Abstract
In factorization formulae for cross sections of scattering processes, final-state jets are described by jet functions, which are a crucial ingredient in the resummation of large logarithms. We present an approach to calculate generic one-loop jet functions, by using the geometric subtraction scheme. This method leads to local counterterms generated from a slicing procedure; and whose analytic integration is particularly simple. The poles are obtained analytically, up to an integration over the azimuthal angle for the observable- dependent soft counterterm. The poles depend only on the soft limit of the observable, characterized by a power law, and the finite term is written as a numerical integral. We illustrate our method by reproducing the known expressions for the jet function for angularities, the jet shape, and jets defined through a cone or kT algorithm. As a new result, we obtain the one-loop jet function for an angularity measurement in e+e− collisions, that accounts for the formally power-suppressed but potentially large effect of recoil. An implementation of our approach is made available as the GOJet Mathematica package accompanying this paper.
Highlights
Large logarithms arise because the cross section involves multiple scales that are widely separated
In this paper we focus on calculating one-loop jet functions, which enter in resummed cross sections starting at next-to-leading logarithmic (NLL ) accuracy
In this paper we developed an automated approach for calculating one-loop jet functions, and provide an implementation in the accompanying Mathematica package called GO
Summary
Technical aspects related to the treatment of Heaviside theta functions in our calculation and infrared safety are discussed in sections 2.2 and 2.3, respectively.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have