Evidence for quark-diquark structure of baryons from fluctuations of conserved charges

TL;DR

This work tests how the hadronic mass spectrum shapes conserved-charge fluctuations in QCD by adopting a string-inspired description: mesons as open strings with quark-antiquark ends and baryons as open strings with quark-diquark ends, yielding a universal Hagedorn density of states controlled by the string tension. By first fitting the PDG hadron spectrum, the authors obtain a Hagedorn temperature $T_H \approx 340~\mathrm{MeV}$ and demonstrate that a continuous PDG-constrained spectrum underestimates lattice QCD fluctuations near $T_c$. They then extract $T_H$ directly from lattice QCD data by matching the second-order net-baryon susceptibility, obtaining $T_H = 323(3)~\mathrm{MeV}$, which yields a spectrum that substantially improves agreement with a broad set of conserved-charge susceptibilities and correlations. The residual discrepancies point to interaction effects not fully captured by the spectral density, yet the results provide thermodynamic evidence in favor of a string-based, quark-diquark baryon structure in the confined phase of QCD.

Abstract

We study fluctuations and correlations of conserved charges in QCD using a string-based description of the hadronic mass spectrum. Mesons and baryons are modeled as open relativistic strings with quark-antiquark and quark-diquark endpoints, respectively, leading to an exponential Hagedorn growth of states with a limiting temperature fixed by the string tension. We find that continuous Hagedorn spectra constrained by experimentally established hadrons underestimate net-baryon number fluctuations obtained in lattice QCD calculations. By extracting the Hagedorn string spectrum directly from lattice QCD through a fit to the second-order net-baryon number susceptibility, we obtain a consistent description of a broad set of fluctuations of conserved charges from LQCD with the Hagedorn temperature $T_H \simeq 323~$MeV, without introducing additional free parameters. Our results provide thermodynamic evidence in support of a string quark-diquark picture of baryons in the confined phase of QCD.

Figures (6)

• Figure 1: Cumulative spectra of hadrons (top panel), baryons (middle panel), and mesons (bottom panel) obtained from the PDG ParticleDataGroup:2024cfk (black solid lines). Also shown are spectra predicted by the quark model Loring:2001kyEbert:2009ub (gray dash-dotted lines). Continuous Hagedorn spectra are obtained from fits of the hadron spectrum to the PDG (blue dashed line) and lattice QCD (red dotted lines) results. The shaded bands indicate the uncertainty of the extracted Hagedorn limiting temperatures (see text for details). We note that the hadronic spectrum includes antibaryon contributions. The middle panel, however, shows baryons only and does not include antibaryon contribution.
• Figure 2: As in Fig. \ref{['fig:had_spec']}, but for mesons separated into nonstrange (top panel) and strange (bottom panel) sectors.
• Figure 3: As in Fig. \ref{['fig:had_spec']}, but for baryons separated into strangeness sectors $S=0,-1,-2,-3$, shown from top to bottom. We note that the spectra do not include antibaryons.
• Figure 4: The second-order fluctuations of the net-baryon number, $\hat{\chi}_2^B$. Shown are the results obtained from the fit of the continuous to all hadrons in the PDG spectrum (blue dashed line) and the fit to the lattice QCD results (red dotted line). The bands represent the uncertainty in the obtained Hagedorn limiting temperatures (see text for details). We note that the uncertainty associated with the PDG-based fit is smaller than the line width on the scale shown. The LQCD results are taken from Ref. Bollweg:2021vqf (LQCD 1) and Abuali:2025tbd (LQCD 2). They correspond to continuum extrapolated and continuum estimated results, respectively. The vertical yellow band marks the temperature of the chiral crossover $T_c = 156\pm1.5~$MeV HotQCD:2018pds.
• Figure 5: As in Fig. \ref{['fig:xbb']} but for the fourth-order fluctuations of the net-baryon number, $\hat{\chi}_4^B$ (top panel), baryon-strangeness correlator, $\hat{\chi}_{11}^{BS}$ (middle panel), and the second-order fluctuations of strangeness, $\hat{\chi}_2^S$ (bottom panel).