Heavy Quarks in the initial stages of Proton-Ion Collisions

TL;DR

This work investigates the very early (pre-equilibrium) stages of proton–ion collisions using the Color Glass Condensate and glasma framework, focusing on heavy quark (charm and bottom) dynamics. It shows that glasma fields, with strong longitudinal color-electric and color-magnetic components, drive substantial diffusion and color decoherence of heavy-quark pairs, leading to notable pair melting on sub-fm timescales. By extending to non-boost-invariant initial conditions and including fluctuations, the study demonstrates how initial-state anisotropies are transmitted to heavy quarks, yielding nonzero elliptic flows (v2) for HQs that are compatible with experimental trends when considering early-time dynamics. The results highlight the importance of pre-equilibrium glasma physics in shaping later QGP observables and provide a pathway to integrate glasma dynamics with kinetic/hydrodynamic descriptions for a more complete understanding of heavy-ion collisions. Overall, the work establishes concrete, gauge-invariant, lattice-based methods to quantify HQ diffusion, color equilibration, and anisotropies arising from the earliest moments after collision, with implications for interpreting HQ and quarkonium signals in small systems.

Abstract

Collisions among heavy ions, like Pb or Au, are a great tool to study the theory of strong interactions, that is Quantum Chromodynamics (QCD). In particular, these experiments are able to give insights on all the complex phases of matter that the theory of QCD allows. In this PhD Thesis we have investigated the initial stages of proton-ion collisions: in particular, we will focus on the first $\sim 0.4$ fm/c ($\sim 10^{-24}$ s) after the collision, which are dominated by very intense gluon fields, in a state called glasma. We investigated the effect of such fields on the dynamics of heavy quarks (charm and beauty) which are created and evolve in this medium. The effect of the initial gluon fields on heavy quarks is quite substantial, in particular we observe that the glasma provokes a $50\%$ dissociation rate on quark-antiquark pairs. Moreover, glasma fields have a large momentum anisotropy, and transmit a large part of such anisotropy to the heavy quarks which evolve in this medium. Finally, we have generalized our study to a non-boost invariant medium, and shown that fluctuations in rapidity do not lead to significant isotropization within glasma timescales.

Figures (48)

• Figure 1: Summary of measurements of $\alpha_s$ as a function of the energy scale $Q$. The curves represent QCD predictions, overlaid with data from lattice QCD and more. Fig. from Bethke:2009jm.
• Figure 2: The contributions of chiral symmetry breaking and of the Higgs mechanism to the masses of the six flavors of quarks. The QCD interaction strongly affects the light quarks ($u$, $d$, $s$), whose total mass is significantly different than the Higgs mass, while the heavy quark masses ($c$, $b$, $t$) are mainly determined by the Higgs mechanism mass_generation_star.
• Figure 3: (left) Lattice QCD calculations of the pressure $p$, energy density $\varepsilon$ and entropy density $s$ of hot QCD matter in thermal equilibrium at temperature $T$Borsanyi:2013biaBazavov:2014pvz show a continuous crossover around $T\sim150$ MeV, from a hadron resonance gas (HRG) at lower temperatures to QGP at higher temperatures. Because QCD is asymptotically free, thermodynamic quantities will reach the Stefan-Boltzmann limit (‘‘non-interacting limit" in the figure) at extremely high temperature. Within the range shown, however, they are around 20% below their Stefan-Boltzmann values. (right) Our current understanding of the expected features of the phase diagram of QCD as a function of temperature and baryon chemical potential. The regions of the phase diagram traversed by the expanding cooling droplets of QGP formed in HICs with varying energies $\sqrt{s_{NN}}$ are sketched. Figures from Bazavov:2014pvzAprahamian:2015qub.
• Figure 4: Schematic representation of the various stages of a HIC as a function of time $t$ and the longitudinal coordinate $z$ (the collision axis). The 'time' variable which is used in the discussion in the text is the proper time $\tau\equiv\sqrt{t^2-z^2}$, which has a Lorentz--invariant meaning and is constant along the hyperbolic curves separating various stages in this picture. Figure from Iancu:2012xa.
• Figure 7: (a) Nuclear modification factor $R_{\text{AA}}^{\text{HF}}$ for heavy flavour electrons compared to the $R_{\text{AA}}$ of $\pi^0$ and $\pi^\pm$ in central Au-Au collisions at $\sqrt{s_{NN}}=200$ GeV. (b) Elliptic flow $v_2^{HF}$ of heavy flavour electrons compared with $v_2$ of $\pi^0$ and $\pi^\pm$ in minimum-bias Au-Au collisions at $\sqrt{s_{NN}}=200$ GeV Nouicer:2012pnNouicer:2009fyNouicer:2011zzSTAR:2007zeaPHENIX:2003qdwPHENIX:2006ujpPHENIX:2006mhb.