Neutrinoless Double Beta Decay v Werner Rodejohann m v = m L - m D M -1 m D T R XVIII LNF Spring School MANITOP May 2016 Massive Neutrinos: Investigating their Theoretical Origin and Phenomenology 1
Contents III) Neutrinoless double beta decay: non-standard interpretations III1) Basics III2) Left-right symmetry III3) SUSY III4) The inverse problem 2
Interpretation of Experiments Master formula: Γ 0 ν = G x ( Q, Z ) |M x ( A, Z ) η x | 2 • G x ( Q, Z ) : phase space factor • M x ( A, Z ) : nuclear physics • η x : particle physics 3
Interpretation of Experiments Master formula: Γ 0 ν = G x ( Q, Z ) |M x ( A, Z ) η x | 2 • G x ( Q, Z ) : phase space factor, typically Q 5 • M x ( A, Z ) : nuclear physics; factor 2-3 uncertainty • η x : particle physics; many possibilities 4
Contents III) Neutrinoless double beta decay: non-standard interpretations III1) Basics III2) Left-right symmetry III3) SUSY III4) The inverse problem 5
III1) Basics • Standard Interpretation: Neutrinoless Double Beta Decay is mediated by light and massive Majorana neutrinos (the ones which oscillate) and all other mechanisms potentially leading to 0 νββ give negligible or no contribution • Non-Standard Interpretations: There is at least one other mechanism leading to Neutrinoless Double Beta Decay and its contribution is at least of the same order as the light neutrino exchange mechanism 6
• Standard Interpretation: d L u L W U ei e − L ν i q ν i e − L U ei W u L d L • Non-Standard Interpretations: u L u L d L d L u L d L u L e − d c L d c W L W e − e − ˜ L e − ˜ u L d R L L e − W χ/ ˜ g L ν L u L χ 0 χ/ ˜ g N R √ h ee 2 g 2 v L χ/ ˜ g ∆ −− χ 0 u L N R χ/ ˜ g e − W R e − u L ˜ W R e − L e − L W L d c W L ˜ d R d c u L u L u L e − u L d L d L d L L 7
Non-Standard Interpretations clear experimental signature: KATRIN (or cosmology) sees nothing but “ | m ee | > 0 . 5 eV” 0 νββ decoupled from cosmology limits on neutrino mass! 8
Energy Scale: • standard amplitude for light Majorana neutrino exchange: � | m ee | | m ee | � GeV − 5 ≃ (2 . 7 TeV) − 5 A l ≃ G 2 ≃ 7 × 10 − 18 F q 2 0 . 5 eV • 9
Energy Scale: • standard amplitude for light Majorana neutrino exchange: � | m ee | � | m ee | GeV − 5 ≃ (2 . 7 TeV) − 5 A l ≃ G 2 ≃ 7 × 10 − 18 F q 2 0 . 5 eV • if new heavy particles are exchanged: c A h ≃ M 5 10
Energy Scale: • standard amplitude for light Majorana neutrino exchange: � | m ee | | m ee | � GeV − 5 ≃ (2 . 7 TeV) − 5 A l ≃ G 2 ≃ 7 × 10 − 18 F q 2 0 . 5 eV • if new heavy particles are exchanged: c A h ≃ M 5 ⇒ for 0 νββ holds: 1 eV = 1 TeV ⇒ Phenomenology in colliders, LFV 11
Schechter-Valle theorem : observation of 0 νββ implies Majorana neutrinos W W d d u u ν e ν e e − e − G 2 (16 π 2 ) 4 MeV 5 ∼ 10 − 25 eV is 4 loop diagram: m BB F ∼ ν explicit calculation: Duerr, Lindner, Merle, 1105.0901 12
mechanism physics parameter current limit test oscillations, � � � U2 light neutrino exchange 0.5 eV ei mi cosmology, � � � neutrino mass S2 � � LFV, 2 × 10 − 8 GeV − 1 � � ei heavy neutrino exchange � � Mi � � collider � � � � V2 flavor, � � 4 × 10 − 16 GeV − 5 ei � � heavy neutrino and RHC � � Mi M4 collider � � WR � � flavor, � � � � ( MR ) ee 10 − 15 GeV − 1 � � Higgs triplet and RHC collider � � m2 M4 � � e − distribution ∆R WR � � flavor, � � Uei ˜ � � Sei 1 . 4 × 10 − 10 GeV − 2 λ -mechanism with RHC � � collider, � � M2 � � e − distribution WR � � flavor, � � 6 × 10 − 9 � Uei ˜ η -mechanism with RHC tan ζ Sei collider, � � � e − distribution � λ ′ 2 � � � � 111 � collider, Λ5 7 × 10 − 18 GeV − 5 short-range / R SUSY flavor Λ SUSY = f ( m˜ g , m˜ uL , m˜ , m χ i ) dR � � � � � sin 2 θ b λ ′ 131 λ ′ � 1 1 2 × 10 − 13 GeV − 2 − � � 113 m2 m2 � � flavor, � � ˜ ˜ long-range / b1 b2 R � � � � collider � λ ′ 131 λ ′ � � 1 × 10 − 14 GeV − 3 ∼ GF 113 � mb Λ3 q SUSY spectrum, 10 − 4 . . . 1 |� g χ �| or |� g χ �| 2 Majorons cosmology 13
Some features • Majoranas and no RHC: rate for q 2 ≫ m 2 m � q m m A ∝ q 2 − m 2 → 1 � m² for q 2 ≪ m 2 � 1 � m² m mass Note: maximum A corresponds to m ≃ � q � : limits on O ( m K ) Majorana neutrinos from K + → π − µ + e + • heavy scalar/vector boson: 1 1 A ∝ q 2 − m 2 → m 2 14
Dib et al. , hep-ph/0006277 15
Chiralities d L u L W U ei e − L m i /q 2 ( m 2 i ≪ q 2 ) q + m i ν i m i A ∝ P L / q P L ∝ ≃ q 2 − m 2 q 2 − m 2 ν i ( m 2 i ≫ q 2 ) 1 /m i e − i i L U ei W u L d L u L d L W e − L ν L ( m 2 i ≪ q 2 ) q + m i q 1 /q A ∝ P R / / N R P L ∝ ≃ q 2 − m 2 q 2 − m 2 q/m 2 ( m 2 i ≫ q 2 ) N R i i i e − R W R u R d R 16
Heavy neutrinos d L u L W � ei e − L ν i q ν i e − L � ei W u L d L if heavier than 100 MeV: S 2 F � 1 m � ⇒ � 1 ∼ 10 − 8 GeV − 1 ei m � < A h = G 2 ≡ G 2 F M i dimensionless LNV parameter: η h = m p � 1 m � ≤ 1 . 7 × 10 − 8 17
Faessler, Gonzalez, Kovalenko, Simkovic, 1408.6077 18
An exact See-Saw Relation Full mass matrix: m diag 0 m D 0 N S U T with U = ν = U M = M diag m T M R 0 T V D R • N is the PMNS matrix: non-unitary R ) − 1 describes mixing of heavy neutrinos with SM leptons • S = m † D ( M ∗ upper left 0 in M gives exact see-saw relation U αi ( m ν ) i U iβ = 0 , or: ei M i | < | N 2 ei m i | = | S 2 ∼ 0 . 3 eV compare with S 2 ∼ 10 − 8 GeV − 1 and | S ei | 2 ≤ 0 . 0052 ei < M i 19
exact see-saw relation gives stronger constraints! 0,01 0,0001 2 M_i |S ei | 1e-06 2 /M_i |S ei | 1e-08 1e-10 1e-12 2 1e-14 |S ei | 1e-16 1e-18 1e-20 1e-22 1e-24 1e-26 1e-28 1 1000 1e+06 1e+09 1e+12 1e+15 1e+18 M i [GeV] ⇒ cancellations required to make heavy neutrinos contribute significantly to 0 νββ 20
TeV scale seesaw with sizable mixing m ν = m 2 D /M R ≃ v 2 /M R A it follows that M R ≃ 10 15 GeV and � ∆ m 2 with m ν ≃ � m ν /M R ≃ 10 − 13 S = m D /M R = then, heavy neutrino contribution to 0 νββ negligible: R ≃ 10 − 41 GeV − 1 S 2 /M R = m 2 D /M 3 m ν /M R ≃ 10 − 7 and still � can make M R TeV, but then mixing R ≃ 10 − 17 GeV − 1 m 2 D /M 3 21
TeV scale seesaw with sizable mixing 1 ( here ω = e 2 iπ/ 3 ) not necessarily correct, m D and M R are matrices and cancellations can occur . . . h 1 h 2 h 3 e.g. m D = v M R = M 0 ω h 1 ω h 2 ω h 3 ω 2 h 1 ω 2 h 2 ω 2 h 3 gives m ν = 0 , add (very) small corrections . . . m D = v , M R = TeV, mixing m D /M R large, 0 νββ contribution large 22
TeV scale seesaw with sizable mixing can also make everything smaller: fǫ 2 0 0 a b k M − 1 = M − 1 M D = m , 0 gǫ 0 b c dǫ R eǫ 2 0 0 1 k dǫ M /GeV m /MeV ǫ a k b c d e f g 5.00 0.935 0.02 1.00 1.35 0.90 1.4576 0.7942 0.2898 0.0948 0.485 G 2 ≃ 10 − 4 GeV 2 q 2 | m ee | F � � A l � � ≃ 10 − 2 � = � � F � 1 q 2 A h G 2 m � � 23
Higgs triplets (type II seesaw) d L u L e − L W √ 2 g 2 v L h ee ∆ −− W e − L u L d L h ee v L ( m ν ) ee | m ee | A ∆ ≃ G 2 < ∼ G 2 = G 2 F F F m 2 m 2 m 2 ∆ ∆ ∆ plays no role in 0 νββ 24
Inverse Neutrinoless Double Beta Decay this is not 76 Se ++ + e − + e − → 76 Ge but rather e − + e − → W − + W − Rizzo; Heusch, Minkowski; Gluza, Zralek; Cuypers, Raidal; . . . e − e − e − W − W − W − L L L N N ∆ −− W − W − W − e − e − e − L L L (a) (b) (c) 25
Inverse Neutrinoless Double Beta Decay - e - --- - W - , s = 16 TeV 2 e > W 1e+08 1e+06 10000 100 1 σ [fb] 0,01 0,0001 1e-06 2 = 1.0 |V ei | 1e-08 2 = 0.0052 |V ei | 1e-10 2 = 5.0 10 -8 (M i /GeV) |V ei | 1e-12 1e-14 1 10 100 1000 10000 1e+05 1e+06 1e+07 1e+08 M i [GeV] �� 2 d cos θ = G 2 dσ �� � t u ( m ν ) i U 2 F + ei 32 π t − ( m ν ) i u − ( m ν ) i 26
Inverse Neutrinoless Double Beta Decay Extreme limits: • light neutrinos: � 2 σ ( e − e − → W − W − ) = G 2 � | m ee | 4 π | m ee | 2 ≤ 4 . 2 · 10 − 18 F fb 1 eV ⇒ way too small • heavy neutrinos: � √ s � 4 � � 2 S 2 ei /M i σ ( e − e − → W − W − ) = 2 . 6 · 10 − 3 fb 5 · 10 − 8 GeV − 1 TeV ⇒ too small • √ s → ∞ : σ ( e − e − → W − W − ) = G 2 � 2 �� F U 2 ei ( m ν ) i 4 π ⇒ amplitude grows with √ s ? Unitarity?? 27
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