A Subleading Power Operator Basis for the Scalar Quark Current

TL;DR

This paper develops a complete operator basis at subleading power for scalar quark currents within Soft Collinear Effective Theory, aiding the understanding of power corrections in collider processes involving scalar production.

Contribution

It introduces a comprehensive basis of power suppressed operators at () order, utilizing helicity selection rules to simplify the construction and classify relevant operators for scalar production.

Findings

Constructed a complete operator basis at () in SCET.

Performed tree level matching to determine Wilson coefficients.

Facilitated analysis of power corrections in collider factorization.

Abstract

Factorization theorems play a crucial role in our understanding of the strong interaction. For collider processes they are typically formulated at leading power and much less is known about power corrections in the $\lambda\ll 1$ expansion. Here we present a complete basis of power suppressed operators for a scalar quark current at $\mathcal{O}(\lambda^2)$ in the amplitude level power expansion in the Soft Collinear Effective Theory, demonstrating that helicity selection rules significantly simplify the construction. This basis applies for the production of any color singlet scalar in $q\bar{q}$ annihilation (such as $b \bar b \to H$). We also classify all operators which contribute to the cross section at $\mathcal{O}(\lambda^2)$ and perform matching calculations to determine their tree level Wilson coefficients. These results can be exploited to study power corrections in both resummed and fixed order perturbation theory, and for analyzing the factorization properties of gauge theory amplitudes and cross sections at subleading power.