Fast Equilibration of Hadrons in an Expanding Fireball

Abstract

Due to long chemical equilibration times within standard hadronic reactions during the hadron gas phase in relativistic heavy ion collisions it has been suggested that the hadrons are "born" into equilibrium after the quark gluon plasma phase. Here we develop a dynamical scheme in which possible Hagedorn states contribute to fast chemical equilibration times of baryon anti-baryon pairs (as well as kaon anti-kaon pairs) inside a hadron gas and just below the critical temperature. Within this scheme, we use master equations and derive various analytical estimates for the chemical equilibration times. Applying a Bjorken picture to the expanding fireball, the kaons and baryons as well as the bath of pions and Hagedorn resonances can indeed quickly chemically equilibrate for both an initial overpopulation or underpopulation of Hagedorn resonances. Moreover, a comparison of our results to (B +B)/π + and K/π + ratios at RHIC, indeed, shows a close match. PACS numbers:(Anti-)strangeness enhancement was first observed at CERN-SPS energies by comparing anti-hyperons, multistrange baryons, and kaons to pp-data. It was considered a signature for quark gluon plasma (QGP) because, using binary strangeness production and exchange reactions, chemical equilibrium could not be reached within the hadron gas phase [1]. It was then proposed that there exists a strong hint for QGP at SPS because strange quarks can be produced more abundantly by gluon fusion, which would account for strangeness enhancement following hadronization and rescattering of strange quarks. Later, multi-mesonic reactions were used to explain secondary production of anti-protons and antihyperons [2,3]. At SPS they give a typical chemical equilibration time τȲ ≈ 1 − 3 fm c using an annihilation cross section of σ ρȲ ≈ σ ρp ≈ 50mb and a baryon density of ρ B ≈ ρ 0 to 2ρ 0 , which is typical for SPS. Therefore, the time scale is short enough to account for chemical equilibration within a cooling hadronic fireball at SPS.A problem arises when the same multi-mesonic reactions were employed in the hadron gas phase at RHIC temperatures where experiments show that the particle abundances reach chemical equilibration close to the phase transition [4]. At RHIC at T = 170 MeV, where σ ≈ 30mb and ρ eq B ≈ ρ eq B ≈ 0.04fm −3 , the equilibrium rate for (anti-)baryon production is τ ≈ 10 fm c , which is considerably longer than the fireball's lifetime in the hadronic stage of τ < 5 fm c . Moreover, τ ≈ 10 fm c was also obtained in Ref.[5] using a fluctuation-dissipation theorem and a significant deviation was found in the population number of various (anti-)baryons from experimental data in the 5% most central Au-Au collisions [6]. These discrepancies suggest that hadrons are "born" into equilibrium, i.e., the system is already in a chemically frozen out state at the end of the phase transition [7,8].In order to circumvent such long time scales it was suggested that near T c there exists an extra large particle density overpopulated with pions and kaons, which drive the baryo...

Bulk and shear viscosities of hot and dense hadron gas

“…On the other hand, an exponentially increasing density of state was necessary to explain the rapid increase in entropy density near the transition region in lattice QCD simulation [31]. Such exponential rise of density of states has also been used to study observables like dilepton production [32] as well as chemical equilibration [33]. Motivated by such observations we take the modified spectral function as [18,34,35] …”

Hadron mass spectrum and the shear viscosity to entropy density ratio of hot hadronic matter

“…When T < 100 MeV, the discreteness of the hadron spectrum becomes relevant and the continuous approximation discussed here gives a poor description of the thermodynamic quantities of a hadron resonance gas. Therefore, to have a hadronic equation of state that is valid at both low temperatures (T < 100 MeV) and higher temperatures a hybrid model containing the measured hadron states plus a continuous Hagedorn spectrum above a certain mass cutoff is more appropriate [16][17][18][19][20].…”

“…[13] that a small value of η/s in QCD should occur in the transition region T ∼ 150-200 MeV owing to the rapid increase in the entropy density observed in lattice simulations [14,15], the effects of an exponentially increasing density of hadronic states on several properties of hot hadronic matter were investigated using the hadron resonance gas model in Refs. [16][17][18][19][20]. It was shown in those studies that the addition of new hadronic states that follow an exponentially increasing hadron mass spectrum as proposed by Hagedorn [21], …”

Hadron yields and the phase diagram of strongly interacting matter

“…[48]) that this could explain the tension, as decays of high mass resonances would affect pions more than protons. Quantitative calculations were made in [49,50,51], where it was shown that reasonable assumptions on high mass resonances based on the Hagedorn spectrum could explain the low p/π. However, these additional states could potentially spoil the agreement with other particle ratios (most notably, multistrange baryons, which could however be included as discussed [52]) and some of the underlying assumptions of the model are not constrained by first principles.…”