Dijet invariant mass distribution near threshold

TL;DR

This paper employs soft-collinear effective theory to analyze and resum large threshold logarithms in the dijet invariant mass distribution near threshold in $e^+e^-$ annihilation, providing a systematic factorization approach.

Contribution

It introduces a novel factorization theorem that separates the cross section into hard, collinear, and soft parts, including a detailed treatment of soft gluon effects near threshold.

Findings

Resummed dijet invariant mass distribution to next-to-leading logarithmic accuracy.

Derived a universal factorization theorem applicable to various threshold processes.

Compared heavy and light quark dijet results, highlighting differences in soft gluon effects.

Abstract

In this paper, using soft-collinear effective theory we study the invariant mass distribution for dijet production in $e^+e^-$-annihilation. Near threshold, where the dijet takes most of the energy, there arise the large threshold logarithms, which are sensitive to soft gluon radiations. To systematically resum the logarithms, we factorize the scattering cross section into the hard, the collinear, and the soft parts. And we additionally factorize the original soft part into the global soft function and the two collinear-soft functions, where the latter can be combined with the collinear parts to form the fragmentation functions to jet (FFJs). The factorization theorem derived here can be easily applicable to other processes near threshold. Using the factorized result, we show the resummed result for the dijet invariant mass to the accuracy of next-to-leading logarithms. We have also obtained the result in the case of the heavy quark dijet and compared it with the case of the light quark.