Vector Leptoquarks Beyond Tree Level II: $\mathcal{O}(\alpha_s)$ Corrections and Radial Modes

TL;DR

This paper provides a detailed analysis of next-to-leading order QCD corrections and radial mode effects in models with vector leptoquarks, clarifying their impact on low- and high-energy observable relations.

Contribution

It extends previous work by computing complete $ ext{O}(rac{ ext{alpha}_s}{ ext{alpha}_4})$ corrections and analyzing radial mode effects in a flavor non-universal gauge model.

Findings

$ ext{O}(rac{ ext{alpha}_s}{ ext{alpha}_4})$ corrections are below 10%.

Radial modes significantly influence the renormalization process.

QCD corrections are subleading compared to leading leptoquark coupling effects.

Abstract

We clarify open issues in relating low- and high-energy observables, at next-to-leading order accuracy, in models with a massive leptoquark embedded in a flavor non-universal $SU(4) \times SU(3) \times SU(2) \times U(1)$ gauge group. Extending previous work on this subject, we present a complete analysis of the $\mathcal{O}(\alpha_s)$ corrections to the matching conditions of semileptonic operators at the high scale. These corrections are not negligible, but they do not exceed the 10% level and are subleading compared to the $\mathcal{O}(\alpha_4)$ corrections proportional to the leading leptoquark coupling, which is expected to be much larger than the QCD coupling in the parameter space region of phenomenological interest. We further analyze the impact of radial modes, both at $\mathcal{O}(\alpha_4)$ and at $\mathcal{O}(\alpha_s)$ accuracy, highlighting their role in the renormalization of the theory.