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

TL;DR

The authors develop SCET_G to describe jet propagation in dense QCD matter and derive all medium-induced parton splitting kernels at first order in opacity, including finite-x corrections, recoil, and phase-space effects. They provide a unified framework with universal transverse momenta and interference phases, reproducing vacuum Altarelli-Parisi kernels at tree level and matching soft-gluon energy-loss limits in the small-x regime. They present explicit expressions for q->qg, q->gq, g->gg, and g->qqbar splittings, plus analytic benchmarks for uniform matter and a master formula enabling numerical implementation. Numerical studies quantify the impact of finite-x, kinematic cuts, and recoil on the splitting intensities, demonstrating the necessity of moving beyond the traditional small-x approximations for accurate jet quenching phenomenology.

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.

Figures (3)

• Figure 1: Feynman diagrams contributing to medium-induced splittings at first order in opacity. Red lines corresponds to Glauber gluons. The kinematics and topology are common to all splitting processes: $q\rightarrow qg$, $g\rightarrow gg$, $g\rightarrow q \bar{q}$, $q\rightarrow gq$.
• Figure 2: The intensity spectrum $x(dN/dx)$ for infinite phase space cuts and neglecting nuclear recoil is shown as a function of the splitting parameter $x$. Comparison of the analytic formulas in Eq. \ref{['finalanalytics01']}-Eq. \ref{['finalanalytics03']} (solid lines) to a numerical integration method (dashed lines) are presented. We also illustrate the difference between the full in-medium splitting results and the small-$x$ approximation on the example of a parton of initial energy $E_0=100\text{GeV}$. The medium parameters are set to: $\mu=0.75~\mathrm{GeV}, \,\lambda_g=1\text{ fm}, \,L=5\text{ fm}$ for definiteness and the scattering length is independent of $\Delta z$.
• Figure 3: Illustration of the effect of phase space cuts and medium recoil on the medium-induced parton splitting. The same QCD medium parameters and initial jet energy as in figure \ref{['fig:numerics']} are used.