# Subleading Power Rapidity Divergences and Power Corrections for $q_T$

## TL;DR

This paper explores subleading power rapidity divergences in quantum chromodynamics, introduces a new regulator within SCET, and computes power corrections to the $q_T$ spectrum, advancing understanding of logarithmic effects at subleading order.

## Contribution

It develops a novel rapidity regulator and scheme for subleading power divergences, and calculates power-suppressed corrections to the $q_T$ spectrum at order $
me^{
m o}(
m ext{alpha}_s)$.

## Key findings

- Power-law rapidity divergences appear at subleading power.
- Complete $q_T^2/Q^2$ suppressed power corrections are computed at $
m O(
m ext{alpha}_s)$.
- The new regulator maintains homogeneity of the power expansion.

## Abstract

A number of important observables exhibit logarithms in their perturbative description that are induced by emissions at widely separated rapidities. These include transverse-momentum ($q_T$) logarithms, logarithms involving heavy-quark or electroweak gauge boson masses, and small-$x$ logarithms. In this paper, we initiate the study of rapidity logarithms, and the associated rapidity divergences, at subleading order in the power expansion. This is accomplished using the soft collinear effective theory (SCET). We discuss the structure of subleading-power rapidity divergences and how to consistently regulate them. We introduce a new pure rapidity regulator and a corresponding $\overline{\rm MS}$-like scheme, which handles rapidity divergences while maintaining the homogeneity of the power expansion. We find that power-law rapidity divergences appear at subleading power, which give rise to derivatives of parton distribution functions. As a concrete example, we consider the $q_T$ spectrum for color-singlet production, for which we compute the complete $q_T^2/Q^2$ suppressed power corrections at $\mathcal{O}(\alpha_s)$, including both logarithmic and nonlogarithmic terms. Our results also represent an important first step towards carrying out a resummation of subleading-power rapidity logarithms.