# Effective Theory for a Heavy Scalar Coupled to the SM via Vector-Like Quarks

## TL;DR

This paper develops an effective field theory framework to analyze the decays of a heavy scalar coupled to the Standard Model via vector-like quarks, including detailed calculations of Wilson coefficients and resummation effects.

## Contribution

It applies the SCET$_{
m BSM}$ framework to a specific model with a heavy scalar and vector-like quarks, providing explicit Wilson coefficient calculations and decay rate analyses.

## Key findings

- Computed Wilson coefficients at leading, next-to-leading, and NNLO orders.
- Analyzed the impact of Sudakov logarithm resummation on decay rates.
- Provided a comprehensive EFT description for heavy scalar decays in this model.

## Abstract

We illustrate the application of the recently developed SCET$_{\rm BSM}$ framework in the context of a specific model, in which the Standard Model (SM) is supplemented by a heavy scalar $S$ and three generations of heavy, vector-like quarks $\Psi$. We construct the appropriate effective field theory for two-body decays of $S$ into SM particles. We explicitly compute the Wilson coefficients of the SCET$_{\rm BSM}$ operators appearing at leading and next-to-leading order (NLO) in an expansion in powers of $v/M_S$, as well as for a subset of operators arising at NNLO, retaining the full dependence on the ratio $M_S/M_\Psi$. For the phenomenologically most relevant decay channels of the heavy scalar, we study the impact of resummation effects of Sudakov logarithms on the decay rates.