Non-standard nucleon decay modes Martin Hirsch Instituto de F´ısica Corpuscular - CSIC Universidad Valencia, Spain http://www.astroparticles.es/ Based on: Renato M. Fonseca, Martin Hirsch, Rahul Srivastava Phys.Rev. D97 (2018) 075026 BLV, Madrid; Oct 21, 2019 – p.1/22 Contents I. Introduction II. BLV operators III. A simple (∆B = 1, ∆L = 3) model example IV. Conclusions BLV, Madrid; Oct 21, 2019 – p.2/22 I. Introduction BLV, Madrid; Oct 21, 2019 – p.3/22 ’Standard’ Proton decay In GUT models, such as SU(5): Georgi & Glashow, 1974 Q L e+ X3,2,−5/6 p c ¯u d¯c 0 d π BLV, Madrid; Oct 21, 2019 – p.4/22 ’Standard’ Proton decay In GUT models, such as SU(5): Georgi & Glashow, 1974 Estimate: Q L e+ 2 X −1 mp 2 αGUT 3,2,−5/6 τp ∝ 32π |hπ|O|pi| 4 MX p c ¯u d¯c Lower limit: π0 d M > 6 × 1014 αGUT GeV X ∼ q (1/40) BLV, Madrid; Oct 21, 2019 – p.4/22 ’Standard’ Proton decay In GUT models, such as SU(5): Georgi & Glashow, 1974 Estimate: Q L e+ 2 X −1 mp 2 αGUT 3,2,−5/6 τp ∝ 32π |hπ|O|pi| 4 MX p c ¯u d¯c Lower limit: π0 d M > 6 × 1014 αGUT GeV X ∼ q (1/40) From low-energy point of view: QQQL u¯cd¯cQL All Λ2 Λ2 d = 6 (B − L) = 0 ucucdcec u¯cQQe¯c Λ2 Λ2 BLV, Madrid; Oct 21, 2019 – p.4/22 ’Standard’ Proton decay In GUT models, such as SU(5): Georgi & Glashow, 1974 Estimate: Q L e+ 2 X −1 mp 2 αGUT 3,2,−5/6 τp ∝ 32π |hπ|O|pi| 4 MX p c ¯u d¯c Lower limit: π0 d M > 6 × 1014 αGUT GeV X ∼ q (1/40) From low-energy point of view: c ¯c QQQL u¯ d QL Λ much lower? 2 2 All Λ Λ Loop induced d = 6 operators! (B − L) = 0 ucucdcec u¯cQQe¯c Λ2 Λ2 see talk by T. Ota BLV, Madrid; Oct 21, 2019 – p.4/22 Proton decay limits Table: 2-body decays Limits dominated Decay mode: T lim/(1033ys) Ref 1/2 by Super-K p → e+π0 16 SK16 n → e+π− 5.3 SK17 All modes − + p → µ+π 7.7 SK16 except n → e π have (B − L) = 0 n → µ+π− 3.5 SK17 p → νπ¯ + 0.39 SK13 See talk by 0 n → νπ¯ 1.1 SK13 M. Miura p → νK¯ + 5.9 SK14 n → e−π+ 0.065 IMB-88 ⇒ Many more 2-body modes can be found in PDG: p → e+η, p → e+ρ, p → e+K ··· ··· BLV, Madrid; Oct 21, 2019 – p.5/22 Proton decay limits Table: 2-body decays Limits dominated Decay mode: T lim/(1033ys) Ref 1/2 by Super-K p → e+π0 16 SK16 n → e+π− 5.3 SK17 All modes − + p → µ+π 7.7 SK16 except n → e π have (B − L) = 0 n → µ+π− 3.5 SK17 p → νπ¯ + 0.39 SK13 See talk by 0 n → νπ¯ 1.1 SK13 M. Miura p → νK¯ + 5.9 SK14 − + n → e π 0.065 IMB-88 PDG lists (B − L) = 2 from IMB-88 ?????? ⇒ Many more 2-body modes can be found in PDG: p → e+η, p → e+ρ, p → e+K ··· ··· BLV, Madrid; Oct 21, 2019 – p.5/22 Proton decay limits Table: 3-body decays Decay mode: T lim/(1033ys) Ref 1/2 Many limits very old! p → e+e+e− 0.79 IMB-99 p → e+π0π0 0.147 IMB-99a PDG lists (B − L) = 2 p → e+π+π− 0.082 IMB-99a from 1991! p → e−π+π+ 0.030 FRE-91 p → e+νν 0.17 SK14a p → µ+νν 0.22 SK14a BLV, Madrid; Oct 21, 2019 – p.6/22 Proton decay limits Table: 3-body decays Decay mode: T lim/(1033ys) Ref 1/2 Many limits very old! p → e+e+e− 0.79 IMB-99 p → e+π0π0 0.147 IMB-99a PDG lists (B − L) = 2 p → e+π+π− 0.082 IMB-99a from 1991! p → e−π+π+ 0.030 FRE-91 No limits on p → e+νν 0.17 SK14a 4-, 5-body decays p → µ+νν 0.22 SK14a BLV, Madrid; Oct 21, 2019 – p.6/22 Proton decay limits Table: 3-body decays Decay mode: T lim/(1033ys) Ref 1/2 Many limits very old! p → e+e+e− 0.79 IMB-99 p → e+π0π0 0.147 IMB-99a PDG lists (B − L) = 2 p → e+π+π− 0.082 IMB-99a from 1991! p → e−π+π+ 0.030 FRE-91 No limits on p → e+νν 0.17 SK14a 4-, 5-body decays p → µ+νν 0.22 SK14a Table: inclusive modes from PDG: Very weak ... Very old ... Decay mode: T lim/(1030ys) Ref 1/2 see also: + p/n → e + anything 0.6 Learned-79 Heeck & Takhistov p/n → µ+ + anything 12 Cherry-81 arXiv:1910.07647 BLV, Madrid; Oct 21, 2019 – p.6/22 II. BLV operators BLV, Madrid; Oct 21, 2019 – p.7/22 (∆L 6=0, ∆B 6=0) operators In the SM: R. Fonseca (∆B +∆L) = 0, ±2, ±4 ··· Sym2Int arXiv:1703.05221 BLV, Madrid; Oct 21, 2019 – p.8/22 (∆L 6=0, ∆B 6=0) operators In the SM: R. Fonseca (∆B +∆L) = 0, ±2, ±4 ··· Sym2Int arXiv:1703.05221 Lowest order operators: d = 5 LLHH ∆L = 2 Majorana neutrino mass BLV, Madrid; Oct 21, 2019 – p.8/22 (∆L 6=0, ∆B 6=0) operators In the SM: R. Fonseca (∆B +∆L) = 0, ±2, ±4 ··· Sym2Int arXiv:1703.05221 Lowest order operators: d = 5 LLHH ∆L = 2 Majorana neutrino mass d = 6 QQQL, u¯cd¯cQL (∆B = 1, ∆L = 1) Nucleon decay u¯cu¯cd¯ce¯c, u¯cQQe¯c (∆(B − L)=0) Decay modes: p → e+π0, n → νπ0, p → νπ+, n → e+π− ... +(e → µ)+(π → K) ... BLV, Madrid; Oct 21, 2019 – p.8/22 (∆L 6=0, ∆B 6=0) operators In the SM: R. Fonseca (∆B +∆L) = 0, ±2, ±4 ··· Sym2Int arXiv:1703.05221 Lowest order operators: d = 5 LLHH ∆L = 2 Majorana neutrino mass d = 6 QQQL, u¯cd¯cQL (∆B = 1, ∆L = 1) Nucleon decay u¯cu¯cd¯ce¯c, u¯cQQe¯c (∆(B − L)=0) d = 7 u¯cd¯cd¯cLH¯ †, d¯cd¯cd¯cLH¯ (∆B = 1, ∆L = −1) Nucleon decay d¯cd¯cQecH†, d¯cQQLH¯ † (∆(B − L)=2) Decay modes: p → νπ+, n → e−π+, p → e−π+K+, p → e−π+π+ ... BLV, Madrid; Oct 21, 2019 – p.9/22 (∆L 6=0, ∆B 6=0) operators In the SM: R. Fonseca (∆B +∆L) = 0, ±2, ±4 ··· Sym2Int arXiv:1703.05221 Lowest order operators: d = 5 LLHH ∆L = 2 Majorana neutrino mass d = 6 QQQL, u¯cd¯cQL (∆B = 1, ∆L = 1) Nucleon decay u¯cu¯cd¯ce¯c, u¯cQQe¯c (∆(B − L)=0) d = 7 u¯cd¯cd¯cLH¯ †, d¯cd¯cd¯cLH¯ (∆B = 1, ∆L = −1) Nucleon decay d¯cd¯cQecH†, d¯cQQLH¯ † (∆(B − L)=2) d = 8 QQQLHH†, ··· ... nothing new BLV, Madrid; Oct 21, 2019 – p.10/22 (∆L 6=0, ∆B 6=0) operators d = 9 u¯cd¯cd¯cu¯cd¯cd¯c, (∆B = 2, ∆L = 0) (n − n¯)-oscillations BLV, Madrid; Oct 21, 2019 – p.11/22 (∆L 6=0, ∆B 6=0) operators d = 9 u¯cd¯cd¯cu¯cd¯cd¯c, (∆B = 2, ∆L = 0) (n − n¯)-oscillations LLHH(HH†) (∆B = 0, ∆L = 2) h.o. Majorana neutrino mass BLV, Madrid; Oct 21, 2019 – p.11/22 (∆L 6=0, ∆B 6=0) operators d = 9 u¯cd¯cd¯cu¯cd¯cd¯c, (∆B = 2, ∆L = 0) (n − n¯)-oscillations LLHH(HH†) (∆B = 0, ∆L = 2) h.o. Majorana neutrino mass u¯cu¯cu¯ce¯cLL, (∆B = 1, ∆L = 3) no p/n-decay u¯cu¯cQLLL LHC? ⇒ both Ops require at least 2 generations of u ⇒ Since mc > mp, proton decay forbidden kinematically BLV, Madrid; Oct 21, 2019 – p.11/22 (∆L 6=0, ∆B 6=0) operators d = 9 u¯cd¯cd¯cu¯cd¯cd¯c, (∆B = 2, ∆L = 0) (n − n¯)-oscillations LLHH(HH†) (∆B = 0, ∆L = 2) h.o. Majorana neutrino mass u¯cu¯cu¯ce¯cLL, (∆B = 1, ∆L = 3) no p/n-decay u¯cu¯cQLLL LHC? d = 10 LLLLHHHH (∆B = 0, ∆L = 4) See talk by R Fonseca BLV, Madrid; Oct 21, 2019 – p.12/22 (∆L 6=0, ∆B 6=0) operators d = 9 u¯cd¯cd¯cu¯cd¯cd¯c, (∆B = 2, ∆L = 0) (n − n¯)-oscillations LLHH(HH†) (∆B = 0, ∆L = 2) h.o. Majorana neutrino mass u¯cu¯cu¯ce¯cLL, (∆B = 1, ∆L = 3) no p/n-decay u¯cu¯cQLLL LHC? d = 10 LLLLHHHH (∆B = 0, ∆L = 4) See talk by R Fonseca d¯cd¯cd¯cL¯L¯LH¯ † (∆B = 1, ∆L = −3) ⇒ Operator requires at least 2 generations of d and L ⇒ Final state, example: n → e−ννK+ ⇒ Since L.L, final state always involve neutrino ⇒ Can establish limits but can not prove ∆L = 3 BLV, Madrid; Oct 21, 2019 – p.12/22 (∆L 6=0, ∆B 6=0) operators d = 9 u¯cd¯cd¯cu¯cd¯cd¯c, (∆B = 2, ∆L = 0) (n − n¯)-oscillations LLHH(HH†) (∆B = 0, ∆L = 2) h.o. Majorana neutrino mass u¯cu¯cu¯ce¯cLL, (∆B = 1, ∆L = 3) no p/n-decay u¯cu¯cQLLL LHC? d = 10 LLLLHHHH (∆B = 0, ∆L = 4) See talk by R Fonseca d¯cd¯cd¯cL¯L¯LH¯ † (∆B = 1, ∆L = −3) n → e−ννK+ d = 11 ∂∂u¯cu¯cQLLL (∆B = 1, ∆L = ±3) 14 operators (!) ∂u¯cu¯cQLLe¯cH, ··· Decay modes: p → e+νν, p → π−e+e+ν¯, n → π−π−e+e+ν¯ ⇒ Final states again always involve neutrinos ⇒ Minimum 3-body decay BLV, Madrid; Oct 21, 2019 – p.13/22 (∆L 6=0, ∆B 6=0) operators d = 9 u¯cd¯cd¯cu¯cd¯cd¯c, (∆B = 2, ∆L = 0) (n − n¯)-oscillations LLHH(HH†) (∆B = 0, ∆L = 2) h.o.