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Neutrinoless Double Beta Decay: Theory

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Neutrinoless Double Beta Decay: Theory Neutrinoless Double Beta Decay: Theory v T -1 Werner Rodejohann mv = m L - m D M R m D SSI 2015 MANITOP 17/08/15 Massive Neutrinos: Investigating their Theoretical Origin and Phenomenology 1 Neutrinos... ...still interesting... 2 What is Neutrinoless Double Beta Decay? (A, Z) (A, Z + 2) + 2 e− (0νββ) → second order in weak interaction, Γ G4 Q5 rare! • ∝ F ⇒ not to be confused with (A, Z) (A, Z + 2) + 2 e− + 2ν ¯ (2νββ) • → e (Γ G4 Q11, but occurs more often...) ∝ F 3 Need to forbid single β decay: • even/even even/even • ⇒ → either direct (0νββ) or two simultaneous decays with virtual (energetically • forbidden) intermediate state (2νββ) 4 Ho,Ho, manymany nucleinuclei inin thisthis condition-condition- '-value )MeV+ '-value A Slide by A. Giuliani, see lecture by Lisa Kaufman 5 35 candidate isotopes • 10 are interesting: 48Ca, 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 124Sn, 130Te, • 136Xe, 150Nd Q-value vs. natural abundance vs. reasonably priced enrichment • vs. association with a well controlled experimental technique vs... no superisotope ⇒ 0ν Natural abundance of different 0νββ candidate Isotopes G for 0νββ-decay of different Isotopes 35 20 18 30 16 25 14 ] -1 12 20 yrs -14 10 15 [10 ν 8 0 G 10 6 Natural abundance [%] 4 5 2 0 0 48 76 82 96 100 110 116 124 130 136 150 48 76 82 96 100 110 116 124 130 136 150 Ca Ge Se Zr Mo Pd Cd Sn Te Xe Nd Ca Ge Se Zr Mo Pd Cd Sn Te Xe Nd Isotope Isotope T 0ν 1/a T 0ν Q−5 1/2 ∝ 1/2 ∝ 6 Neutrinoless Double Beta Decay (A, Z) (A, Z + 2) + 2 e− (0νββ) Lepton Number Violation → ⇒ Standard Interpretation (neutrino physics) • Non-Standard Interpretations (BSM = neutrino physics) • 6 Int. J. Mod. Phys. E20, 1833 (2011) [1106.1334]; J. Phys. G39, 124008 (2012) [1206.2560]; 1507.00170 7 Why should we probe Lepton Number Violation? L and B accidentally conserved in SM • effective theory: = + 1 + 1 + ... • L LSM Λ LLNV Λ2 LLFV, BNV, LNV baryogenesis: B is violated • B, L often connected in GUTs • GUTs have seesaw and Majorana neutrinos • µ ˜µν B (chiral anomalies: ∂µJB,L = c Gµν G = 0 with Jµ = qi γµ qi and • L 6 Jµ = ℓi γµ ℓi) P P Lepton Number Violation as important as Baryon Number Violation ⇒ 0νββ is NOT a neutrino mass experiment!! 8 Upcoming/running experiments: exciting time!! best limit was from 2001, improved 2012 Name Isotope Source = Detector; calorimetric with Source 6= Detector high ∆E low ∆E topology topology AMoRE 100Mo X – – – CANDLES 48Ca – X – – COBRA 116Cd (and 130Te) – – X – CUORE 130Te X – – – DCBA/MTD 82Se / 150Nd – – – X EXO 136Xe – – X – GERDA 76Ge X – – – CUPID 82Se / 100Mo / 116Cd / 130Te X – – – KamLAND-Zen 136Xe – X – – LUCIFER 82Se / 100Mo / 130Te X – – – LUMINEU 100Mo X – – – MAJORANA 76Ge X – – – MOON 82Se / 100Mo / 150Nd – – – X NEXT 136Xe – – X – SNO+ 130Te – X – – SuperNEMO 82Se / 150Nd – – – X XMASS 136Xe – X – – see lecture by Lisa Kaufman 9 Interpretation of Experiments Master formula: Γ0ν = G (Q, Z) (A, Z) η 2 x |Mx x| G (Q, Z): phase space factor • x (A, Z): nuclear physics • Mx η : particle physics • x 10 Interpretation of Experiments Master formula: Γ0ν = G (Q, Z) (A, Z) η 2 x |Mx x| G (Q, Z): phase space factor; calculable • x (A, Z): nuclear physics; problematic • Mx η : particle physics; interesting • x 11 Interpretation of Experiments Master formula: Γ0ν = G (Q, Z) (A, Z) η 2 x |Mx x| G (Q, Z): phase space factor, typically Q5 • x (A, Z): nuclear physics; factor 2-3 uncertainty • Mx η : particle physics; many possibilities • x 12 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 0νββ give negligible or no contribution dL uL W Uei − eL νi q νi − eL Uei W u dL L prediction of (100 ǫ) % of all neutrino mass mechanisms − (lecture by Andre De Gouvea) 13 Paths to Neutrino Mass quantum number approach ingredient L mν scale of messenger “SM” −12 RH ν NR ∼ (1, 0) hNRΦL hv h = O(10 ) (Dirac mass) “effective” new scale 2 – h Lc ΦΦ L h v Λ = 1014 GeV (dim 5 operator) + LNV Λ “direct” Higgs triplet c 1 2 ∆ ∼ (3, −2) hL ∆L + µΦΦ∆ hvT Λ = M (type II seesaw) + LNV hµ ∆ 2 “indirect 1” RH ν c (hv) 1 NR ∼ (1, 0) hNRΦL + NRMRN Λ = MR (type I seesaw) + LNV R MR h 2 “indirect 2” fermion triplets (hv) 1 Σ ∼ (3, 0) hΣ LΦ + TrΣMΣΣ Λ = MΣ (type III seesaw) + LNV MΣ h plus seesaw variants (linear, double, inverse,...) plus radiative mechanisms plus extra dimensions plusplusplus 14 dL uL W Uei − eL i ν q i ν − eL Uei W uL dL U 2 from charged current • ei m /E from spin-flip and if neutrinos are Majorana particles • i i amplitude proportional to coherent sum (“effective mass”) m = U 2 m | ee| ei i P m/E eV/100 MeV is tiny: only N can save the day! ≃ A 15 Dirac vs. Majorana in V A theories: observable difference always suppressed by (m/E)2 − In terms of degrees of freedom (helicity and particle/antiparticle): • νD =(ν↑,ν↓, ν¯↑, ν¯↓) versus νM =(ν↑,ν↓) weak interactions act on chirality (left-/right-handed) • chirality is not a good quantum number (“spin flip”): L = + m • ↓ E ↑ Dirac: • − − m – what we produce from a W is ℓ (¯ν↑ + E ν¯↓) − − – the ν¯↓ CANNOT interact with another W to generate another ℓ : ∆L = 0 Majorana: • − − m – what we produce from a W is ℓ (ν↑ + E ν↓) − − – the ν↓ CAN interact with another W to generate another ℓ : ∆L = 2 amplitude (m/E) probability (m/E)2 ⇒ ∝ ⇒ ∝ 16 Dirac vs. Majorana Z-decay: • Γ(Z ν ν ) m2 → D D 1 3 ν Γ(Z ν ν ) ≃ − m2 → M M Z Meson decays • 2 2 + − + + 2 −30 meµ BR(K π e µ ) meµ = Uei Uµi mi 10 | | → ∝| | ∼ eV X neutrino-antineutrino oscillations • 1 P (ν ν¯ )= U U U ∗ U ∗ m m e−i(Ej −Ei)t α → β E2 αj βj αi βi i j Xi,j 17 The effective mass Im α (2) . 2i β |mee | e (3) . 2i |mee | e mee (1) Re |mee | Amplitude proportional to coherent sum (“effective mass”): m U 2 m = U 2 m + U 2 m e2iα + U 2 m e2iβ | ee|≡ ei i | e1| 1 | e2| 2 | e3| 3 P = f θ , U , m , sgn(∆m2 ),α,β 12 | e3| i A 7 out of 9 parameters of neutrino physics! 18 Fix known things, vary unknown things... normal invertiert 2 2 m3 m2 2 ∆m21 2 m1 2 ∆m32 νe νµ ντ 2 ∆m31 2 m2 2 ∆m21 2 m2 m1 3 19 The usual plot 20 Alternative processes The lobster: 2 2 + − + + 2 −30 meµ BR(K π e µ ) meµ = Uei Uµi mi 10 | | → ∝| | ∼ eV X 21 The usual plot (life-time instead of m ) | ee| Normal Inverted 32 10 30 10 (yrs) ν ] 1/2 28 10 [T 26 10 Excluded by HDM 0.0001 0.001 0.01 0.1 0.0001 0.001 0.01 0.1 m (eV) light 22 Which mass ordering with which life-time? Σ m m β | ee| 2 2 2 2 2 2 2 2i(α−β) NH ∆mA ∆m⊙ + Ue3 ∆mA ∆m⊙ + Ue3 ∆mAe q | | q | | p 0pν > 28−29 0.05 eV 0.01 eV 0.003 eV T1/2 10 yrs ≃ ≃ ∼ ⇒ ∼ IH 2 ∆m2 ∆m2 ∆m2 1 sin2 2θ sin2 α A A A − 12 p p p p 0ν > 26−27 0.1 eV 0.05 eV 0.03 eV T1/2 10 yrs ≃ ≃ ∼ ⇒ ∼ QD 3m m m 1 sin2 2θ sin2 α 0 0 0 − 12 > p 0ν > 25−26 0.1 eV T1/2 10 yrs ∼ ⇒ ∼ 23 Plot against other observables θ 12 Normal Inverted Normal Inverted 0 0 10 10 CPV CPV CPV CPV (+,+) (+) (+,+) (+) (+,-) (-) (+,-) (-) (-,+) (-,+) (-,-) (-,-) -1 -1 10 10 > (eV) > (eV) ee ee <m <m -2 -2 10 10 -3 -3 10 10 0.01 0.1 0.01 0.1 0.1 1 0.1 1 m (eV) β Σ m (eV) i Complementarity of m = U 2 m , m = U 2 m2 and Σ= m | ee| ei i β | ei| i i p P 24 CP violation! Dirac neutrinos! something else does 0νββ! 25 Neutrino Mass m(heaviest) > m2 m2 0.05 eV | 3 − 1|≃ ∼ p 3 complementary methods to measure neutrino mass: Method observable now [eV] near [eV] far [eV] pro con 2 model-indep.; final?; Kurie |Uei|2 m 2.3 0.2 0.1 i theo. clean worst pP best; systemat.; mi . Cosmo. 0 7 0 3 0 05 NH/IH model-dep. P 2 fundament.; model-dep.; νββ Ueimi . 0 | | 0 3 0 1 0 05 NH/IH theo. dirty P see lectures by Alessandro Melchiorri and Joe Formaggio 26 Recent Results 76Ge: • – GERDA: T > 2.1 1025 yrs 1/2 × – GERDA + IGEX + HDM: T > 3.0 1025 yrs 1/2 × 136Xe: • 25 – EXO-200: T > 1.1 10 yrs (first run with less exposure: T > 1.6 × 1025 yrs. .) 1/2 × 1/2 – KamLAND-Zen: T > 2.6 1025 yrs 1/2 × Xe-limit is stronger than Ge-limit when: G 2 T >T Ge MGe yrs Xe Ge G Xe Xe M 27 Current Limits on mee | | NME 76Ge 136Xe 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.
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