Melting of $c \bar c$ and $b \bar b$ pairs in the pre-equilibrium stage of proton-nucleus collisions at the Large Hadron Collider

We study the melting of $c\bar c$ and $b\bar b$ pairs in the early stage ofhigh-energy proton-nucleus collisions. We describe the early stage in terms ofan evolving $SU(3)$ glasma stage, that is dominated by intense,out-of-equilibrium gluon fields. On top of these fields, we liberate heavyquark-antiquark pairs, whose constituents are let evolve according torelativistic kinetic theory coupled to the gluon fields. We define apair-by-pair probability that the pair melts during the evolution, which werelate to the fluctuations of the color charges induced by the interaction ofthe quarks with the gluon fields. We find that color decorrelation is the mainmelting mechanism within the pre-equilibrium stage. Moreover, we estimate thatwithin $\Delta \tau\approx0.4-0.5$ fm/c after the formation time of the pairs,about $50\%$ of $c\bar c$ and $b\bar b$ pairs are melted.