � cos sin � � � � � � light e � � � � � � � � � � � sin cos � � � � � � heavy s � � light heavy sin 2 � cos 2 � ( ) ( ) + Susanne Mertens 12 Mertens et al. , 1409.0920 22

] Imprint of keV neutrinos on ß-spectrum sin 2 � ( ) keV neutrino m � heavy Susanne Mertens 1 3 Mertens et al. , 1409.0920 23

(i) energy resolving detector (differential) or (ii) counting detector (integral) or (iii) time-of-flight 24