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 $p\to {\pi }^0{e}^{+}$ indicates gauge boson mediation, with the potential for observation of $p\to {\eta }^0{e}^{+}$ mode. Alternatively, if decay is through the $p\to K^{+}\overline{\nu }$ 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 $p\to {\pi }^{+}\overline{\nu }$, $p\to {\eta }^0{\mu }^{+}$, $p\to K^0{e}^{+}$, 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 both accurately and precisely constrain the parameter space of the $SU(5)$ model in question.

Figure 1

The Feynman diagrams of the leading order contribution toward Majorana neutrino masses at the $SU(5)$ (left panel) and the SM (right panel) levels.

Figure 2

Viable parameter space of the model (shaded in gray) for the $M\ge 1\mathrm{TeV}$ and $M\ge 10\mathrm{TeV}$ scenarios with contours of constant values for $M_{\mathrm{GUT}}/({10}^{15}\mathrm{GeV})$ (red solid lines), ${\alpha }_{\mathrm{GUT}}$ (blue dot-dashed lines), and $m_0/(\sqrt{\mathrm{\Delta }{m}_{31}^2}/2)$ (green solid lines). For additional details, see the text.

Figure 3

Proton decay signatures via gauge boson and scalar leptoquark mediations within $M\ge 1\mathrm{TeV}$ and $M\ge 10\mathrm{TeV}$ scenarios for four specific points and eight channels, as indicated. Black lines are current experimental limits, blue vertical bars are predictions for gauge boson mediation signatures, red vertical bars are predictions for the scalar leptoquark mediations, and gray dashed lines represent future experimental sensitivities after a ten-year period of data taking at 90% C.L.

Figure 4

Contours of constant $\mathrm{\Gamma }(p\to {\pi }^0{\mu }^{+})$ for the gauge boson (blue) and scalar leptoquark (red) mediation for points Q and ${\mathrm{Q}}^{\prime }$, as indicated.