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

Understand

In this Letter we report the first calculation of all ${\cal O}(\alpha_s)$ 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 $q \rightarrow qg$, $g\rightarrow gg$, $q \rightarrow g q$, $g \rightarrow q\bar{q}$ 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.