Threshold Resummation for Dijet Cross Sections

TL;DR

The paper develops a factorization-based framework for threshold resummation of dijet cross sections at large momentum transfer, extending prior heavy-quark results to massless final-state partons and highlighting the role of color exchange. By decomposing the cross section into initial-state jets, final-state jets, and a soft function connected through a hard scattering in color space, it derives how soft-gluon radiation is governed by a soft anomalous-dimension matrix and Mellin-space evolution. It shows that initial-state radiation enhances the cross section while final-state jets induce Sudakov suppression, with the net effect depending on the color structure of the subprocess and the jet definition. The formalism is general across jet algorithms and lays out a path to explicit resummed expressions, with future work to compute the soft anomalous dimensions and deliver LL and NLL results for various flavor channels.

Abstract

We construct dijet differential cross sections at large momentum transfer, in which threshold logarithms have been summed to all orders in perturbation theory. This extends previous work on heavy quark production, by treating collinear singularities associated with hard, massless partons in the final state. The resummed corrections enable us to define, in the sense of factorization, the underlying color exchange mechanism. The influence of color exchange on the resummed cross section is contained in the eigenvalues and eigenvectors of an anomalous dimension matrix, which describes the factorization of coherent soft gluons from the hard scattering. The precise formulas depend on the partonic scattering angles and energies, as well as on the method used to define the jets in the final state. For cone dijets at fixed invariant mass, we find leading logarithmic corrections that, like those in the Drell-Yan process, are positive, and which grow with increasing dijet invariant mass. Other choices of dijet cross section can give, however, qualitatively different behavior, even at leading logarithm.

Figures (4)

• Figure 1: Configuration of cones in the partonic center of mass frame at partonic threshold.
• Figure 2: Reduced diagram that represents the generic leading region for the dijet cross section.
• Figure 3: Factorized form of the cross section into initial-state and final-state jet functions ($\psi$ and $J$, respectively) and the color-dependent soft function $S_{LI}^{({\rm f})}$. At lowest order, $S_{LI}^{({\rm f})}$ is given simply by the set of all diagrams in which a single gluon connects any two ordered eikonal lines moving in different directions. The construction of $S_{LI}^{({\rm f})}$ beyond lowest order in discussed in Sec. 3.2.
• Figure 4: Factorized eikonal cross section. With an appropriate choice of color normalization factor $1/{\cal N}$, the soft function $S^{({\rm f})}_{LI}$ is the same as in Fig. \ref{['factfig']}. The eikonal jet functions $j_{\rm OUT}$ and $j_{\rm IN}$ are defined in Eqs. ( \ref{['eq:eikjet']}) and ( \ref{['eq:eikoutjet']}), respectively.