Proton stability in grand unified theories, in strings, and in branes

TL;DR

This review comprehensively surveys proton stability across non-SUSY and SUSY grand unifications, extra-dimensional GUTs, and string/M-theory constructions. It details how proton decay probes unification scales via dimension-6 gauge operators and dimension-5 Higgs-triplet operators, while emphasizing suppression mechanisms such as doublet-triplet splitting, R-parity, and higher-dimensional symmetries. The work synthesizes experimental bounds with theoretical predictions, outlines how texture and Planck-scale effects shape decay channels and lifetimes, and discusses future experiments that could decisively discriminate among competing unification schemes. It also highlights the interplay between proton stability, neutrino masses, dark matter, and quantum gravity effects, outlining a roadmap for using proton decay as a window into fundamental theory. Overall, proton decay remains a critical, testable probe of the structure and scale of unification, with a broad landscape of models offering distinctive decay patterns and lifetimes.

Abstract

A broad overview of the current status of proton stability in unified models of particle interactions is given which includes non - supersymmetric unification, SUSY and SUGRA unified models, unification based on extra dimensions, and string-M-theory models. The extra dimensional unification includes 5D and 6D and universal extra dimensional (UED) models, and models based on warped geometry. Proton stability in a wide array of string theory and M theory models is reviewed. These include Calabi-Yau models, grand unified models with Kac-Moody levels $k>1$, a new class of heterotic string models, models based on intersecting D branes, and string landscape models. The destabilizing effect of quantum gravity on the proton is discussed. The possibility of testing grand unified models, models based on extra dimensions and string-M-theory models via their distinctive modes is investigated. The proposed next generation proton decay experiments, HyperK, UNO, MEMPHYS, ICARUS, LANNDD (DUSEL), and LENA would shed significant light on the nature of unification complementary to the physics at the LHC. Mathematical tools for the computation of proton lifetime are given in the appendices. Prospects for the future are discussed.

Figures (11)

• Figure 1: Idealized $p \to e^+ \pi^0$ decay in Super-Kamiokande Viren:1999pk.
• Figure 2: Idealized $p \to K^+ \nu$ decay in Super-Kamiokande, $K^+ \to \pi^+ \pi^0$ case Viren:1999pk
• Figure 3: Idealized $p \to K^+ \nu$ decay in Super-Kamiokande, $K^+ \to \mu^+\nu_{\mu}$ case Viren:1999pk
• Figure 4: Experimental lower bounds on proton decay partial lifetimes Rubbia:2004yq
• Figure 5: Gauge contributions to the decay of the proton. In this case the decay of the proton is mediated by vector leptoquarks. The fields $\Psi$, $\psi$ and $\Phi$ are quark fields and $l$ corresponds to the leptons. A possible contribution is: $\Psi=u_L$, $\psi=(u^C)_L$, $\Phi=(d^C_{\alpha})_L$ and $l=e_{\beta L}$. $\alpha, \beta=1,2$.