Resummation for heavy quark and jet cross sections
Nikolaos Kidonakis
TL;DR
The paper develops a comprehensive, color-space framework for threshold resummation in hadronic production of heavy quarks, dijets, direct photons, and W bosons. It derives and diagonalizes soft anomalous dimension matrices for a wide set of partonic channels, enabling RG-improved resummed cross sections at next-to-leading and higher logarithmic accuracy. Fixed-order expansions up to one- and two-loops are provided and shown to agree with exact NLO results in relevant limits, with numerical demonstrations for top-quark production at the Tevatron. The formalism is general and adaptable to differential distributions, offering improved precision for high-mass final states in hadron collisions and guiding future phenomenological applications.
Abstract
We review the resummation of threshold logarithms for heavy quark, dijet, direct photon, and W boson production cross sections in hadronic collisions. Beyond leading logarithms the resummed cross section is sensitive to the color exchange in the hard scattering. The resummation is formulated at next-to-leading logarithmic or higher accuracy in terms of anomalous dimension matrices which describe the factorization of soft gluons from the hard scattering. We give results for the soft anomalous dimension matrices at one loop for the full range of partonic subprocesses involved in heavy quark, dijet, direct photon, and W boson production. We discuss the general diagonalization procedure that can be implemented for the calculation of the resummed cross sections, and we give numerical results for top quark production at the Fermilab Tevatron. We also present analytical results for the one- and two-loop expansions of the resummed cross sections.