Evidence for chiral symmetry restoration in heavy-ion collisions

TL;DR

This paper investigates how chiral symmetry restoration influences heavy-ion collision outcomes in the 3-20 GeV energy range, explaining the 'horn' in the $K^+/\pi^+$ ratio and exploring phase diagram features.

Contribution

It introduces a microscopic model incorporating CSR effects into heavy-ion collision simulations, providing explanations for observed particle ratio structures and phase transition signals.

Findings

CSR increases strangeness production at certain energies.

The 'horn' in $K^+/\pi^+$ ratio is explained by CSR effects.

The study explores the phase diagram and critical point prospects.

Abstract

We study the effect of the chiral symmetry restoration (CSR) on heavy-ion collisions observables in the energy range $\sqrt{s_{NN}}$ = 3-20 GeV within the Parton-Hadron-String Dynamics (PHSD) transport approach. The PHSD includes the deconfinement phase transition as well as essential aspects of CSR in the dense and hot hadronic medium, which are incorporated in the Schwinger mechanism for particle production. Our systematic studies show that chiral symmetry restoration plays a crucial role in the description of heavy-ion collisions at $\sqrt{s_{NN}}$ = 3-20 GeV, realizing an increase of the hadronic particle production in the strangeness sector with respect to the non-strange one. Our results provide a microscopic explanation for the "horn" structure in the excitation function of the $K^+/\pi^+$ ratio: the CSR in the hadronic phase produces the steep increase of this particle ratio up to $\sqrt{s_{NN}} \approx $ 7 GeV, while the drop at higher energies is associated to the appearance of a deconfined partonic medium. Furthermore, the appearance/disappearance of the "horn" structure is investigated as a function of the system size. We additionally present an analysis of strangeness production in the ($T,\mu_B$)-plane (as extracted from the PHSD for central Au+Au collisions) and discuss the perspectives to identify a possible critical point in the phase diagram.

Equations

$$\frac{P(s\bar{s})}{P(u\bar{u})}=\frac{P(s\bar{s})}{P(d\bar{d})}={\gamma }_s=\exp \left(-\pi \frac{m_s^2-m_q^2}{2\kappa }\right),$$

$$\frac{<\bar{q}q>}{<\bar{q}q{>}_V}=1-\frac{{\Sigma }_{\pi }}{f_{\pi }^2{m}_{\pi }^2}{\rho }_S-\sum _h\frac{{\sigma }_h{\rho }_S^h}{f_{\pi }^2{m}_{\pi }^2},$$

$$m_s^{\ast }=m_s^0+(m_s^v-m_s^0)\left|\frac{<\bar{q}q>}{<\bar{q}q{>}_V}\right|,m_q^{\ast }=m_q^0+(m_q^v-m_q^0)\left|\frac{<\bar{q}q>}{<\bar{q}q{>}_V}\right|,$$

Full text

1 Introduction

In this contribution we summarize the results from our study in Ref. [1] that investigates the strangeness enhancement in nucleus-nucleus collisions [2, 3] or the ’horn’ in the $K^{+}/\pi^{+}$ ratio [4, 5]. Previously both phenomena have been addressed to a deconfinement transition. Indeed, the actual experimental observation could not be described within conventional hadronic transport theory [6, 7, 8] and remained a major challenge for microscopic approaches. Only recently, the Parton-Hadron-String Dynamics (PHSD), a transport approach describing heavy-ion collisions on the basis of partonic, hadronic and string degrees-of-freedom, obtained a striking improvement on this issue when including chiral symmetry restoration (CSR) in the string decay for hadronic particle production [9].

2 Chiral symmetry restoration in the string fragmentation process

Our studies are performed within the PHSD transport approach that has been described in Refs. [10, 11]. PHSD incorporates explicit partonic degrees-of-freedom in terms of strongly interacting quasiparticles (quarks and gluons) in line with an equation-of-state from lattice QCD (lQCD) as well as dynamical hadronization and hadronic elastic and inelastic collisions in the final reaction phase.

2.1 Strings in (P)HSD

The string formation and decay represents the dominant particle production mechanism in nucleus-nucleus collisions for bombarding energies from $2\,$AGeV to $160\,$AGeV. In PHSD, the primary hard scatterings between nucleons are described by string formation and decay in the FRITIOF Lund model [12]. The production probability $P$ of massive $s\bar{s}$ or $qq\bar{q}\bar{q}$ pairs is suppressed in comparison to light flavor production ($u\bar{u}$, $d\bar{d}$) according to the Schwinger-like formula [13], i.e.

[TABLE]

with $\kappa\approx 0.176$ GeV2 denoting the string tension and $m_{s},m_{q}=m_{u}=m_{d}$ the appropriate (dressed) strange and light quark masses. Inserting the constituent (dressed) quark masses $m^{v}_{u}\approx 0.33$ GeV and $m^{v}_{s}\approx 0.5$ GeV in the vacuum a value of $\gamma_{s}\approx 0.3$ is obtained from Eq.(1). This ratio is expected to be different in a nuclear medium and actually should depend on the in-medium quark condensate $<\bar{q}q>$.

2.2 The scalar quark condensate

As it is well known the scalar quark condensate $<\bar{q}q>$ is viewed as an order parameter for the restoration of chiral symmetry at high baryon density and temperature. In leading order the scalar quark condensate $\langle\bar{q}q\rangle$ can be evaluated in a dynamical calculation as follows [14]

[TABLE]

where $\sigma_{h}$ denotes the $\sigma$-commutator of the relevant mesons $h$. Furthermore, $<\bar{q}q>_{V}$ denotes the vacuum condensate, $\Sigma_{\pi}\approx$ 45 MeV is the pion-nucleon $\Sigma$-term, $f_{\pi}$ and $m_{\pi}$ the pion decay constant and pion mass, respectively. The quantities $\rho_{S}$ and $\rho_{S}^{h}$ denote the nucleon scalar density and the scalar density for a meson of type $h$, respectively. The scalar density of mesons $h$ is evaluated in the independent-particle approximation, whereas the nucleon scalar density $\rho_{S}$ has to be determined in a suitable model with interacting degrees-of-freedom in order to match our knowledge on the nuclear EoS at low temperature and finite density. A proper (and widely used) approach is the non-linear $\sigma-\omega$ model for nuclear matter which is used here with different parameter sets (NL1,NL2,NL3).

The main idea in Ref. [9] is to consider effective masses for the dressed quarks in the Schwinger formula (1) for the string decay in a hot and dense medium. The effective quark masses can be expressed in terms of a scalar coupling to the quark condensate $\langle\bar{q}q\rangle$ in first order as follows:

[TABLE]

using $m_{s}^{0}\approx$ 100 MeV and $m_{q}^{0}\approx 7$ MeV for the bare quark masses.

3 Application to nucleus-nucleus collisions and discussions

In this section we first study the excitation function of the particle ratios $K^{+}/\pi^{+}$, $K^{-}/\pi^{-}$ and $(\Lambda+\Sigma^{0})/\pi$ at midrapidity from 5% central Au+Au collisions. As already described in Ref. [9], the inclusion of CSR in PHSD is responsible for the strong strangeness enhancement at AGS and low SPS energies. The experimental observations of the ratios $K^{+}/\pi^{+}$ and $(\Lambda+\Sigma^{0})/\pi$ show the well-known ”horn” structure, which is reproduced by the PHSD calculations with CSR. In fact, CSR gives rise to a steep increase of these ratios at energies lower than $\sqrt{s_{NN}}\approx 7\,$GeV, while the drop at larger energies is associated to the appearance of a deconfined partonic medium. We point out that even adopting different parametrizations for the $\sigma-\omega$ model, we recover the same ”horn” feature.

Secondly, we analyze the dependence of the strange to non-strange particle ratios on the size of the colliding system (cf. also Ref. [16]). The inclusion of CSR gives a strangeness enhancement also in case of smaller system size with respect to Au+Au collisions and this holds for all three particle ratios. In fact, when considering central collisions, a sizeable volume of the system is affected by the partial restoration of chiral symmetry even in case of light ions. Concerning the ”horn” structure in the $K^{+}/\pi^{+}$ ratio, we notice that the peak of the excitation function becomes less pronounced in case of Ca+Ca and it disappears completely in case of C+C collisions. With decreasing system size the low energy rise of the excitation functions becomes less pronounced. We can see also that the peak for Ca+Ca is shifted to larger energies with respect to the Au+Au case. Differently from the $K^{+}/\pi^{+}$, the $(\Lambda+\Sigma^{0})/\pi$ ratio preserves the same structure for all three colliding systems.

Finally, we study which parts of the phase diagram in the ($T,\mu_{B}$)-plane are probed by heavy-ion collisions with special focus on the strangeness production. One sees in Fig. 4 that the probed region shifts to larger baryon chemical potentials and smaller temperatures when lowering the beam energy. In addition, it becomes apparent from Fig. 4 that it will be very hard to identify a critical point in the ($T,\mu_{B}$)-plane experimentally since the spread in $T$ and $\mu_{B}$ is very large at all bombarding energies of interest.

Acknowledgements

The authors acknowledge the support by BMBF, HIC for FAIR, H-QM and the HGS-HIRe for FAIR. The computational resources were provided by the LOEWE-CSC.