# The Energy Distribution of Subjets and the Jet Shape

## TL;DR

This paper develops a theoretical framework to analyze the energy distribution within subjets of a jet, incorporating resummation techniques and addressing previous inconsistencies, with applications to proton-proton collisions.

## Contribution

It introduces a factorization approach for subjet energy distributions at small radii, resolves previous inconsistencies, and improves jet shape calculations by including recoil effects.

## Key findings

- Provides one-loop matching coefficients for subjet distributions.
- Resolves inconsistencies in previous cone jet results.
- Numerical results for jet shapes in proton-proton collisions at NLO+LL.

## Abstract

We present a framework that describes the energy distribution of subjets of radius $r$ within a jet of radius $R$. We consider both an inclusive sample of subjets as well as subjets centered around a predetermined axis, from which the jet shape can be obtained. For $r \ll R$ we factorize the physics at angular scales $r$ and $R$ to resum the logarithms of $r/R$. For central subjets, we consider both the standard jet axis and the winner-take-all axis, which involve double and single logarithms of $r/R$, respectively. All relevant one-loop matching coefficients are given, and an inconsistency in some previous results for cone jets is resolved. Our results for the standard jet shape differ from previous calculations at next-to-leading logarithmic order, because we account for the recoil of the standard jet axis due to soft radiation. Numerical results are presented for an inclusive subjet sample for $pp \to {\rm jet}+X$ at next-to-leading order plus leading logarithmic order.