Transport properties of bottomed mesons in a hot mesonic gas

Abstract

In this work we evaluate the $B$-meson drag and diffusion coefficients in a hot medium constituted of light mesons ($\ensuremath{\pi}$, $K$, $\overline{K}$, and $\ensuremath{\eta}$). We treat the $B$-meson and ${B}^{*}$-meson interactions with pseudo-Goldstone bosons in chiral perturbation theory at next-to-leading order within the constraints from heavy quark symmetry and employ standard unitarization techniques of next-to-leading order amplitudes in order to account for dynamically generated resonances (leading to a more efficient heavy-flavor diffusion) and thus reach higher temperatures. We estimate individual meson contributions from the gas to the transport coefficients and perform a comparison with other findings in literature. We report a bottom relaxation length of about 80 fm at a temperature of 150 MeV and for typical momenta of 1 GeV, at which our approach is reliable. Compared to a charm relaxation length of 40 fm in the same conditions, we conclude that the $B$ mesons provide a cleaner probe of the early stages of a heavy-ion collision.