Probing Neutron Skin through Event-by-Event Pion Asymmetry in Heavy-ion collisions

TL;DR

This paper introduces an event-by-event observable, $\Delta n_{\pi}=n_{\pi^-}-n_{\pi^+}$, in ultra-peripheral Au+Au collisions at $\sqrt{s_{NN}}=3$ GeV as a new probe of the gold neutron skin thickness $\Delta r_{np}$. Using the SMASH transport model with halo-type neutron skins implemented via a Woods-Saxon distribution, the authors show that $\langle\Delta n_{\pi}\rangle$ and the correlation measures between $(\pi^-+\pi^+)$ and $(\pi^- - \pi^+)$ scale with $\Delta r_{np}$, while the slopes between specific $\Delta n_{\pi}$ pairs (notably $(-1,1)$, $(-1,2)$, $(0,1)$, and $(0,2)$) exhibit a strong linear dependence on $\Delta r_{np}$. The study also reveals substantial model dependence when comparing SMASH to UrQMD, partly due to Coulomb effects and transport-model differences; nonetheless, extracting slopes from multiple $\Delta n_{\pi}$ pairs in experimental data could constrain $\Delta r_{np}$ and help discriminate between models. The work provides a new methodological pathway to constrain the nuclear symmetry energy and the equation of state of asymmetric nuclear matter through pion-charge asymmetries in peripheral heavy-ion collisions.

Abstract

In this work, we propose a novel approach for probing the neutron skin thickness of gold (Au) by analyzing the event-by-event distribution of $π^{-}$ and $π^{+}$ yield differences. This is achieved through SMASH simulations of ultra-peripheral Au+Au collisions at $\sqrt{s_{\rm NN}}=3$ GeV. Our results demonstrate that the mean value of $Δn_π = n_{π^{-}} - n_{π^{+}}$, along with the Pearson correlation and mutual information between $(π^{-}+π^{+})$ and $(π^{-}-π^{+})$, all scale linearly with the neutron skin thickness. Moreover, the slope of the line connecting two distinct $Δn_π$ values in the event-by-event distribution also exhibits a linear dependence on the neutron skin thickness. The most sensitive $Δn_π$ pairs are identified as $(-1, 1)$, $(-1, 2)$, $(0, 1)$, and $(0, 2)$. These findings establish a new pathway for determining the neutron skin thickness. Finally, by comparing SMASH and UrQMD simulations under identical initial conditions, we observe that individual slope values depend on the specific collision model. However, by extracting slopes from multiple $Δn_π$ pairs in experimental event-by-event data and inferring the corresponding neutron skin thickness, one can assess which model better aligns with the true physical value.

Figures (7)

• Figure 1: (Color online) The neutrons and protons are mixed in the nucleus, and the root-mean-square radius of the neutron distribution is larger than that of the proton distribution, forming the neutron skin structure shown in the gray area.
• Figure 2: (Color online) The sampling results of the initial distribution are shown in the figure, where the red dashed line represents the proton sampling results, and the dark gray to light gray solid lines correspond to the neutron sampling results for neutron skin thicknesses of 0.14 fm, 0.18 fm, 0.22 fm, and 0.26 fm, respectively.
• Figure 3: (Color online) Density plot of $\Delta n_{\pi}$ from Au-Au collisions at various neutron skin thicknesses. The red part indicates the relative error.
• Figure 4: (Color online) The relationship between the slope formed by two different $\Delta n_{\pi}$ values in the histogram and the neutron skin thickness is shown. The two lines in the figure represent two sets of SMASH collision data with the same initial state, and the short-line segments denote the relative uncertainties.
• Figure 5: (Color online) Comparison of the relationship between the neutron skin thickness $\Delta r_{np}$ and the following three physical quantities: (a) the mean value of $\Delta n_{\pi}$; (b) the Pearson correlation between $(\pi^{-}+\pi^{+})$ and $(\pi^{-}-\pi^{+})$; (c) the mutual information between $(\pi^{-}+\pi^{+})$ and $(\pi^{-}-\pi^{+})$. The red dashed line represents the results from the SMASH model, while the blue solid line represents the results from the UrQMD model.