The cathode tube effect: heavy quarks probing the Glasma in p-Pb collisions

Abstract

We study the propagation of charm quarks in the early stage of high energy proton-lead collision, considering the interaction of these quarks with the evolving Glasma by means of the Wong equations. Neglecting quantum fluctuations at the initial time the Glasma is made of longitudinal fields, but the dynamics leads to a quick formation of transverse fields; we estimate such a formation time as $\Delta t\approx 0.1$ fm/c which is of the same order of the formation time of heavy quark pairs $t_{\mathrm{formation}}\approx 1/(2m)$. Limiting ourselves to the simple case of a static longitudinal geometry, we find that heavy quarks are accelerated by the strong transverse color fields in the early stage and this leads to a tilting of the $c-$quarks spectrum towards higher $p_T$ states. This average acceleration can be understood in terms of drag and diffusion of $c-$quarks in a hot medium and appears to be similar to the one felt by the electrons ejected by the electron cannon in a cathode tube: we dub this effect as {\it cathode tube effect}. The tilting of the spectrum affects the nuclear modification factor, $R_{\mathrm{pPb}}$, suppressing this below one at low $p_T$ and making it larger than one at intermediate $p_T$. We compute $R_{\mathrm{pPb}}(p_T)$ after the evolution of charm quarks in the gluon fields and we find that its shape is in qualitative agreement with the measurements of the same quantity for $D-$mesons in proton-lead collisions.

arXiv comment9 pages, 5 figures. In V2: -) A new figure has been added, new Fig. 3. -) Parameters choice has been explained better. -) Discussion about the effect has been improved: now the reshape of the c-quarks spectrum due to the color fields has been reinterpreted as a diffusion in momentum space

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