Bayesian inference of the magnetic component of quark-gluon plasma

Abstract

The chromo-magnetic monopoles (CMM), emergent topological excitations of non-Abelian gauge fields carrying chromo-magnetic charge, have long been postulated to play an important role in the vacuum confinement of quantum chromodynamics (QCD), the deconfinement transition at temperature $T_c\approx 160\rm MeV$, as well as the strongly coupled nature of quark-gluon plasma (QGP). While such CMMs have been found to provide solutions for challenging puzzles from heavy-ion collision measurements, they were typically introduced as model assumptions in the past. Here we show how their very existence can be determined and their abundance extracted in a data-driven way for the first time. Using the \textsc{cujet3} framework for calculations of jet energy loss and analyzing a comprehensive experimental data set for nuclear modification factor ($R_{\mathrm{AA}}$) and elliptic flow ($v_2$) of high-transverse-momentum hadrons, the fraction of CMMs in the QGP is obtained by Bayesian inference and is found to be substantial in the $1\sim 2 T_c$ region. The posterior CMM fraction is further validated by excellent agreement with additional data and is also shown to predict QGP transport properties quantitatively consistent with the state-of-the-art knowledge.

Figures (4)

• Figure 1: Posterior marginal and pairwise distributions of parameters. Blue regions (lower triangle) show samples from the unconstrained posterior, while orange regions (upper triangle) represent results from the monotonic scenario for $\chi_T(T)$.
• Figure 2: Posterior predictive distributions (PPDs) for $R_{AA}$ (left) and $v_2$ (right) computed from CUJET, using parameter samples located within the 95% joint credible boundary of the constrained posterior distributions. Centrality intervals serving as validation (training) datasets are represented by filled (transparent) theory bands and solid (open) data points. Experimental data from PHENIX Adare:2008qaAdare:2012wgPHENIX:2013yhu, ALICE ALICE:2018vuuALICE:2012vgf, ATLAS ATLAS:2015qmbATLAS:2011ah, and CMS CMS:2012aaCMS:2012zexKhachatryan:2016odnSirunyan:2017pan collaborations are respectively shown as diamond, square, star, and circle symbols. In the $R_{AA}$ plot, open circles with lighter color are CMS data within $10-30\%$ and $30-50\%$ centrality bins.
• Figure 3: Posterior distribution of $\chi_T(T)$ in the monotonic scenario is shown as orange band. The $68\%$ and $95\%$ credibility intervals from Bayesian analysis in the unconstrained scenario (blue shaded bands) as well as the cujet3.1 model assumptions of $\chi_T$ based on quark number susceptibilities ($\chi_T^u$, green dash-dotted) and Polyakov loop ($\chi_T^L$, green dotted) are shown for comparison.
• Figure 4: Transverse-momentum-transfer-squared per unit path length (upper left), shear viscosity (lower left), and diffusion parameter (right) are shown as functions of temperature. In all sub-figures, red lines and bands respectively represent the median and $95\%$ credibility interval of the current Bayesian analysis, and orange dash-dotted (gold dotted) lines corresponds to previous cujet3.1 (cujet2) simulations with (without) chromo-magnetic degrees of freedom. Results from other models are included for comparison: jet collaboration model-combined extraction of $\hat{q}$JET:2013cls; jetscape Bayesian analyses of $\hat{q}$ based on energetic particles JETSCAPE:2020shqJETSCAPE:2020mzn and $\eta/s$ for soft particles JETSCAPE:2024cqe; diffusion parameter computed from lattice QCD simulations Banerjee:2011raDing:2012spHotQCD:2025fbd, UrQMD's simulation based on hadron resonance gas(hrg) model Lang:2012nqy, Duke's Langevin-based model Cao:2011etCao:2012jt, Catania's quasi-particle models(qpm) for solving the Boltzmann(bm) and Langevin(lgv) equations Scardina:2017ipo, phsdBratkovskaya:2011wpSong:2015sfaSong:2015ykw, TAMU's T-Maxtrix calculation using free-energy(F) and inner-energy(U) assumptions vanHees:2007meRiek:2010fkLiu:2016ysz, and amy hard thermal loop(htl) Arnold:2003zc and SUBATECH's leading order(lo) Gossiaux:2008jvPeshier:2008bg perturbative QCD calculations.