Proton Decay

Home , Proton decay

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

⇒ 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

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

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. 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) p → e−νν ∂u¯cu¯cQLLe¯cH, ··· d = 13 ∂u¯cu¯cdcQQe¯cLL (∆B = 1, ∆L =+3) ···

BLV, Madrid; Oct 21, 2019 – p.14/22 d = 13 operators

Consider example operator:

∂u¯cu¯cdc(QL)(QL)¯ec

⇒ d = 13 is lowest order with 3 charged leptons

⇒ Decay modes: p → e+e+e+π−π−, p → e+e+νπ¯ −, p → e+ν¯νπ¯ 0, n → e+e+e+π−π−π−, n → e+e+νπ¯ −π−, n → e+ν¯νπ¯ −, ···

⇒ At least 4-body, with 3 charged leptons at least 5-body ﬁnal state

BLV, Madrid; Oct 21, 2019 – p.15/22 d = 13 operators

Consider example operator:

∂u¯cu¯cdc(QL)(QL)¯ec

⇒ d = 13 is lowest order with 3 charged leptons

⇒ Decay modes: p → e+e+e+π−π−, p → e+e+νπ¯ −, p → e+ν¯νπ¯ 0, n → e+e+e+π−π−π−, n → e+e+νπ¯ −π−, n → e+ν¯νπ¯ −, ···

⇒ At least 4-body, with 3 charged leptons at least 5-body ﬁnal state

⇒ d = 13 is ∝ Λ−9, estimate:

Λ ∼ 1 TeV ⇒ τ ∼ 10(32−34) ys

⇒ Operators with d = 13 can be searched for at LHC, without conﬂict with p-decay

BLV, Madrid; Oct 21, 2019 – p.15/22 III.

A simple (∆B =1, ∆L =3) model

BLV, Madrid; Oct 21, 2019 – p.16/22 Particle content

′ (Sd, Sd)=(3¯, 1, 1/3) - Scalar “down quark” Su =(3¯, 1, −2/3) - Scalar “up quark” (N, Nc)=(1, 1, 0) - Left- and right-handed Weyl fermions

BLV, Madrid; Oct 21, 2019 – p.17/22 Particle content

′ (Sd, Sd)=(3¯, 1, 1/3) - Scalar “down quark” Su =(3¯, 1, −2/3) - Scalar “up quark” (N, Nc)=(1, 1, 0) - Left- and right-handed Weyl fermions

Q L e+/ν S3¯,1,1/3 Problem: Proton decay p Q Q π0 d/u π+

BLV, Madrid; Oct 21, 2019 – p.17/22 Particle content

′ (Sd, Sd)=(3¯, 1, 1/3) - Scalar “down quark” Su =(3¯, 1, −2/3) - Scalar “up quark” (N, Nc)=(1, 1, 0) - Left- and right-handed Weyl fermions

Q L e+/ν S3¯,1,1/3 Problem: Proton decay p Q Q 0 π0 + Add Z3(L) symmetry: d/u π+ SM ﬁelds: L(L)= −L(ec)= 1 L(Q, uc, dc)= 0

New ﬁelds: c ′ N , Su, (Sd, Sd) ⇒ L = −1 N ⇒ L = 1

BLV, Madrid; Oct 21, 2019 – p.17/22 Lagrangian

Given the particle content and lepton number assignments:

c c c c c ∗ L = LSM + Yν LN H + Y1u N Su + Y2N d Sd

c c ′ ′ c + Y3e u Sd + Y4QLSd + µSuSdSd + mN NN + ···

BLV, Madrid; Oct 21, 2019 – p.18/22 Lagrangian

Given the particle content and lepton number assignments:

c c c c c ∗ L = LSM + Yν LN H + Y1u N Su + Y2N d Sd

c c ′ ′ c + Y3e u Sd + Y4QLSd + µSuSdSd + mN NN + ···

′ ⇒ µSuSdSd violates L in 3 units. For µ → 0 the model conserves L ′ ⇒ µSuSdSd - three (scalar) colour triplets. Two copies of Sd needed

BLV, Madrid; Oct 21, 2019 – p.18/22 Lagrangian

Given the particle content and lepton number assignments:

c c c c c ∗ L = LSM + Yν LN H + Y1u N Su + Y2N d Sd

c c ′ ′ c + Y3e u Sd + Y4QLSd + µSuSdSd + mN NN + ···

′ ⇒ µSuSdSd violates L in 3 units. For µ → 0 the model conserves L ′ ⇒ µSuSdSd - three (scalar) colour triplets. Two copies of Sd needed

⇒ Yν - Dirac neutrino masses. Since ∆L = 3 neutrinos are Dirac particles

BLV, Madrid; Oct 21, 2019 – p.18/22 Lagrangian

Given the particle content and lepton number assignments:

c c c c c ∗ L = LSM + Yν LN H + Y1u N Su + Y2N d Sd

c c ′ ′ c + Y3e u Sd + Y4QLSd + µSuSdSd + mN NN + ···

′ ⇒ µSuSdSd violates L in 3 units. For µ → 0 the model conserves L ′ ⇒ µSuSdSd - three (scalar) colour triplets. Two copies of Sd needed

⇒ Yν - Dirac neutrino masses. Since ∆L = 3 neutrinos are Dirac particles

c ⇒ mN NN vector-like mass, conserves lepton number. Minimal model to ﬁt neutrino data needs 3 N c and 1 N

BLV, Madrid; Oct 21, 2019 – p.18/22 Lagrangian

Given the particle content and lepton number assignments:

c c c c c ∗ L = LSM + Yν LN H + Y1u N Su + Y2N d Sd

c c ′ ′ c + Y3e u Sd + Y4QLSd + µSuSdSd + mN NN + ···

′ ⇒ µSuSdSd violates L in 3 units. For µ → 0 the model conserves L ′ ⇒ µSuSdSd - three (scalar) colour triplets. Two copies of Sd needed

⇒ Yν - Dirac neutrino masses. Since ∆L = 3 neutrinos are Dirac particles

c ⇒ mN NN vector-like mass, conserves lepton number. Minimal model to ﬁt neutrino data needs 3 N c and 1 N

c c ⇒ Y1u N Su needed to ﬁx lepton number of Su.

BLV, Madrid; Oct 21, 2019 – p.18/22 Proton decay

5-body ﬁnal state 4-body ﬁnal state all decay products visible at least one neutrino

BLV, Madrid; Oct 21, 2019 – p.19/22 Proton decay

5-body ﬁnal state 4-body ﬁnal state all decay products visible at least one neutrino

Half-life estimate: 15 2 −1 + − J0 2 mp W 35 τ (p → 3e 2π ) ∼ A 2 ∼ 10 ys (for Λ ∼ 1 TeV) f(5) fπ µhpi with J0 ≃ 0.1 and A∝ 2 8 mN mS

BLV, Madrid; Oct 21, 2019 – p.19/22 Proton decay

5-body ﬁnal state 4-body ﬁnal state all decay products visible at least one neutrino

Half-life estimate: 15 2 −1 + − J0 2 mp W 35 τ (p → 3e 2π ) ∼ A 2 ∼ 10 ys (for Λ ∼ 1 TeV) f(5) fπ µhpi with J0 ≃ 0.1 and A∝ 2 8 mN mS

Ratio of phase space factors: f(4)/f(5) ∼ 103

′ Note: µSuSdSd in both diagrams!

BLV, Madrid; Oct 21, 2019 – p.19/22 Proton decay

Example only! All couplings: Y ∼ 1

All masses:

mS ∼ 1 TeV

BLV, Madrid; Oct 21, 2019 – p.20/22 Proton decay

Example only! All couplings: Y ∼ 1

All masses:

mS ∼ 1 TeV

⇐ SK p → e+νν only for comparison, limit does not apply for this model

⇒ Hyper-K should be able to improve limit by (4-5) orders of mag.

BLV, Madrid; Oct 21, 2019 – p.20/22 LHC phenomenology

′ ⇒ Sd and Sd are leptoquarks, See also talks by limits from ATLAS/CMS apply S. Fajfer D.M. Morse

BLV, Madrid; Oct 21, 2019 – p.21/22 LHC phenomenology

′ ⇒ Sd and Sd are leptoquarks, See also talks by limits from ATLAS/CMS apply S. Fajfer D.M. Morse

⇒ Exotic ﬁnal states from Su:

− + If Br(Su → 2e + 2j) ∼ Br(Su → e + 3j) Requires: mS > mS + m ′ ∗ ± u d Sd Final state from pair production (SuSu): pp → 3e + 5j and mSu > mN ⇒ few events, but low SM background

BLV, Madrid; Oct 21, 2019 – p.21/22 Conclusions

⇒ (∆B = 1, ∆L = 1) has been studied extensively

⇒ Stringent limits on 2-body decay modes of n/p exist

⇒ Limits on n-body decay modes of n/p weak

⇒ Identifying ∆L = 3 p-decay needs 5-body ﬁnal state

⇒ Current sensitivity Λ(d = 13) ≃ 1 TeV

BLV, Madrid; Oct 21, 2019 – p.22/22