Anomalies and accidental symmetries: charging the scalar leptoquark under $L_\mu$-$L_\tau$

TL;DR

This paper proposes gauging the $L_-_ au$ symmetry to address conceptual issues with the $S_3$ scalar leptoquark explanation of flavor anomalies, showing it can be consistent with high-scale physics and constraining its mass to a few TeV.

Contribution

It introduces a gauged $L_ - L_ au$ symmetry to resolve problems with the $S_3$ leptoquark model and analyzes the mass scales compatible with stability and experimental bounds.

Findings

Gauging $L_ - L_ au$ removes diquark and lepton flavor violation issues.

Leptoquark mass cannot be much heavier than a few TeV without destabilizing the Higgs.

Additional $U(1)$ gauge symmetry can be hidden at high scales without affecting low-energy phenomenology.

Abstract

While the $S_3$ scalar leptoquark presents a possible tree-level explanation of the $b \to s \ell \ell$ flavour anomalies, it suffers from two conceptual problems which are often disregarded by model-builders. Firstly, the quantum numbers of the $S_3$ allow for a renormalisable diquark operator that would trigger rapid proton decay unless its coupling were tuned away. Secondly, one expects the leptoquark to have generic couplings to leptons, which require tuning to avoid stringent experimental bounds on lepton flavour violation. By gauging a $U(1)$ current that acts as $L_\mu - L_\tau$ on the Standard Model (SM) fermions, and under which the leptoquark has charge $-1$, one can remedy both these problems. The additional $U(1)$, which is spontaneously broken at some high scale, is associated with a massive $Z^\prime$ gauge boson and a scalar SM singlet $\Phi$, which play no direct role in mediating the anomalous $B$ meson decays. By computing one- and two-loop mass corrections, we show that this pair of particles can be hidden away at much higher mass scales without destabilising either the Higgs or the leptoquark masses. The only low-energy relic of gauging $L_\mu - L_\tau$ is thus the accidental global symmetry structure of the lagrangian. On the other hand, we find quite generally that an $S_3$ leptoquark that mediates the $b \to s \ell \ell$ anomalies cannot be much heavier than a few TeV without itself inducing large Higgs mass corrections.