UCI-TR-2019-24 Inclusive Nucleon Decay Searches as a Frontier of Baryon Number Violation Julian Heeck1, ∗ and Volodymyr Takhistov2, y 1Department of Physics and Astronomy, University of California, Irvine Irvine, California, 92697-4575, USA 2Department of Physics and Astronomy, University of California, Los Angeles Los Angeles, California, 90095-1547, USA Proton decay, and the decay of nucleons in general, constitutes one of the most sensitive probes of high-scale physics beyond the Standard Model. Most of the existing nucleon decay searches have focused primarily on two-body decay channels, motivated by Grand Unified Theories and supersymmetry. However, many higher-dimensional operators violating baryon number by one unit, ∆B = 1, induce multi-body nucleon decay channels, which have been only weakly constrained thus far. While direct searches for all such possible channels are desirable, they are highly impractical. In light of this, we argue that inclusive nucleon decay searches, N ! X+anything (where X is a light Standard Model particle with an unknown energy distribution), are particularly valuable, as are model-independent and invisible nucleon decay searches such as n ! invisible. We comment on complementarity and opportunities for such searches in the current as well as upcoming large- scale experiments Super-Kamiokande, Hyper-Kamiokande, JUNO, and DUNE. Similar arguments apply to ∆B > 1 processes, which kinematically allow for even more involved final states and are essentially unexplored experimentally. CONTENTS I. INTRODUCTION I. Introduction 1 Baryon number B and lepton number L are seem- ingly accidentally conserved in the Standard Model (SM), II. Nucleon decay operators 2 which makes searches for their violation extremely impor- A. Operator dimension d = 6 2 tant. So far we have not observed any B or L violating B. Operator dimension d > 6 3 processes despite decades of experimental investigation, C. UV-complete example 5 yet there are many reasons to expect that these symme- tries could be broken. The linear combination B +L is in III. Exclusive nucleon decay searches 6 principle already violated by 3 + 3 units within the SM itself through non-perturbative instanton effects, albeit IV. Inclusive nucleon decay searches for ∆B = 1 highly suppressed [1]. From a more fundamental top- processes 8 down perspective, global symmetries such as U(1) and A. Model-independent and invisible mode B U(1) are expected to be violated at some level by quan- searches 8 L tum gravity effects [2, 3], which is however difficult to 1. Isotope fission products 9 quantify. Furthermore, baryon number violation is one 2. Nuclear de-excitation emission 10 of the key prerequisites for successful baryogenesis [4], B. N X+anything 11 which would address the observed baryon{antibaryon 1. !N asymmetry of our Universe. Explicit B-violation and as- (e±!; µ±; π±;K±; ρ±;K∗;±) + anything 11 sociated proton decay is a defining prediction of Grand 2. N (π0;K0; η; ρ, !; K∗;0) + anything 12 Unified Theories (GUTs) [5, 6] that unify the three forces 3. N ! γ + anything 12 of the SM into a single gauge group, offering an expla- 4. N ! ν + anything 12 arXiv:1910.07647v2 [hep-ph] 8 Jan 2020 ! nation for the observed charge quantization as well as V. Processes with ∆B > 1 12 gauge coupling unification. GUTs typically lead to effec- d B L A. ∆B = 2, ∆L = 0 13 tive dimension-six ( = 6) operators with ∆ = ∆ = 1 p e+π0 B. ∆B = 2, ∆L = 2 14 that induce two-body nucleon decays such as ± and n e+π−, mediated by heavy gauge bosons! with C. ∆B > 2 15 ! D. Inclusive searches for ∆B > 1 15 family-universal couplings [7{9]. It has to be stressed, however, that the significance of VI. Conclusions 15 nucleon decays stretches far beyond GUTs. ∆B = 0 pro- cesses generically appear in numerous theoretical6 exten- Acknowledgements 15 sions of the SM, such as supersymmetry (SUSY) [8], typi- cally mediated at the renormalizable level by leptoquarks and diquarks [10{13]. A somewhat model-independent approach to study ∆B = 0 operators is through the ∗ [email protected] SM effective field theory6 (SMEFT), neglecting model- y [email protected] dependent interference effects [14{18]. This allows one to 2 identify higher-dimensional operators with a flavor struc- II. NUCLEON DECAY OPERATORS ture that can make rather unconventional nucleon decay channels dominant. Further, higher-dimensional d > 6 Several well-motivated theoretical models such as operators typically induce nucleon decays with multi- GUTs or R-parity-violating SUSY lead to nucleon de- body final states and even in simple UV-complete models cay, typically with specific two-body channels such as one can encounter more complicated nucleon decay chan- p e+π0 or p νK¯ + being dominant [8, 9]. In order nels such as n e+e−ν [19] or p π+π+e−νν [12, 16]. ! ! ! ! to discuss nucleon decay in its generality without being Hence, there is a vast landscape of possible motivated restricted to a certain model, we instead consider various nucleon decay modes of varying complexity. possible higher-dimensional operators that can mediate these processes, an approach1 that goes back to Refs. [14{ 18]. We aim to determine which operators lead to two- Experimentally, an extensive nucleon decay search pro- body and which lead to multi-body nucleon decays. gram has been carried out over multiple decades, cover- ing more than 60 decay channels [20]. The most sensi- tive searches, coming from the Super-Kamiokande (SK) A. Operator dimension d = 6 experiment [21, 22] (see Ref. [23] for a review), have already pushed the nucleon lifetime limits for certain In the SMEFT, operators that exhibit ∆B = 1 start channels above 1034 yr [24], twenty-four orders of mag- to appear at operator mass dimension d = 6. Keeping nitude beyond the age of our Universe. The frontier of the flavor structure, these ∆B = ∆L = 1 operators can baryon number violation searches will be spearheaded be written as by next-generation large-scale underground neutrino ex- periments, namely the Jiangmen Underground Neutrino 1 αβγ C C d=6 = yabcd (da,αub,β)(Qi,c,γ ijLj;d) Observatory (JUNO) [25], the Deep Underground Neu- L 2 αβγ C C trino Experiment (DUNE) [26], and Hyper-Kamiokande + yabcd (Qi,a,αijQj,b,β)(uc,γ `d) (HK) [27]. It is of paramount importance to take full C C + y3 αβγ (Q Q )(Q L ) advantage of these considerable efforts and to identify abcd il jk i,a,α j,b,β k,c,γ l;d potential new signals in order to ensure that interesting 4 αβγ C C + yabcd (da,αub,β)(uc,γ `d) + h.c. ; (1) channels are not overlooked due to theoretical biases. where α; β; γ denote the color, i; j; k; l the SU(2)L, and a; b; c; d the family indices [14{18]. u, d, and ` are the In this work we revisit nucleon decay channels arising right-handed up-quark, down-quark, and lepton fields, from higher-dimensional operators and discuss some of while Q and L are the left-handed quark and lepton dou- the possible resulting final states. While systematically blets, respectively. The yj couplings have mass dimen- searching through all of the kinematically allowed nu- sion 2 and the first-generation entries are constrained cleon decay channels with increased final-state complex- to be−< ( (1015) GeV)−2 due to the induced two-body ity would constitute the strongest probes, this approach nucleon decays.O Specifically, all of the above operators quickly becomes highly impractical beyond the simplest generate the well-constrained decay p e+π0 with a of the modes. In view of this, we highlight the impor- rate of order ! inclusive nucleon decay searches tance of . Although these 2 searches are not as sensitive as exclusive ones looking at 1 yj Γ(p e+π0) 1111 : (2) a particular channel, they allow one to cover very broad 34 15 −2 ! ' 2 10 yr (3 10 GeV) parameter space in a model-independent manner and are × × practically far more feasible. This approach is particu- A variety of other two-body nucleon decay channels are larly fruitful to revisit in view of the upcoming large-scale induced as well, including muon and kaon modes once experiments. we consider second-generation flavor indices. Three-body decay modes with similar rates are induced as well [29] but ultimately lead to weaker constraints. This paper is organized as follows: in Sec. II we dis- Operators in d=6 involving either charm, top, bot- cuss higher-dimensional operators that lead to nucleon tom or tau are seeminglyL unconstrained by nucleon de- decay and argue in particular that many of them lead cay since these particles are heavier than the proton; it to multibody final states that are not covered in cur- is however possible to go through heavy off-shell par- rent searches. In Sec. III we provide a brief overview of ticles and still induce nucleon decay, as emphasized in current and upcoming detectors as well as existing ex- Ref. [30] for operators involving a tau and more gener- clusive nucleon-decay searches. We discuss and propose ally in Ref. [31] (see also Ref. [32] for a UV-complete possible inclusive searches as well as model-independent signatures in Sec. IV. Sec. V is devoted to a short dis- cussion of ∆B > 1 processes such as dinucleon decay, which would also profit from inclusive searches. Finally, 1 This approach does not cover the case of beyond-the-SM light + we conclude in Sec. VI. particles X that could lead for example to p ! ` + X [28]. 3 example with scalar leptoquarks).