Deconfinement can be described by the spontaneous breaking of Z(3) center symmetry. The relevant quantities to study are the Polyakov loop and its susceptibilities. The Polyakov loop reflects the free energy of a static quark immersed in a hot gluonic medium. At low temperatures its thermal expectation value vanishes, signaling color confinement, while at high temperatures it is nonzero, resulting in a finite energy of a static quark and consequently the deconfinement of color. It is thus an order parameter for the deconfining phase transition.The Polyakov loop susceptibility, on the other hand, represents fluctuations of the order parameter. It exhibits a peak at the transition temperature, and a width that signals the temperature window in which the phase transition takes place. While the basic thermodynamic functions of the SU(3) pure gauge theory, such as pressure and entropy, are well established within the lattice approach, the temperature dependence of the renormalized Polyakov loop and its susceptibilities are less clear. A careful study of these quantities will improve our understanding of the QCD phases.In SU(3) gauge theory, the Polyakov loop is a complexvalued operator. One can therefore explore the fluctuations of the order parameter along the longitudinal (real) and transverse (imaginary) directions. However, the proper renormalization for these composite gluonic correlators remains ambiguous. One way to circumvent this problem is to consider the ratios of susceptibilities [1]. . In the pure gauge limit (N f = 0), the ratio R T is discontinuous at T c , and change only weakly with temperature on either side of the transition. This feature makes the ratio ideal for probing deconfinement. At high temperatures, the Z(3) symmetry is spontaneously broken. The pure gauge result indicates a small value for this ratio. In terms of an effective potential, this finding suggests that, around the global minimum associated with the symmetrybroken vacuum, the curvature in the transverse direction is much steeper than that in the longitudinal direction.In the presence of light quarks, the Polyakov loop is no longer a true order parameter for deconfinement owing to the explicit breaking of the Z(3) symmetry. The ratio is smoothened and vary continuously across the pseudocritical temperature. One expects that the width of the crossover transition depends on the number of flavors and the values of quark masses. The value of R T at high temperatures is found to deviate substantially from the pure gauge limit. An interpretation of this feature is still lacking.We conclude that the ratio of Polyakov loop susceptibilities provides an excellent signal for the deconfinement phase transition. One immediate application of this work is to constrain the parameters used in effective models, thus providing a more realistic description of the QCD phase structure [2]. Further, more detailed lattice calculations are needed in order to obtain robust results for the gluonic correlation functions, as well as a better understanding of...
We calculate the Polyakov loop susceptibilities in the SU(3) lattice gauge theory using the Symanzik improved gauge action on different-sized lattices. The longitudinal and transverse fluctu- ations of the Polyakov loop, as well as, that of its absolute value are considered. We analyze their properties in relation to the confinement-deconfinement phase transition. We also present results based on simulations of (2+1)-flavor QCD on 323×8 lattice using Highly Improved Staggered Quark (HISQ) action by the HotQCD collaboration. The influences of fermions on the Polyakov loop fluctuations are discussed. We show, that ratios of different susceptibilities of the Polyakov loop are sensitive probes for critical behavior. We formulate an effective model for the Polyakov loop potential and constrain its parameters from existing quenched lattice data including fluctuations. We emphasize the role of fluctuations to fully explore the thermodynamics of pure gauge theory within an effective approach
We propose a resolution of the discrepancy between the proton yield predicted by the statistical hadronization approach and data on hadron production in ultra-relativistic nuclear collisions at the LHC. Applying the S-matrix formulation of statistical mechanics to include pion-nucleon interactions, we reexamine their contribution to the proton yield, taking resonance widths and the presence of nonresonant correlations into account. The effect of multi-pion-nucleon interactions is estimated using lattice QCD results on the baryon-charge susceptibility. We show that a consistent implementation of these features in the statistical hadronization model, leads to a reduction of the predicted proton yield, which then quantitatively matches data of the ALICE collaboration for Pb-Pb collisions at the LHC.
Motivated by recent lattice QCD studies, we explore the effects of interactions on strangeness fluctuations in strongly interacting matter at finite temperature. We focus on S-wave Kπ scattering and discuss the role of the K * 0 (800) and K * (1430) resonances within the S-matrix formulation of thermodynamics. Using the empirical Kπ phase shifts as input, we find that the Kπ S-wave interactions provide part of the missing contribution to the strangeness susceptibility. Moreover, it is shown that the simplified treatment of the interactions in this channel, employed in the hadron resonance gas approach, leads to a systematic overestimate of the strangeness fluctuations. In particular, the HRG results for the strangeness and mixed strangeness-baryon number susceptibilities (χ SS and χ BS ) are clearly below those of the lattice, while the results for the thermodynamic pressure and the baryon number susceptibility are in good agreement.This motivates the search for hitherto unknown strange hadrons, which could reduce or eliminate this discrepancy. In the PDG database, there are around twenty unconfirmed states with a mass below 2.0 GeV. Although these are not established resonances, the interactions in the corresponding scattering channels may yield important contribution to thermodynamic quantities.More generally, a possible origin of the discrepancy is interaction strength in channels carrying net strangeness that so far have not been accounted for. Given the corresponding empirical scattering phase shifts, both confirmed and unconfirmed resonances as well as nonresonant interactions can be handled in a unified, modelindependent way, using the S-matrix approach of Ref. [3].The strange scalar channel, with the unconfirmed K * 0 (800) resonance, a.k.a. κ, is a prime candidate. Since the corresponding phase shifts for S-wave Kπ scattering are fairly well determined, this channel is well suited for the S-matrix approach. In addition, the counterpart of κ in the scalar-isoscalar channel, the f 0 (500), a.k.a. σ, though considered to be established [4], is unlike a typical resonance. Since the ππ S-wave phase shifts are known with reasonable accuracy, also this channel is a prime candidate for the S-matrix approach to thermodynamics. In this study we focus on the strange scalar channel and its contribution to strangeness susceptibilities.With the relatively low mass of the interaction strength in the κ channel, it potentially has a large impact on the thermodynamics, in particular on χ SS , owing to the moderate suppression by the Boltzmann factor. In Fig. 1, we illustrate the effect of the κ resonance on pressure and strangeness fluctuation within the HRG approach. For the PDG particle spectrum, we use only confirmed baryons (i.e. three and four star resonances) and established mesons. The contribution of κ to the thermodynamics is approximated by that of an ideal gas of zero-width mesons with mass m κ = 0.682 GeV and degeneracy four. Indeed, the inclusion of this single state improves the HRG result on χ SS dramatica...
We compute the correlation of the net baryon number with the electric charge (χBQ) for an interacting hadron gas using the S-matrix formulation of statistical mechanics. The observable χBQ is particularly sensitive to the details of the pion-nucleon interaction, which are consistently incorporated in the current scheme via the empirical scattering phase shifts. Comparing to the recent lattice QCD studies in the (2 + 1)-flavor system, we find that the natural implementation of interactions and the proper treatment of resonances in the S-matrix approach lead to an improved description of the lattice data over that obtained in the hadron resonance gas model. 25.75.Ld, 12.38.Mh, 24.10.Nz Introduction.-Recent lattice QCD (LQCD) results on the equation of states and the fluctuations of conserved charges provide a very detailed description of the QCD thermal medium [1][2][3][4][5]. In particular the local fluctuations of conserved charges can be probed by appropriate combinations of mixed susceptibilities. An accurate determination of these quantities is also needed to reliably extend the LQCD calculations to finite densities using the Taylor's expansion scheme [6].Confinement dictates that hadrons, instead of quarks and gluons, fill the physical spectrum of QCD, while the spontaneous breaking of chiral symmetry makes pions exceptionally light due to their role as (pseudo-) Goldstone bosons. We thus expect that at low temperatures the partition function can be effectively described by an interacting gas of low-mass hadrons such as pions, kaons, and nucleons.A well-known effective approach which adopts the hadronic degrees of freedom in describing the thermodynamics of strongly interacting matter is the hadron resonance gas (HRG) model. This model assumes that resonance formation dominates the interactions of the confined phase, and as a first approximation, treats the resonances as an ideal gas. The approach gives a satisfactory description of the particle yields measured in heavy ion collisions [7][8][9][10][11][12][13][14], and is capable of providing an overall successful interpretation of LQCD results on bulk properties below the transition temperature [1][2][3][4][5][15][16][17].Nevertheless, the HRG model also makes some simplifying assumptions which are not necessarily consistent with the known hadron physics. Some of the problematic cases include the zero-width treatment of broad resonances [18-20] (e.g. the σ-and κ-meson), and the neglect of non-resonant contributions from both attractive and repulsive channels in computing the thermal observables [21].Very precise information about the hadronic interactions has emerged from the impressive volume of experimental data [22], carefully analyzed by theory such as
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