Radiative corrections relating leptoquark-fermion couplings probed at low and high energy

Scalar leptoquarks (LQ) with masses between 2 TeV and 50 TeV are prime candidates to explain deviations between measurements and Standard-Model predictions in decay observables of $b$-flavored hadrons (``flavor anomalies''). Explanations of low-energy data often involve order-one LQ-quark-lepton Yukawa couplings, especially when collider bounds enforce a large LQ mass. This calls for the calculation of radiative corrections involving these couplings. Studying such corrections to LQ-mediated $b\to c\tau \nu$ and $b\to s\ell^+\ell^-$ amplitudes, we find that they can be absorbed into finite renormalizations of the LQ Yukawa couplings. If one wants to use Yukawa couplings extracted from low-energy data for the prediction of on-shell LQ decay rates, one must convert the low-energy couplings to their high-energy counterparts, which subsume the corrections to the on-shell LQ-quark-lepton vertex. We present compact formulae for these correction factors and find that in scenarios with $S_1$, $R_2$, or $S_3$ LQ the high-energy coupling is always smaller than the low-energy one, which weakens the impact of collider data on the determination of the allowed parameter spaces. For the $R_2$ scenario addressing $b\to c\tau \nu$, in which one of the two involved Yukawa coupling must be significantly larger than 1, we find this coupling reduced by 15\% at high energy. If both $S_1$ and $R_2$ are present, the high-energy coupling can also be larger and the size of the correction is unbounded, because tree contribution and vertex corrections involve different couplings. We further present the conversion formula to the $\overline{\rm MS}$ scheme for the Yukawa couplings of the $S_3$ scenario.