A Subleading Power Operator Basis for the Scalar Quark Current

TL;DR

This work constructs a complete Soft Collinear Effective Theory (SCET) operator basis up to O(λ^2) for a color-singlet scalar produced by q q̄ annihilation, leveraging helicity building blocks to exploit angular-momentum constraints. It demonstrates how helicity selection rules dramatically simplify the basis, classifies all operators contributing to the cross section at this order, and performs tree-level matching to obtain their Wilson coefficients. Notably, ultrasoft-insertion coefficients vanish at tree level due to RPI relations, while subsubleading contributions are organized into well-defined operator classes (P_perp insertions, bbgg, bbqq, bbbb) with explicit Feynman rules. The results provide a foundation for systematic subleading-power calculations in both fixed-order and resummed perturbation theory, with direct relevance to Higgs production and other color-singlet scalar processes.

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 $λ\ll 1$ expansion. Here we present a complete basis of power suppressed operators for a scalar quark current at $\mathcal{O}(λ^2)$ 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 $\mathcal{O}(λ^2)$ 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.