# Probing low energy scalar leptoquarks by the leptonic $W$ and $Z$ couplings

## TL;DR

This paper calculates detailed one-loop effects of scalar leptoquarks on W and Z leptonic decays, including finite terms and external momenta corrections, revealing significant impacts on precision electroweak constraints.

## Contribution

It provides the first comprehensive calculation of finite and momentum-dependent corrections to leptoquark contributions, improving upon previous leading-logarithmic approximations.

## Key findings

- Finite terms can be as large as 20% for LQ masses below 1.5 TeV.
- Corrections can significantly affect constraints from Z-pole data.
- Results impact models addressing B-physics anomalies.

## Abstract

We compute the generic one-loop contribution involving scalar leptoquarks (LQ) to the $W$ and $Z$ leptonic decay widths. In our computation we include for the first time the finite terms and the corrections due to the external momenta of the electroweak bosons, which is a step beyond the leading-logarithmic approximation considered in the literature so far. We show that the terms we include can be numerically quite significant. They amount to about $20\%$ for scalar LQ masses below $1.5$~TeV, as currently allowed by the direct searches at the LHC. To further illustrate the relevance of our results we revisit a model with two light scalar LQs, proposed to accommodate the $B$-physics anomalies. We show that the finite terms we computed can reduce the tension with the $Z$-pole data.