Correlations of Feed-down Hadrons in a Thermal Model

TL;DR

The paper investigates how strong resonance decays (feed-down) influence fluctuations of net conserved quantum numbers and balance functions in a thermal hadron gas at zero baryochemical potential across temperatures between 140 and 200 MeV. It adopts a Grand Canonical Hadron Gas framework and uses Therminator2 to include all known hadrons up to $2.5$ GeV/$c^2$ and their decay channels, computing stable yields and two-particle cumulants. The results show substantial feed-down effects: at $T=160$ MeV the observable proton density increases by about a factor of 3 due to FD, and correlated FD densities often dominate over thermal pairs, with non-charge balancing correlations exhibiting strong temperature dependence. These findings imply that FD must be accounted for when interpreting net-proton fluctuations and balance-function measurements in RHIC and LHC; however, the idealized model and lack of experimental acceptance mean that further work with realistic dynamical modeling is needed.

Abstract

We examine the potential impact of strong decays on the magnitude of fluctuations of net quantum numbers and integrals of balance functions based on a thermal hadron gas model. The calculations are based on a comprehensive list of known hadrons with masses up to 2.5 GeV/$c^2$ and include all decays of these hadrons with known branching fractions. The calculations are performed at vanishing baryo-chemical potential for temperatures between 140 and 200 MeV. We show that the decays feed-down substantially impact the single yield of measurable ``stable particles" as well as those of correlated densities of these species. Decays can then potentially have large and non-trivial impacts on measurements of net quantum number cumulants and balance functions. These observations are particularly important in the context of the search for the QCD critical point at the RHIC Beam Energy Scan as well as efforts to determine chemical susceptibilities near the phase transition at RHIC or LHC energies. Results obtained in this work also shed light on the importance of feed-down in measurements of balance functions in elementary p-p and nucleus-nucleus collisions.

Figures (6)

• Figure 1: (left) Thermal density of individual hadron species plotted as a function of their index $\alpha\in[1,353]$; (right) Average thermal density vs. species mass. Densities are computed with the thermal model presented in the text for selected temperatures and vanishing baryo-chemical potential.
• Figure 2: (top) Thermal densities of stable hadrons computed at selected temperatures;(middle) densities obtained after adding FD from unstable higher mass hadrons; (bottom) Ratio of densities with and without FD.
• Figure 3: Correlated pair densities of stable hadrons $\alpha$ emitted jointly with pions (top), kaons (middle), and protons (bottom) at selected temperatures. The right-most entries, labeled $\Sigma_{\alpha}$ correspond to the sum $\sum_{\alpha} C_2(\alpha|\beta)$ for $\beta = \pi^+, K^+, p$.
• Figure 4: Evolution with the hadron gas temperature of the correlated pair densities of stable hadrons $\alpha$ emitted jointly with a $\pi^{+}$.
• Figure 5: Normalized correlated pair densities of stable hadrons $\alpha$ emitted jointly with pions (top), kaons (middle), and protons (bottom) normalized by their respective integrals.