# The role of the $S_3$ GUT leptoquark in flavor universality and collider searches

## TL;DR

This paper explores how the $S_3$ scalar leptoquark, emerging from an $SU(5)$ GUT model, can explain recent lepton universality violations in B meson decays, and assesses its detectability at colliders through flavor and collider data.

## Contribution

It demonstrates the viability of the $S_3$ leptoquark in addressing flavor anomalies within an $SU(5)$ GUT framework, including the role of a second leptoquark $ ilde{R}_2$ for gauge unification.

## Key findings

- Large $S_3$ couplings to $ au$ leptons are favored by global fits.
- $B o K^{(*)} ar
u
u$ decay is highly sensitive to the model parameters.
- Collider searches for $ au$ final states constrain the leptoquark parameter space.

## Abstract

We investigate the ability of the $S_3$ scalar leptoquark to address the recent hints of lepton universality violation in $B$ meson decays. The $S_3$ leptoquark with quantum numbers $(\overline{\mathbf{3}},\mathbf{3},1/3)$ naturally emerges in the context of an $SU(5)$ GUT model without any conflict with the stringent limits from observed nucleon stability. Scalar leptoquark $S_3$ with left-handed couplings to 2nd and 3rd generations of charged leptons and down-type quarks seems well-suited to address both $R_{K^{(*)}}$ and $R_{D^{(*)}}$. We quantify this suitability with numerical fits to a plethora of relevant flavor observables. The proposed $SU(5)$ model calls for a second leptoquark state, i.e., $\tilde{R}_2$ with quantum numbers $(\mathbf{3},\mathbf{2},1/6)$, if one is to generate gauge coupling unification and neutrino mass. We accordingly include it in our study to investigate $\tilde{R}_2$'s ability to offset adverse effects of $S_3$ and thus improve a quality of numerical fits. A global fit of the leptoquark Yukawa couplings shows that large couplings of light $S_3$ to $\tau$ leptons are preferred. We furthermore identify $B \to K^{(*)} \bar\nu\nu$ as the most sensitive channel to probe the preferred region of parameter space. Large couplings of $S_3$ to $\tau$ leptons are finally confronted with the experimental searches for $\tau$ final states at the Large Hadron Collider. These searches comprise a study of decay products of the leptoquark pair production, as well as, and more importantly, an analysis of the high-mass $\tau\tau$ final states.