Inconsistencies in, and short pathlength correction to, $$R_{AA}(p_T)$$ R AA ( p T ) in  $$\textrm{A}+\textrm{A}$$ A + A and $$\textrm{p} + \textrm{A}$$ p + A collisions

Abstract We present the first leading hadron suppression predictions in $$\textrm{Pb}+\textrm{Pb}$$ Pb + Pb and $$\textrm{p}+\textrm{Pb}$$ p + Pb collisions from a convolved radiative and collisional energy loss model in which partons propagate through a realistic background and in which the radiative energy loss receives a short pathlength correction. We find that the short pathlength correction is small for D and B meson $$R_{AA}(p_T)$$ R AA ( p T ) in both $$\textrm{Pb}+\textrm{Pb}$$ Pb + Pb and $$\textrm{p}+\textrm{Pb}$$ p + Pb collisions. However the short pathlength correction leads to a surprisingly large reduction in suppression for $$\pi $$ π mesons in $$\textrm{p}+\textrm{Pb}$$ p + Pb and even $$\textrm{Pb}+\textrm{Pb}$$ Pb + Pb collisions. We systematically check the consistency of the assumptions used in the radiative energy loss derivation-such as collinearity, softness, and large formation time-with the final numerical model. While collinearity and softness are self-consistently satisfied in the final numerics, we find that the large formation time approximation breaks down at modest to high momenta $$p_T \gtrsim 30~\textrm{GeV}$$ p T ≳ 30 GeV . We find that both the size of the small pathlength correction to $$R_{AA}(p_T)$$ R AA ( p T ) and the $$p_T$$ p T at which the large formation time assumption breaks down are acutely sensitive to the chosen distribution of scattering centers in the plasma.