# Next-to-leading power corrections to $V+1$ jet production in $N$-jettiness subtraction

## TL;DR

This paper analytically derives and validates next-to-leading power corrections to one-jet production in N-jettiness subtraction, improving precision in perturbative QCD calculations for vector-boson plus jet processes.

## Contribution

It provides the first analytical derivation of NLP-LL corrections for one-jet production in N-jettiness subtraction, including universal and process-dependent factors.

## Key findings

- Derived NLP-LL corrections through ${\cal O}(\alpha_S)$
- Presented simple formulae separating universal and process-dependent NLP corrections
- Validated analytic results with numerical comparisons showing good agreement

## Abstract

We discuss the subleading power corrections to one-jet production processes in $N$-jettiness subtraction using vector-boson plus jet production as an example. We analytically derive the next-to-leading power leading logarithmic corrections (NLP-LL) through ${\cal O}(\alpha_S)$ in perturbative QCD, and outline the calculation of the next-to-leading logarithmic corrections (NLP-NLL). Our result is differential in the jet transverse momentum and rapidity, and in the vector boson momentum squared and rapidity. We present simple formulae that separate the NLP corrections into universal factors valid for any one-jet cross section and process-dependent matrix-element corrections. We discuss in detail features of the NLP corrections such as the process independence of the leading-logarithmic result that occurs due to the factorization of matrix elements in the subleading soft limit, the occurrence of poles in the non-hemisphere soft function at NLP and the cancellation of potential $\sqrt{\mathcal{T}_1/Q}$ corrections to the $N$-jettiness factorization theorem. We validate our analytic result by comparing them to numerically-fitted coefficients, finding good agreement for both the inclusive and the differential cross sections.