[Paper Review] Distinct Hagedorn temperatures from particle spectra: a higher one for mesons, a lower one for baryons

Wojciech Broniówski|ArXiv.org|Aug 11, 2000

High-Energy Particle Collisions Research3 citations

TL;DR

This paper proposes that mesons and baryons have distinct Hagedorn temperatures—195 MeV for mesons and 141 MeV for baryons—based on fitting experimental particle spectra. Using dual string models, it explains the higher mesonic temperature as arising from faster combinatorial growth due to single-string excitations, while baryons, with three-string excitations, grow more slowly, leading to a lower effective Hagedorn temperature.

ABSTRACT

We analyze experimental particle spectra and show that the Hagedorn temperature is significantly larger for mesons than for baryons. The effect can be explained within dual string models: excitations of three strings in the baryon produce ``faster'' combinatorics than a single string in the meson, hence lead to a more rapid growth of baryons than mesons. Predictions of other approaches for the gross features of particle spectra are also discussed.

Motivation & Objective

• To investigate whether the Hagedorn hypothesis of exponentially growing hadronic resonance spectra applies uniformly across all hadrons.
• To determine if mesons and baryons exhibit different Hagedorn temperatures based on experimental particle spectrum data.
• To explain the observed difference in Hagedorn temperatures using dual string models and combinatorial statistics of hadronic excitations.
• To assess the validity of the Hagedorn hypothesis in the non-asymptotic mass range up to 1.8 GeV using least-squares fits.
• To explore the implications of distinct Hagedorn temperatures for models of hadron spectroscopy and heavy-ion collision phenomenology.

Proposed method

• Fits of the cumulative number of states $N_{\text{theor}}(m)$ to the form $\int_0^m \rho_{\text{theor}}(m') dm'$, with $\rho_{\text{theor}}(m) = f(m) \exp(m/T)$, using experimental data from the Particle Data Tables.
• Application of least-squares fitting to $\log N_{\text{theor}}$ over the mass range up to 1.8 GeV, excluding the lightest state, to extract $T_H$ and normalization parameters.
• Use of a slowly varying function $f(m) = A / (m^2 + (500\,\text{MeV})^2)^{5/4}$ to model the spectral density, with alternative forms tested for robustness.
• Analysis of effective Hagedorn temperature $T_{\text{eff}}$ via $1/T_{\text{eff}} = 1/T + f'(\bar{m})/f(\bar{m})$, to assess non-asymptotic behavior.
• Employment of dual string models to explain the difference in growth rates: single-string excitation in mesons vs. three-string excitation in baryons.
• Use of the compound hadron model with $n$-quanta excitations to model resonance states, fitting $\Delta E$ to data to validate the model.

Experimental results

Research questions

• RQ1 Do mesons and baryons exhibit different Hagedorn temperatures based on experimental particle spectra?
• RQ2 Can the observed difference in Hagedorn temperatures be explained by dual string models and combinatorial statistics of hadronic excitations?
• RQ3 Is the Hagedorn hypothesis of exponential spectral growth valid at masses below 1.8 GeV, despite non-asymptotic behavior?
• RQ4 What is the role of three-string excitations in baryons compared to single-string excitations in mesons in determining the rate of state growth?
• RQ5 Does the observed flattening of cumulant curves above 1.8 GeV suggest a physical limit to light-flavor resonance production, such as a 'light-flavor desert'?

Key findings

• The Hagedorn temperature for mesons is found to be $T_{\text{meson}} = 195\,\text{MeV}$, significantly higher than $T_{\text{baryon}} = 141\,\text{MeV}$, based on least-squares fits to experimental spectra.
• The difference in Hagedorn temperatures is not an artifact of fitting; it would require approximately 500 additional meson states to make the meson and baryon cumulant lines parallel.
• The effective Hagedorn temperature $T_{\text{eff}}$ varies with mass, indicating that the current data range is not asymptotic, but the observed $T_H$ values are robust within the fit range.
• Dual string models explain the higher mesonic $T_H$ as a consequence of faster combinatorial growth from single-string excitations compared to the three-string excitations in baryons.
• The compound hadron model with $n$-quanta excitations yields $\Delta E^{{\rm mes}} = 100\,\text{MeV}$ and $\Delta E^{{\rm bar}} = 106\,\text{MeV}$, indicating similar excitation scales despite different $T_H$ values.
• The cumulant curves flatten above 1.8 GeV, suggesting a possible physical cutoff in light-flavor resonance production, consistent with the 'light-flavor-desert hypothesis' and recent challenges to infinite Regge trajectories.