Jet polarisation in an anisotropic medium

We study the evolution of an energetic jet which propagates in an anisotropic quark-gluon plasma, as created in the intermediate stages of ultrarelativistic heavy-ion collisions. We argue that the partons of the jet should acquire a non-zero average polarisation proportional to the medium anisotropy. We first observe that the medium anisotropy introduces a difference between the rates for transverse momentum broadening along the two directions perpendicular to the jet axis. In turn, this difference leads to a polarisation-dependent bias in the BDMPS-Z rates for medium-induced gluon branching. Accordingly, the daughter gluons in a branching process can carry net polarisation even if their parent gluon was unpolarised. Using these splitting rates, we construct kinetic equations which describe the production and transmission of polarisation via multiple branching in an anisotropic medium. The solutions to these equations show that polarisation is efficiently produced via quasi-democratic branchings, but then it is rapidly washed out by the subsequent branchings, due to the inability of soft gluons to keep trace of the polarisation of their parents. Based on that, we conclude that a net polarisation for the jet should survive in the final state if and only if the medium anisotropy is sizeable as the jet escapes the medium.