[Paper Review] Toward Initial Conditions of Conserved Charges Part II: The ICCING Monte Carlo Algorithm

Carzon, Patrick, Mauricio Martínez+3 more|arXiv (Cornell University)|Nov 27, 2019

High-Energy Particle Collisions Research8 citations

TL;DR

This paper introduces the ICCING Monte Carlo algorithm to model initial-state fluctuations of conserved charges—baryon number, strangeness, and electric charge—in heavy-ion collisions at top collider energies. By sampling gluon-to-quark-antiquark splitting probabilities over the initial energy density, ICCING generates spatially correlated charge distributions that differ significantly from bulk energy density, with strangeness showing enhanced eccentricity linked to initial-state geometry. This enables new probes of charge diffusion and transport in the quark-gluon plasma.

ABSTRACT

At top collider energies where baryon stopping is negligible, the initial state of heavy ion collisions is overall charge neutral and predominantly composed of gluons. Nevertheless, there can also be significant local fluctuations of the baryon number, strangeness, and electric charge densities about zero, perturbatively corresponding to the production of quark/antiquark pairs. These previously ignored local charge fluctuations can permit the study of charge diffusion in the quark-gluon plasma (QGP), even at top collider energies. In this paper we present a new model denoted ICCING (Initial Conserved Charges in Nuclear Geometry) which can reconstruct the initial conditions of conserved charges in the QGP by sampling a ($g ightarrow q\bar{q}$) splitting probability over the initial energy density. We find that the new charge distributions generally differ from the bulk energy density; in particular, the strangeness distribution is significantly more eccentric than standard bulk observables and appears to be associated with the geometry of hot spots in the initial state. The new information provided by these conserved charges opens the door to studying a wealth of new charge- and flavor-dependent correlations in the initial state and ultimately the charge transport parameters of the QGP.

Motivation & Objective

• To develop a model that reconstructs initial conditions of conserved charges in the quark-gluon plasma beyond the standard assumption of zero net charge density.
• To address the limitation in existing hydrodynamic models that neglect local fluctuations of baryon number, strangeness, and electric charge in high-energy heavy-ion collisions.
• To enable the study of charge diffusion and flavor-dependent correlations in the QGP by generating spatially correlated initial charge distributions.
• To quantify how initial charge distributions, particularly strangeness, differ from bulk energy density and correlate with geometric hot spots in the initial state.

Proposed method

• The ICCING algorithm samples the probability of gluon-to-quark-antiquark splitting ($g \rightarrow q\bar{q}$) over the initial energy density profile using a Monte Carlo approach.
• It redistributes energy and charge based on a spatially varying splitting rate derived from the energy density, with normalization adjusted for lattice discretization.
• The model uses a Gaussian-like charge deposition profile with a radius of $ r \approx 0.5\,\text{fm} $, adjusted to $ 0.48\,\text{fm} $ on a $ 0.06\,\text{fm} $ lattice grid to maintain proper normalization.
• Charge densities are computed via discretized normalization over grid points within a circular region, ensuring total charge conservation.
• The algorithm incorporates geometric scaling and the MV model to relate initial energy density to charge distribution, with parameters tuned to match bulk observables.
• It estimates the proportionality constant $ a $ in the splitting rate using an order-of-magnitude argument based on pion multiplicity and entropy conservation.

Experimental results

Research questions

• RQ1 How do local fluctuations of conserved charges—baryon number, strangeness, and electric charge—arise in the initial state of high-energy heavy-ion collisions despite overall charge neutrality?
• RQ2 To what extent do the spatial distributions of these conserved charges differ from the bulk energy density profile?
• RQ3 Can strangeness serve as a distinct probe of initial-state geometry due to its enhanced eccentricity compared to standard bulk observables?
• RQ4 How do discretization effects and normalization on a finite lattice influence the absolute scale of initial charge densities?
• RQ5 What is the quantitative relationship between the initial charge distribution and final-state anisotropic flow or cumulants?

Key findings

• The strangeness distribution exhibits significantly higher eccentricity than the bulk energy density, indicating a strong correlation with initial-state geometric hot spots.
• The model produces local charge densities on the order of $ \sim 1\,\text{fm}^{-3} $ at the center of a single quark, with overlapping quarks increasing this to $ \sim 3\,\text{fm}^{-3} $ for baryons.
• Electric charge density scales up by a factor of 2 due to the $ +2/3 $ charge of up quarks, while strangeness density can reach $ \sim -6\,\text{fm}^{-3} $ in cases of two overlapping strange quarks.
• The parameter $ a $ in the splitting rate is estimated to be $ \mathcal{O}(100\,\text{fm}^{-1}) $, consistent with order-of-magnitude expectations from pion multiplicity and entropy conservation.
• Discretization effects increase the central density by approximately 10% compared to continuous normalization, with the final normalization adjusted via lattice sum over grid points.
• The initial charge distributions generated by ICCING are not trivially related to the energy density, opening new avenues for studying charge transport and diffusion in the QGP.