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.
Vector Leptoquarks Beyond Tree Level II: $\mathcal{O}(\alpha_s)$ Corrections and Radial Modes · Around
J. C. Pati and A. Salam, Lepton Number as the Fourth Color , Phys. Rev. D10
1974
Earlier work this paper cites.
M. Bohm, H. Spiesberger and W. Hollik, On the One Loop Renormalization of the Electroweak Standard Model and Its Application to Leptonic Processes , Fortsch. Phys. 34