Charm quark production in heavy-ion collisions as a signature of pre-equilibrium

This paper proposes that precise measurements of total charm production in heavy-ion collisions, when combined with improved calculations of initial hard scatterings, can serve as a signature to infer properties of the pre-equilibrium stage, despite current theoretical uncertainties.

The Gist

Imagine a heavy-ion collision (smashing two heavy atomic nuclei together at nearly the speed of light) as a massive, chaotic party that starts with a bang and settles down into a calm crowd.

The Setting: The "Pre-Party" Chaos
When these nuclei collide, they don't instantly become a smooth, hot soup of particles (called a Quark-Gluon Plasma or QGP). Before they settle down, there is a brief, chaotic "pre-party" phase. During this time, the pressure is lopsided (pushing harder sideways than forward), and the ingredients (gluons and quarks) aren't yet mixed evenly. Scientists call this the pre-equilibrium phase.

Usually, scientists think that heavy particles called charm quarks are only created in the very first split-second "hard crash" of the collision, like sparks flying off a hammer hitting an anvil. Once that initial crash is over, the number of charm quarks is thought to stay the same.

The New Idea: The "Pre-Party" Spark
This paper asks a simple question: Could the chaotic "pre-party" phase also be creating these heavy charm quarks?

The authors suggest that because this pre-equilibrium phase is incredibly dense and energetic (even more so than the later, calmer phases), it might actually be a factory for charm quarks. They compare this to how light particles (dileptons) are known to be produced during this phase. If light particles can be made here, maybe heavy ones can too.

The Experiment: Running the Simulation
To test this, the authors used a complex computer simulation (like a high-tech weather model, but for subatomic particles). They modeled the chaotic pre-party phase using two different approaches:

1. The "Realistic" Model: A detailed simulation of how particles bounce and interact (QCD kinetic theory).
2. The "Simplified" Model: A smoother, easier-to-calculate version that assumes the chaos follows a specific pattern (the Romatschke-Strickland model).

They calculated how many charm-anticharm pairs would be born during this brief, chaotic window before the system cools down.

The Findings: A Surprising Contribution
The results were interesting:

• Yes, it happens: The pre-equilibrium phase does produce charm quarks. It's not just a trickle; it's a "non-negligible" amount.
• The Timing: Unlike light particles that might be made throughout the event, heavy charm quarks are mostly made very early, right when the chaos is at its peak.
• The Size: Depending on the specific conditions of the collision, this "pre-party" production could account for 10% to 50% of the total charm quarks found in the final debris. That is a significant chunk!

The Problem: The Foggy Measurement
Here is the catch: While the math says this extra production exists, we currently can't prove it with real-world data.

Why? Because our current measurements of the total number of charm quarks produced in these collisions have a huge "fog of uncertainty." It's like trying to hear a whisper (the pre-equilibrium charm) in a room where the main speaker (the initial hard crash) is shouting, and we aren't even sure how loud the main speaker is supposed to be. The theoretical calculations for the "main speaker" have large error bars, making it impossible to tell if the "whisper" is actually there or just part of the noise.

The Solution: Better Microphones
The paper concludes that to find this hidden "pre-party" charm, we need much more precise measurements.

• We need to measure the total charm production in heavy-ion collisions with the same precision we have for proton collisions.
• We need to better understand how the "nuclear environment" changes the production rates.

The Bottom Line
This paper proposes that the chaotic early moments of a heavy-ion collision are a hidden factory for heavy charm quarks. While we can't see it clearly yet due to measurement uncertainties, if future experiments (like the upcoming ALICE 3 and LHCb upgrades) get precise enough, they could use the total count of charm quarks as a detective tool to learn exactly how the "pre-party" chaos behaves and how the universe thermalizes after a massive collision.

Technical Summary

Technical Summary: Charm Quark Production in Heavy-Ion Collisions as a Signature of Pre-equilibrium

Problem Statement
In ultrarelativistic heavy-ion collisions, the formation of a quark-gluon plasma (QGP) is preceded by a pre-equilibrium phase characterized by longitudinal pressure anisotropy and chemical non-equilibrium (gluon dominance). While electromagnetic radiation (specifically dileptons in the 2–5 GeV/$c^2$ mass range) has been established as a probe for this phase, the production of heavy quarks (charm) during pre-equilibrium remains largely unexplored. Conventionally, charm production is attributed to initial hard scatterings, with the total charm yield assumed to be conserved thereafter. However, the total charm production cross-section in nucleus-nucleus collisions remains a leading source of uncertainty in interpreting quarkonium suppression. This paper investigates whether charm production during the pre-equilibrium phase constitutes a non-negligible fraction of the total yield and if it can serve as a complementary probe to dileptons, specifically sensitive to the gluon abundance in the early stage.

Methodology
The authors employ a theoretical framework combining perturbative QCD with effective kinetic theory to model the pre-equilibrium dynamics.

• Production Rate Calculation: The charm-anti-charm ($c\bar{c}$) pair production rate is calculated to leading order in perturbation theory. The rate includes contributions from quark-antiquark annihilation and gluon fusion, utilizing matrix elements dependent on the invariant mass $Q$ and the relative velocity of incoming particles.
• Pre-equilibrium Dynamics: The evolution of the phase-space distributions for gluons and quarks is modeled using effective kinetic theory (EKT) of QCD. The system is described via conformal Bjorken flow, characterized by a universal scaling variable $\tilde{w} = \tau T_{\text{eff}} / (4\pi\eta/s)$, where $\tau$ is the Bjorken time and $\eta/s$ is the shear viscosity to entropy density ratio.
• Scaling Analysis: The authors test the universality of the production rate by expressing the differential yield as a function of dimensionless ratios ($m_c/T_{\text{eq}}$, $Q/T_{\text{eq}}$). They compare results from EKT simulations at different coupling strengths ($\lambda = 5, 10, 20$) against a simplified Romatschke-Strickland (RS) model, which parametrizes momentum anisotropy and quark suppression.
• Integration and Comparison: The instantaneous production rates are integrated over time and transverse area to obtain the total pre-equilibrium yield. These results are compared against estimates of charm production from initial hard scatterings in Pb+Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV. The hard scattering baseline is derived using NLO pQCD calculations (MadGraph) with EPPS21 nuclear parton distribution functions (nPDFs), normalized to ALICE proton-proton data. A data-driven alternative is also presented, estimating the initial hard scattering yield in Pb+Pb by combining proton-nucleus ($p$+Pb) modification factors ($R_{pA}$).

Key Results

• Non-Negligible Contribution: The study finds that pre-equilibrium charm production contributes a significant fraction to the total charm yield. Depending on the rapidity and the specific theoretical assumptions (coupling strength, $\eta/s$), this contribution ranges from approximately 10% to values comparable to the yield from initial hard scatterings.
• Sensitivity to Initial Conditions: Unlike dilepton production, which exhibits universal scaling at late times, charm production retains sensitivity to initial conditions. The scaling functions for the integrated yield show significant disagreement between different EKT coupling strengths and the RS model, particularly for masses around and above the charm mass. This is attributed to the fact that heavy-flavor production extends to earlier times where the system has not yet lost memory of its initial state.
• Model Dependence: The RS model generally predicts a larger yield than the EKT simulations, partly because the RS parametrization effectively starts at $\tau=0$, whereas EKT simulations begin at an initial time $\tau = 1/Q_s$.
• Rapidity Distribution: The pre-equilibrium yield is found to be larger for lower values of $\eta/s$ (e.g., 0.16 vs. 0.32), consistent with findings for dilepton production.
• Uncertainty Dominance: The ability to isolate the pre-equilibrium signal is currently limited by large theoretical uncertainties in the baseline calculation of initial hard scatterings. The uncertainties in the nuclear modification factor ($R_{AA}$) due to nPDFs and scale variations are substantial (up to a factor of 5 between bounds). Consequently, the pre-equilibrium contribution at mid-rapidity could account for 10–50% of the central value of the hard scattering estimate, or potentially up to 100% of the total yield within the upper bounds of theoretical uncertainty.

Significance and Claims
The paper concludes that precise measurements of total charm production in heavy-ion collisions, when combined with improved theoretical calculations of initial hard scatterings, can be used to infer information about the pre-equilibrium stage. The authors assert that charm production is complementary to dilepton production because it is also sensitive to the gluon abundance in the pre-equilibrium phase.

However, the authors are modest regarding current extraction capabilities. They state that a direct extraction of the pre-equilibrium charm production is not yet possible due to the large uncertainties in the total charm production cross-section in nucleus-nucleus collisions. The paper posits that future progress relies on:

1. Reducing theoretical uncertainties in the initial hard scattering calculations (specifically nPDFs and scale variations).
2. Achieving precision measurements of total charm yields in nucleus-nucleus collisions comparable to those in proton-proton and proton-nucleus systems.

The authors identify the upcoming ALICE 3, ALICE 2, LHCb Upgrade 1, and LHCb Upgrade 2 (U1/U2) programs as critical for achieving the necessary precision to isolate the pre-equilibrium signal. If these experimental goals are met, the difference between the measured nucleus-nucleus yield and the yield estimated from proton-proton and proton-nucleus data could provide a new, direct access point to the thermalization process in heavy-ion collisions.