Heavy flavour $z_g$ in dense medium with late emission approximation

We study the $z_g$ distribution for heavy flavour, i.e. bottom and charm quark, jets propagating through the dense QCD medium. We extend the late emission approximation for ASW formula to heavy flavours. % We consider both the normalised and $N_{\rm jet}$ normalised $z_g$ distributions, and the ratio of the latter distributions to the vacuum ones, called the R ratio. We demonstrate that since there is no collinear singularity in the medium, there is no principal need to use the Sudakov safety technique for medium-induced emission (MIE). We see that contrary to the vacuum case, the normalised $z_g$ distribution is sensitive to the dead cone angle value. In particular, for the case of $N_{jet}$ normalised distribution with $\theta_g\le \theta_{cut}$, it is possible to directly probe the dead cone gluons in the medium. Our results can be useful to guide the experimental measurements of the heavy flavour jet substructure in dense QCD medium.
Comment: 42 pages, 29 figures