Speaker
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.
