Magnetic properties of the hadron resonance gas with physical magnetic moments

TL;DR

The study extends the Hadron Resonance Gas framework to a uniform magnetic field by incorporating physical, including anomalous, magnetic moments of hadrons. It derives relativistic energy spectra in the field, implements these in HRG using the QMHRG2020 hadron list, and computes diagonal and non-diagonal conserved-charge susceptibilities up to $B \le 0.15$ GeV$^2$, comparing with lattice QCD data. The results show that anomalous magnetic moments, especially in octet baryons, substantially modify susceptibilities and improve lattice agreement, though uncertainties in Delta(1232) moments remain important. The work also discusses implications for hadron yields and emphasizes that the current framework remains valid only within modest magnetic fields, beyond which hadron structure and resonance behavior would require more intricate modeling.

Abstract

We study magnetic properties of the Hadron Resonance Gas in the presence of a strong ($0 \le B \le 0.15~{\rm GeV}^2$) uniform magnetic field, using physical values of the magnetic moments of hadrons, i.e., including their anomalous parts. The values of these moments are taken from experiment, or when unavailable, from theoretical estimates. We evaluate the conserved charge susceptibilities, finding the expected sizable effects of the anomalous magnetic moments, in particular of the octet baryons, such as the proton and neutron, where they are exceptionally large. We also study in detail the large effects of the magnetic moments of the $Δ(1232)$ states, for which various theoretical estimates and experimental values differ significantly. We compare our model results with the lattice QCD data and find reasonable agreement within the model uncertainty.

Figures (5)

• Figure 1: Normalized histogram density for the baryon number susceptibility $\chi_{BB}$ in HRG, plotted as a function of the hadron mass $M$ at $T=145~{\rm MeV}$ (a) and $T=100~{\rm MeV}$ (b), and at magnetic field strength $B=0.15~{\rm GeV}^2$. The HRG contribution in each bin is shown in light blue color, while the individual contributions from baryon octet and decuplet states are shown in different colors and are labeled accordingly.
• Figure 2: Same as Fig. \ref{['fig:histchiBB']}, but for the electric charge susceptibility $\chi_{QQ}$ and the non-diagonal baryon-strangeness susceptibility $\chi_{BS}$ at $T=145~{\rm MeV}$.
• Figure 3: Diagonal and non-diagonal conserved charge susceptibilities at zero magnetic field, plotted as functions of the temperature $T$. The red solid line represents our HRG model calculation, the black symbols denote the lattice data from Bollweg:2021vqf, and the blue curve represents the lattice data digitized from Ding:2025jfz.
• Figure 4: Conserved charge susceptibilities, plotted as functions of the magnetic field $B$. The orange bands represent the lattice QCD data digitized from Ding:2025jfz. The black points correspond to the data at $B=0$ from Bollweg:2021vqf. The horizontal black lines indicate the values of our model susceptibilities at $B=0$, plotted for a reference. The solid magenta lines show the HRG calculation with the $g=2Q$ (or $\kappa=0$) prescription. The remaining bands and lines show various predictions of HRG with hadrons having the physical values of the $g$-factors, but for different values of $g$ for the $\Delta$ isobars, as indicated in the legends and specified in Table \ref{['tab:hadrons']} (see the text for details). This affects the plots in panels (a), (c), and (e), but not for (b), (d), or (f), where $\Delta$ does not contribute and where the HRG results with physical $g$-factors are drawn with dashed red lines. The solid purple lines in panel (d) and (f) represent the results with the addition of $K^\ast(700)$ states in the hadron list.
• Figure 5: Proton and $\Delta^{++}(1232)$ primordial multiplicities in HRG, plotted as functions of the magnetic field $B$ at $T=155~{\rm MeV}$. The case without the anomalous magnetic moments ($\kappa=0$) is indicated with dashed lines while the solid lines represent the $\kappa \neq 0$ scenario. The bands for $\Delta^{++}$ correspond to the uncertainty of its anomalous magnetic moments, analogically to Fig. \ref{['fig:suscsmallB']}.