# Helicity Methods for High Multiplicity Subleading Soft and Collinear Limits

## TL;DR

This paper develops helicity-based methods to analyze subleading power corrections in soft and collinear limits of multi-leg gauge theory amplitudes, enabling more precise calculations for multi-jet observables at the LHC.

## Contribution

It introduces a novel combination of spinor-helicity expansion and effective theory relations to efficiently extract subleading power logarithms in high multiplicity amplitudes.

## Key findings

- Power law singularities from amplitude expansions lead to derivatives of parton distributions.
- Techniques enable efficient computation of power corrections for N-jettiness at the LHC.
- Subleading power effects can be systematically included in amplitude analyses.

## Abstract

The factorization of multi-leg gauge theory amplitudes in the soft and collinear limits provides strong constraints on the structure of amplitudes, and enables efficient calculations of multi-jet observables at the LHC. There is significant interest in extending this understanding to include subleading powers in the soft and collinear limits. While this has been achieved for low point amplitudes, for higher point functions there is a proliferation of variables and more complicated phase space, making the analysis more challenging. By combining the subleading power expansion of spinor-helicity variables in collinear limits with consistency relations derived from the soft collinear effective theory, we show how to efficiently extract the subleading power leading logarithms of $N$-jet event shape observables directly from known spinor-helicity amplitudes. At subleading power, we observe the presence of power law singularities arising solely from the expansion of the amplitudes, which for hadron collider event shapes lead to the presence of derivatives of parton distributions. The techniques introduced here can be used to efficiently compute the power corrections for $N$-jettiness subtractions for processes involving jets at the LHC.