Perturbative unitarity constraints on generic Yukawa interactions

TL;DR

This paper derives unitarity bounds on Yukawa couplings with arbitrary quantum numbers and applies these to models explaining anomalies in muon g-2 and B meson decays, showing the couplings are near perturbative limits.

Contribution

It provides compact formulas for Yukawa coupling bounds considering various group representations and applies them to phenomenological models of current anomalies.

Findings

Yukawa couplings in relevant models are near the perturbative limit.

Derived bounds depend on the fields' group representations.

Models can still explain anomalies within these unitarity constraints.

Abstract

We study perturbative unitarity constraints on generic Yukawa interactions where the involved fields have arbitrary quantum numbers under an $\prod_i SU(N_i) \otimes U(1)$ group. We derive compact expressions for the bounds on the Yukawa couplings for the cases where the fields transform under the trivial, fundamental or adjoint representation of the various $SU(N)$ factors. We apply our results to specific models formulated to explain the anomalous measurements of $(g-2)_\mu$ and of the charged- and neutral-current decays of the $B$ mesons. We show that, while these models can generally still explain the observed experimental values, the required Yukawa couplings are pushed at the edge of the perturbative regime.