Experimental Tests of Baryon and Lepton Number Conservation

TL;DR

This paper surveys experimental tests of Baryon number and Lepton number conservation, explaining that these are accidental symmetries in the SM and that their violation points to new organizing principles such as unification and the origin of the cosmic matter-antimatter asymmetry. It adopts a unified EFT framework to classify violations by operator content and dimensionality, connecting low-energy observables to high-scale physics and to UV completions like GUTs, SUSY, and extra dimensions. The review compares a broad spectrum of experimental approaches, including nucleon decays, neutron-antineutron oscillations, neutrinoless double beta decay, charged-lepton flavor violation, and cosmology, emphasizing complementarity across detectors, processes, and energy scales. It argues that discoveries or increasingly stringent null results constrain the underlying theory, inform the origin of neutrino masses and baryogenesis, and motivate diversified experimental programs that probe the stability of matter and the fundamental organizing principles of nature.

Abstract

Baryon number ($B$) conservation underlies the apparent stability of ordinary matter by forbidding the decay of nucleons, while lepton number ($L$) conservation plays a central role in the structure of lepton interactions and the possible origin of neutrino mass. In the Standard Model, $B$ and $L$ are accidental global symmetries rather than imposed fundamental principles. However, they are expected to be violated in many extensions of the theory, including frameworks of unification and processes in the early Universe. This review summarizes the status of experimental tests of $B$ and $L$ conservation and discusses them within a unified framework for interpreting current and future searches across different processes and experimental approaches, outlining historical and theoretical motivation, key physical processes, as well as their broader connections and complementarity to other searches.

Figures (8)

• Figure 1: Representative processes of baryon number ($B$) and lepton number ($L$) violation. (a) Proton decay illustrated by $p \to e^{+}\pi^{0}$ that violates $\Delta B = 1$ and $\Delta L = 1$. (b) Neutron-antineutron ($n-\bar{n}$) oscillations that induce $\Delta B = 2$ violation. (c) Neutrinoless double-beta decay ($0\nu\beta\beta$) that induces $\Delta L = 2$ in nuclear transitions.
• Figure 2: Schematic flow from fundamental theory to experimental observables. Symmetry constraints and selection rules govern the allowed structures at each analysis stage, while effective descriptions provide a universal bridge between microscopic theory and experimentally accessible observables.
• Figure 3: Landscape of $B$-violating and $L$-violating transitions in the $(\Delta B,\Delta L)$ plane, indicating the lowest SMEFT operator dimension $d$ at which each class can arise. Adapted from Ref. Heeck:2019kgr and extended to incorporate lepton flavor violation.
• Figure 4: Historical evolution of experimental lower limits on the proton partial lifetime, primarily corresponding to the benchmark decay channel $p \rightarrow e^+ \pi^0$. Earlier results based on more general or distinct searches are included to illustrate the development of techniques. Detection principles are denoted as follows: liquid scintillator (SC, Ref. Reines:1954pgReines:1958pfBackenstoss1960Giamati:1962peKropp:1965pdGurr:1967pcBergamasco1974Reines:1974pb), searches for fission fragments from radioactive ore (FI, using $^{232}$Th Flerov:1958zz, $^{130}$Te EvansJr:1977zuj, $^{39}$K Fireman:1979xr), and fine-grained calorimeters primarily employing iron $^{26}$Fe (IC, from NUSEX Battistoni:1982vv, KGF Krishnaswamy:1985tho, Soudan Soudan-1:1986zji, Frejus Frejus:1990myz experiments), water Cherenkov (WC, from Homestake Cherry:1981uq, IMB Irvine-Michigan-Brookhaven:1983iapGajewski:1989ghMcGrew:1999nd, Kamiokande Arisaka:1985lki, Super-Kamiokande Super-Kamiokande:1998maeSuper-Kamiokande:2009yitSuper-Kamiokande:2016exgSuper-Kamiokande:2020wjk experiments). A confirmed detection signal would manifest as a finite measured lifetime, and the historical record contextualizes sensitivity evolution up to discovery.
• Figure 5: Illustrative relationship between the effective scale $\Lambda$ of physics beyond SM and the nucleon lifetime $\tau$ for $\Delta B = 1$ operators of different mass dimension $d$, assuming order unity Wilson coefficients and dimensional analysis up to hadronic matrix elements and phase-space factors. Horizontal lines indicate representative benchmark lifetimes $\tau \sim 10^{30}$ years and $\tau \sim 10^{35}$ years. If $B$ violation is observed, a measured lifetime would map onto a corresponding scale $\Lambda$ for each operator class, enabling interpretation of the underlying physics.