Anisotropic fluctuations of momentum and angular momentum of heavy quarks in the pre-equilibrium stage of pA collisions at the LHC

TL;DR

This work investigates heavy-quark diffusion in the pre-equilibrium glasma created in high-energy pA collisions by solving 3+1D SU$(3)$ classical Yang–Mills dynamics on a lattice with MV initial conditions and a realistic proton structure, including longitudinal fluctuations that break boost invariance. In the $M\to\infty$ limit, heavy-quark momentum and angular-momentum broadening are computed from time-correlations of color-electric fields via the Wong equations, with momentum broadening split into longitudinal and transverse components and angular-momentum anisotropy quantified by $\Delta_2$. The study finds that both $\langle \delta p_L^2(\tau)\rangle$ and $\langle \delta p_T^2(\tau)\rangle$ grow but with a pronounced longitudinal dominance, and $\Delta_2$ remains sizable ($\sim 0.4-0.6$) during the early 0.2–0.4 fm window, indicating persistent anisotropies; including $\,\eta$-dependent fluctuations can greatly increase the bulk $P_L/P_T$ but does not isotropize heavy-quark momenta, suggesting the need for dynamical heavy quarks and a later QGP transport stage for quantitative phenomenology. The results advance initial-state modeling of glasma and inform future efforts to couple pre-equilibrium dynamics to heavy-quark observables.

Abstract

We simulate the real-time evolution of the $SU(3)$-glasma generated in the early stages of high-energy proton-nucleus collisions, employing classical lattice gauge theory techniques. Our setup incorporates a realistic modeling of the proton's internal structure and includes longitudinal fluctuations in the initial state, enabling the study of genuinely non-boost-invariant collision dynamics. Focusing on the momentum and angular momentum anisotropies of heavy quarks in the infinite mass limit, we find that the system retains significant anisotropy well beyond the characteristic timescale $τ= 1/Q_s$. This persistence of anisotropy is further confirmed in the more realistic, non-boost-invariant scenario, across a range of fluctuation amplitudes. These findings pave the way for future investigations involving dynamical heavy quarks and more quantitative initializations of the glasma.

Figures (6)

• Figure 1: Energy density (legend on the right side) produced in a pA collision in one event, represented in the transverse plane for three values of $\tau$: left panel corresponds to $\tau=0.001$ fm, center panel to $\tau=0.05$ fm, right panel to $\tau=0.2$ fm.
• Figure 2: Energy density $\varepsilon$, versus proper time, averaged over the transverse plane (for the pA case, the average over the transverse plane has been performed using $T_p(\mathbf{x}_\perp)$ as a weight, see main text). Error bars are also shown (for the AA case the error is smaller than the line width).
• Figure 3: Longitudinal momentum broadening $\langle \delta p_L^2(\tau)\rangle$ (black), and transverse momentum broadening $\langle \delta p_T^2(\tau)\rangle$ (blue) for a pA collision, along with the corresponding error bars. The green line corresponds to the function $a+b\log(\tau/\bar{\tau})$ where we put $\bar{\tau}=0.4$ fm, $a=0.88$ GeV$^2$ and $b=0.26$ GeV$^2$. Similarly, the orange solid line represents the function $c + d \log(\tau/\tilde{\tau})$ where we put $\tilde{\tau}=0.2$ fm, $c=0.30$ GeV$^2$ and $d=0.01$ GeV$^2$.
• Figure 4: $\Delta_2$ (black) and $\Delta_2-\Delta_2^{\text{geom}}$ (blue) versus proper time for pA collisions, along with the corresponding error bars.
• Figure 5: The ratio of the longitudinal pressure over the transverse pressure $P_L/P_T$, versus proper time for different values of $\Delta$. Error bars are also shown.