Gauge and Scalar Boson Mediated Proton Decay in a Predictive SU(5) GUT Model

We assess proton decay signatures in the simplest viable $SU(5)$ model with regard to constraints on parameters governing the Standard Model fermion mass spectrum. Experimental signals for all eight two-body proton decay processes result from exchange of two gauge bosons, a single scalar leptoquark, or their combination. Consequently, it enables us to delve into an in-depth anatomy of proton decay modes and anticipate future signatures. Our findings dictate that observing a proton decay into $p\to\pi^0e^+$ indicates gauge boson mediation, with the potential for observation of $p\to\eta^0e^+$ mode. Alternatively, if decay is through $p\to K^+\overline\nu$ process, it is mediated by a scalar leptoquark, possibly allowing the observation of $p\to\pi^0\mu^+$. Detection of both $p\to\pi^0 e^+$ and $p\to K^+\overline\nu$ could enhance $p\to\pi^0\mu^+$ through constructive interference. The model predicts inaccessibility of $p\to\pi^+\overline\nu$, $p\to\eta^0\mu^+$, $p\to K^0e^+$, and $p\to K^0\mu^+$, regardless of the dominant mediation type, in the coming decades. In summary, through a comprehensive analysis of proton decay signals, gauge coupling unification, and fermion masses and mixing, we precisely constrain the parameter space of the $SU(5)$ model in question.