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

Matthew D. Sievert, Ivan Vitev, and Boram Yoon

1903.06170

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→q qbar processes is fully captured by the light-

The fraction of a parton's energy carried away by certain medium-induced QCD branching processes at first and second orders in opacity. This quantity loosely corresponds to "radiative parton energy loss," although in this case the fraction of radiated energy need not be small. Note that for light quarks and for gluons, the second-order corrections result in a flattening of the "energy loss" dependence: less energy loss for lower-energy partons, and more energy loss for higher-energy partons.

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.