Medium-induced parton splitting kernels from Soft Collinear Effective Theory with Glauber gluons

TL;DR

This paper derives comprehensive medium-induced parton splitting kernels within Soft Collinear Effective Theory with Glauber gluons, including corrections beyond small-x approximation, and provides analytic results for simplified scenarios to aid phenomenological modeling.

Contribution

It introduces a complete derivation of medium-induced parton splitting kernels using extsc{SCET}_G, incorporating all relevant corrections and offering analytic solutions for simplified cases.

Findings

Derived splitting kernels including all corrections beyond small-x approximation.

Provided analytic results for infinite transverse momentum and uniform medium scenarios.

Demonstrated numerical implementation of medium recoil, geometry, and phase space cuts.

Abstract

We derive the splitting kernels for partons produced in large $Q^2$ scattering processes that subsequently traverse a region of strongly-interacting matter using a recently-developed effective theory \SCETG. We include all corrections beyond the small-$x$ approximation, consistent with the power counting of \SCETG. We demonstrate how medium recoil, geometry and expansion scenarios, and phase space cuts can be implemented numerically for phenomenological applications. For the simplified case of infinite transverse momentum kinematics and a uniform medium, we provide closed-form analytic results that can be used to validate the numerical simulations.