A complete set of in-medium splitting functions to any order in opacity

Matthew D Sievert,Ivan Vitev,Boram Yoon

doi:10.1016/j.physletb.2019.06.019

Matthew D Sievert, Ivan Vitev + Show 1 more

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https://doi.org/10.1016/j.physletb.2019.06.019

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Abstract

In this Letter we report the first calculation of all O(αs) medium-induced branching processes to any order in opacity. Our splitting functions results are presented as iterative solutions to matrix equations with initial conditions set by the leading order branchings in the vacuum. The flavor and quark mass dependence of the in-medium q→qg, g→gg, q→gq, g→qq¯ processes is fully captured by the light-front wavefunction formalism and the color representation of the parent and daughter partons. We include the explicit solutions to second order in opacity as supplementary material and present numerical results in a realistic strongly-interacting medium produced in high center-of-mass energy heavy ion collisions at the Large Hadron Collider. Our numerical simulations show that the second order in opacity corrections can change the energy dependence of the in-medium shower intensity. We further find corrections to the longitudinal and angular distributions of the in-medium splitting kernels that may have important implications for jet substructure phenomenology.

Highlights

In Quantum Chromodynamics (QCD), the probability of one parton to split into a two-parton system is governed by the well-known Altarelli-Parisi splitting functions in vacuum [1]
These probabilities are the key ingredients in all modern high-precision calculations in the theory of strong interactions and in Monte-Carlo event generators for high energy physics
Quark and gluon splitting kernels play an essential role in understanding the radius dependence of inclusive cross sections and of jet substructure

Summary

INTRODUCTION

In Quantum Chromodynamics (QCD), the probability of one parton to split into a two-parton system is governed by the well-known Altarelli-Parisi splitting functions in vacuum [1]. Works investigated the convergence of the opacity series to second and third order, utilizing the soft gluon emission limit available at the time [14, 18] These studies used models of the QCD medium density carefully chosen to smooth out the non-Abelian LPM interference pattern, making certain integrals analytically calculable. The rest of our Letter is organized as follows: in Section II we outline the analytic derivation of all medium-induced splitting functions Their numerical evaluation is discussed, and explicit new results to second order in opacity are given.

UNIVERSAL FEATURES OF MEDIUM-INDUCED PARTON BRANCHING

RESULTS

CONCLUSIONS