Soft pion enhacement due to resonance decays with spectral functions
Submission Date: December 2024
Abstract:
Hydrodynamical models have shown great success in describing the experimental data measured from heavy-ion collisions. Nevertheless, there still are disparities between the predictions of these models and the transverse momentum spectrum of low momentum pions, leading to the so called soft-pion puzzle. In this thesis, we investigate two approaches to address the soft-pion enhancement observed in Pb-Pb collisions at $\sqrt{s_{NN}} = 2.76\, \mathrm{TeV}$ and $\sqrt{s_{NN}} = 5.02\, \mathrm{TeV}$ using the hadron resonance gas (HRG) model combined with the blast-wave framework. The first approach examines how the number of resonances included in the HRG model affects the blast-wave model fit-parameters when accounting for resonance feed-down. By varying the decay lists used to compute the pion spectrum at 0–5\% centrality, we observe that while the inclusion of additional states improves the model’s fit to data, the reduced chi-squared values ($\chi^2/\text{dof}$) remain significantly above unity, particularly at $\sqrt{s_{NN}} = 5.02\, \mathrm{TeV}$. This suggests that increasing the number of resonances alone is insufficient to resolve the soft-pion puzzle. The second approach explores the impact of broad spectral functions on the soft-pion spectrum. We focus on $\rho$ meson, for which we consider three spectral function parametrizations, namely: Breit-Wigner, phase-shift, and thermal spectral function. Meanwhile, other resonances are described using either a Dirac-delta or a Breit-Wigner distributions. By studying the feed-down of resonances and their contribution to the final pion yield we find that in-medium modifications to the $\rho$-meson spectral function generate the biggest enhancement to the low-$p_T$ region of the pion spectrum, with the largest cumulative feed-down observed at $p_T = 0.1\, \mathrm{GeV}$, corresponding to increases of approximately $10\%$ at $\sqrt{s_{NN}} = 2.76\, \mathrm{TeV}$ and $12\%$ at $\sqrt{s_{NN}} = 5.02\, \mathrm{TeV}$. These results highlight the potential of spectral functions in addressing the soft-pion enhancement observed in heavy-ion collisions at LHC energies.
