The quark-gluon plasma produced in heavy-ion collisions is anisotropic throughout its evolution. This anisotropy changes the physics of jet-medium interaction, making it dependent on the momentum direction of the jet. In this paper we analyze transverse momentum broadening of a jet parton interacting with soft gluons in an anisotropic plasma. Our analysis equally applies to momentum broadening of quasiparticles in kinetic theory. We subtract contribution from instability modes in the deep infrared and discuss how our calculation should be complemented in that regime. The resulting anisotropic collision kernel for momentum broadening is qualitatively different from the equilibrium collision kernel and from the isotropic ansatz used in effective kinetic theory. Because of increased medium screening, there is substantially less transverse broadening at low and intermediate momenta.
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