Back-to-back heavy quark pair production in Semi-inclusive DIS

TL;DR

This paper calculates one-loop corrections to heavy quark pair production in semi-inclusive deep inelastic scattering within TMD factorization, including polarized gluon distributions and soft factors, providing new theoretical insights and observables.

Contribution

It introduces a one-loop correction framework for heavy quark pair production in SIDIS, incorporating polarized gluon TMDs and a soft factor, advancing the theoretical understanding of azimuthal distributions.

Findings

Derived finite hard coefficients using a subtraction method.

Identified the soft and collinear divergences proportional to tree level.

Constructed weighted cross sections to extract linearly polarized gluon distributions.

Abstract

The one-loop correction to heavy quark pair back-to-back production in unpolarized semi-inclusive deep inelastic scattering is given in this work in the framework of transverse momentum dependent(TMD) factorization. Both unpolarized and linearly polarized TMD gluon distribution functions are taken into account. A subtraction method based on diagram expansion is used to get finite hard coefficients. It is found the soft and collinear divergences of one-loop amplitude is proportional to tree level ones and can be expressed through several basic scalar triangle and bubble integrals. The subtraction of these divergences is spin independent. Beyond tree level an additional soft factor related to final heavy quark pair must be added into the factorization formula. This soft factor affects the azimuthal angle distribution of virtual photon in a nonperturbative way. Integrating over virtual photon azimuthal angle we construct three weighted cross sections, which depend on only three additional integrated soft factors. These weighted cross sections can be used to extract linearly polarized gluon distribution function. In addition, lepton azimuthal angle is unintegrated in this work, which provides more observables. All hard coefficients relevant to lepton and virtual photon azimuthal angle distributions are given at one-loop level.