Masakiyo Kitazawa

The analytic structure of the partition function in finite-volume systems is investigated at complex chemical potentials in a minimal mean-field effective model of QCD with finite-size effects incorporated. We discuss the temperature dependence of the Lee-Yang zeros and their relation to the edge singularity for various system sizes. Different methods for locating the critical point based on finite-size scaling of Lee-Yang zeros and susceptibility ratios are compared. We demonstrate that these methods can successfully identify the critical point, whereas a careful treatment of corrections from irrelevant operators is crucial for its accurate determination.

We give a systematic account of the soft mode dynamics of QCD critical point and the two-flavor color superconductivity based on the two-flavor Nambu–Jona-Lasinio model and investigate their effects on electromagnetic observables in relativistic heavy-ion collisions (HICs). We first demonstrate that the collective excitations coupled to the fluctuations of the respective order parameters are the soft modes associated with the phase transitions, in the sense that they acquire a prominent spectral strength in the low-energy and low-momentum region near the phase transitions, and the peak energy goes down, i.e., becomes softened and eventually vanishes at the critical point. It is shown that the diquark soft mode of the 2SC gives rise to the pseudogap, i.e., a depression in the density of states of the quark spectra around the Fermi surface above but in the vicinity of the critical temperature. Then, exploiting the ideas that were developed in condensed matter physics for describing the ‘para-conductivity’ in the normal phase of metal superconductors, we show that the soft modes cause an anomalous enhancement of electric conductivity and the dilepton production rate and discuss their relevance to HICs.

We investigate the thermodynamic properties of fermionic excitations in heavy-quark QCD on the lattice with Wilson fermions. The grand potential is calculated analytically in the hopping parameter expansion (HPE) on the basis of the cumulant expansion. Using the grand potential, we compute the quark number susceptibilities and their ratios up to next-to-leading order in the HPE. The ratio of fourth- to second-order susceptibilities is shown to be unity (nine) in the deconfined (confined) phase at the leading order. Excitation properties of baryonic and quark modes in each phase are also investigated utilizing the Boltzmann statistics. We obtain an analytic formula for the quark excitation energy in the deconfined phase, while that for baryonic excitations in the confined phase is decomposed into flavor multiplets.

We investigate the thermodynamic properties of fermionic excitations in heavy-quark QCD on the lattice with Wilson fermions. The grand potential is calculated analytically in the hopping parameter expansion (HPE) on the basis of the cumulant expansion. Using the grand potential, we compute the quark number susceptibilities and their ratios up to next-to-leading order in the HPE. The ratio of fourth- to second-order susceptibilities is shown to be unity (nine) in the deconfined (confined) phase at the leading order. Excitation properties of baryonic and quark modes in each phase are also investigated utilizing the Boltzmann statistics. We obtain an analytic formula for the quark excitation energy in the deconfined phase, while that for baryonic excitations in the confined phase is decomposed into flavor multiplets.

There has been increasing interest in recent years in using relativistic heavy-ion collisions to probe nuclear structure, such as static nuclear deformation. Here we discuss the role of quantum zero-point fluctuations of the surface vibration of spherical nuclei in relativistic heavy-ion collisions. To this end, we employ an approach to describe the vibration in the space-fixed frame, which has been well established in the field of low-energy heavy-ion fusion reactions. We particularly consider the quadrupole vibration of $^{58}$Ni in $^{58}$Ni+$^{58}$Ni reaction and the octupole vibration of $^{208}$Pb in $^{208}$Pb+$^{208}$Pb reaction. We show that the surface vibration leads to comparable eccentricity parameters to those for static deformation, while they give significantly different distributions of the initial states, suggesting the importance of the proper treatment of the surface vibration in heavy-ion collisions. We perform similar analysis also for triaxial deformation and gamma-soft vibration.

We investigate the volume and lifetime of the high-baryon-density matter created in heavy-ion collisions and estimate the optimal collision-energy range to realize the high-baryon-density region over a large space-time volume. We simulate central collisions of gold ions for the center-of-mass energy per nucleon pair s N N = 2.4 − 19.6 GeV with a microscopic transport model JAM. We discover that the optimal range is around s N N = 3 − 5 GeV , where a baryon density exceeding three times the normal nuclear density is realized with a substantially large space-time volume. Higher and lower energies are disfavored due to short lifetime and low density, respectively. We also point out that event-by-event fluctuations of the space-time density profile are large, indicating the importance of the event selection in the experimental analysis.

We propose a method to numerically determine the location of a critical point in general systems using the finite-size scaling of Lee-Yang zeros. This method makes use of the fact that the ratios of Lee-Yang zeros on various spatial volumes intersect at the critical point. While the method is similar to the Binder-cumulant analysis, it is advantageous in suppressing the finite-volume effects arising from the mixing of variables in general systems. We show that the method works successfully for numerically locating the critical point in the three-dimensional three-state Potts model with a nonzero external field. Published by the American Physical Society 2025