TMD factorization for dijet and heavy-meson pair in DIS

TL;DR

This paper develops a TMD factorization framework for di-jet and heavy-meson pair production in deep-inelastic scattering, introducing a new soft function and calculating its properties at one and two loops.

Contribution

It introduces a novel soft function for TMD factorization in DIS processes and computes its one-loop form and two-loop anomalous dimension.

Findings

Calculated the new soft function at one loop with rapidity divergence regulation.

Derived the two-loop anomalous dimension of the soft function.

Established the sensitivity of the cross-section to gluon TMD distributions.

Abstract

We study a transverse momentum dependent (TMD) factorization framework for the processes of di-jet and heavy meson pair production in deep-inelastic-scattering in an electron-proton collider, considering the measurement of the transverse momentum imbalance of the two hard probes in the Breit frame. For the factorization theorem we employ soft-collinear and boosted-heavy-quark effective field theories. The factorized cross-section for both processes is sensitive to gluon unpolarized and linearly polarized TMD distributions and requires the introduction of a new soft function. We calculate the new soft function here at one loop, regulating rapidity divergences with the $\delta$-regulator. In addition, using a factorization consistency relation and a universality argument regarding the heavy-quark jet function, we obtain the anomalous dimension of the new soft function at two loops.