# SCET 2017

Mar 14 – 16, 2017
Wayne State University
US/Eastern timezone

## Fragmentation to a jet with small radius and in the large $z$ limit

Mar 14, 2017, 10:50 AM
40m
McGregor Memorial Conference Center

### Speaker

Lin Dai (University of Pittsburgh)

### Description

We introduce the jet fragmentation function (JFF) to describe the fragmentation of a parton into a jet, and discuss how these objects are related to the standard jet functions. Calculating the JFF to next-to-leading order, we show that these objects satisfy the standard DGLAP evolution equations, with a natural scale that depends upon $R$. By using standard renormalization group evolution, we can therefore resum logarithms of $R$.

In the large $z$ limit, where $z$ is the ratio of the jet energy to the mother parton energy, large logarithms of both $R$ and $1 − z$ can appear, requiring resummation in order to have a well defined perturbative expansion. Using soft-collinear effective theory, we study the fragmentation function to a jet (FFJ) in this endpoint region. We derive a factorization theorem for this object, separating collinear and collinear-soft modes. This allows for the resummation using renormalization group evolution of the logarithms $\ln R$ and $\ln (1 − z)$ simultaneously.

### Primary authors

Lin Dai (University of Pittsburgh) Chul Kim (SeoulTech) Adam Leibovich (University of Pittsburgh)