Starting SQM 2024: Theory state-of-the-art

We study the dynamical chiral symmetry breaking/restoration for various numbers of light quarks flavors and colors using the Nambu-Jona-Lasinio (NJL) model of quarks in the Schwinger-Dyson equation framework, dressed with a color-flavor dependence of effective coupling. For fixed and varying , we observe that the dynamical chiral symmetry is broken when exceeds its critical value . For a fixed and varying , we observe that the dynamical chiral symmetry is restored when reaches its critical value . Strong interplay is observed between and , i.e., larger values of tend to strengthen the dynamical generated quark mass and quark-antiquark condensate, while higher values of suppress both parameters. We further sketch the quantum chromodynamics (QCD) phase diagram at a finite temperature T and quark chemical potential μ for various and . At finite T and μ, we observe that the critical number of colors is enhanced, whereas the critical number of flavors is suppressed as T and μ increase. Consequently, the critical temperature , , and co-ordinates of the critical endpoint in the QCD phase diagram are enhanced as increases and suppressed when increases. Our findings agree with the lattice QCD and Schwinger-Dyson equations predictions.

The 2 + 1 SU(3) Polyakov linear sigma model is used to investigate the respective influence of a finite volume and a magnetic field on the quark-hadron phase boundary in the plane of baryon chemical potential () versus temperature (T) of the quantum chromodynamics (QCD) phase diagram. The calculated results indicate sizable shifts of the quark-hadron phase boundary to lower values of for increasing magnetic field strength, and an opposite shift to higher values of for decreasing system volume. Such shifts could have important implications for the extraction of the thermodynamic properties of the QCD phase diagram from heavy ion data.

Nuclear matter at extremely high temperature and high density is expected to undergo a phase transition to a different state of matter, that is made of deconfined quarks and gluons, such as Quark Gluon Plasma (QGP). The QGP is believed to have existed in early universe just after the Big Bang and/or inside neutron stars. High energy heavy-ion collisions have been carried out in various experiments at AGS, SPS, RHIC and LHC accelerator facilities at Brookhaven National Laboratory (BNL) and European Organization for Nuclear Research (CERN) to create and explore such new state of matter. The experimental results at the highest possible energy regions at RHIC and LHC indicate that the new state of matter has indeed been formed with a partonic degree of freedom, and the phase transition seems to be a smooth crossover that is also expected from the theoretical calculations in the high temperature region of the Quantum Chromo Dynamics (QCD) phase diagram. In the high density area of the QCD phase diagram, the transition is expected to be a first order phase transition and there could be a critical end point for the first order phase transition. The high density region can be reached by lowering the beam energy to a few GeV to a few 10 GeV. Experimental studies with heavy-ion collisions aiming at this high density region are currently being pursued at SPS and RHIC. Future facilities at FAIR, NICA, HIAF and J-PARC are planned. The STAR experiment has been extensively working on the beam energy scan program at RHIC especially around this beam energy region in order to find the first order phase transition as well as signatures from the critical end point in the QCD phase diagram. The recent experimental results of STAR collaboration from the RHIC beam energy scan program will be presented and discussed in this proceedings.

Recently it has been found that quantum chromodynamics (QCD) phase diagram possesses a duality between chiral symmetry breaking and pion condensation. For the first time this was revealed in the QCD motivated toy model. Then it was demonstrated in effective models as well and new additional dualities being found. We briefly recap the main features of this story and then discuss its applications as a tool to explore the QCD phase structure. The most appealing application is the possibility of getting the results on the QCD phase diagram at large baryon density. Taking the idea from large 1 / N c universalities it was argued that the scenario of circumventing the sign problem with the help of dualities seems plausible. It is also discussed that there is a persistent problem about whether there should be catalysis or anti-catalysis of chiral symmetry breaking by chiral imbalance. One can probably say that the issue is settled after lattice results (first principle approach), where the catalysis was observed. But they used an unphysically large pion mass so it is still interesting to get additional indications that this is the case. It is shown just by the duality property that there exists catalysis of chiral symmetry breaking. So, having in mind our results and the earlier lattice simulations, one can probably claim that this issue is settled. It is demonstrated that the duality can be used to obtain new results. As an example, it is showcased how the phase structure of dense quark matter with chiral imbalance (with possibility of inhomogeneous phases) can be obtained from the knowledge of a QCD phase diagram with isopin asymmetry.

The STAR detector upgrades for the BES II and beyond physics program

The phase diagram of quantum chromodynamics under different external parameters, such as the temperature, baryon chemical potential, and magnetic field strength, is studied using the method of lattice supercomputer simulation. The calculations are carried out with three light quarks u, d, and s using an imaginary chemical potential. The results for real values of chemical potential μ are obtained by the method of analytic continuation. Using the renormalized chiral condensate and Polyakov loop, the positions (critical temperature) and widths of the confinement–deconfinement and chiral symmetry breaking–restoration phase transitions are determined as functions of the magnetic field and baryon density.

The phase diagram of quantum chromodynamics (QCD) and its associated thermodynamic properties of quark-gluon plasma (QGP) are studied in the presence of time-dependent magnetic field. The study plays a pivotal role in the field of cosmology, astrophysics, and heavy-ion collisions. In order to explore the structure of quark-gluon plasma to deal with the dynamics of quarks and gluons, we investigate the equation of state (EoS) not only in the environment of static magnetic field but also in the presence of time-varying magnetic fields. So, for determining the equation of state of QGP at nonzero magnetic fields, we revisited our earlier model where the effect of time-varying magnetic field was not taken into consideration. Using the phenomenological model, some appealing features are noticed depending upon the three different scales: effective mass of quark, temperature, and time-independent and time-dependent magnetic fields. Earlier the effective mass of quark was incorporated in our calculations, and in the current work, it is modified for static and time-varying magnetic fields. Thermodynamic observables including pressure, energy density, and entropy are calculated for a wide range of temperature- and time-dependent as well as time-independent magnetic fields. Finally, we claim that the EoS are highly affected in the presence of a magnetic field. Our results are notable compared to other approaches and found to be advantageous for the measurement of QGP equation of state. These crucial findings with and without time-varying magnetic field could have phenomenological implications in various sectors of high-energy physics.

We study dynamical chiral symmetry breaking for quarks in the fundamental representation of SU(N c) for the N f number of light quark flavors. We also investigate the phase diagram of quantum chromodynamics at finite temperature T and/or in the presence of a constant external magnetic field eB. The unified formalism for this analysis is provided by a symmetry-preserving Schwinger–Dyson equation treatment of a vector × vector contact interaction model which encodes several well-established features of quantum chromodynamics to mimic the latter as closely as possible. Deconfinement and chiral symmetry restoration are triggered above a critical value of N f at T = 0 = eB. On the other hand, increasing temperature itself screens strong interactions, thus ensuring that a smaller value of N f is sufficient to restore chiral symmetry at higher temperatures. We also observe the well-known phenomenon of magnetic catalysis for a strong enough magnetic field. However, we note that if the effective coupling strength of the model decreases as a function of magnetic field, it can trigger inverse magnetic catalysis in a certain window of this functional dependence. Our model allows for the simultaneous onset of dynamical chiral symmetry breaking and confinement for each case. Qualitative as well as quantitative predictions of our simple but effective model are in reasonably satisfactory agreement with lattice results and other reliable and refined predictions based upon intricate continuum studies of quantum chromodynamics.

We study the impact of steady, homogeneous, and external parallel electric and magnetic field strengths ( ) on the chiral symmetry breaking-restoration and confinement-deconfinement phase transition. We also sketch the phase diagram of quantum chromodynamics (QCD) at a finite temperature T and in the presence of background fields. The unified formalism for this study is based on the Schwinger-Dyson equations, symmetry preserving vector-vector contact interaction model of quarks, and an optimal time regularization scheme. At , in the purely magnetic case (i.e., ), we observe the well-known magnetic catalysis effect. However, in a pure electric field background ( ), the electric field tends to restore the chiral symmetry and deconfinement above the pseudo-critical electric field . In the presence of both and , we determine the magnetic catalysis effect in the particular region where dominates over , whereas we observe the chiral inhibition (or electric chiral rotation) effect when overshadows eB. At finite T, in the pure electric field case, the phenomenon of inverse electric catalysis appears to exist in the proposed model. Conversely, for a pure magnetic field background, we observe the magnetic catalysis effect in the mean-field approximation and inverse magnetic catalysis with -dependent coupling. The combined effects of and on the pseudo-critical yields an inverse electromagnetic catalysis, with and without an -dependent effective coupling of the model. The findings of this study agree well with the already predicted results obtained via lattice simulations and other reliable effective models of QCD.

The quantum chromodynamics (QCD) phase diagram, which reveals the state of strongly interacting matter at different temperatures and densities, is key to answering open questions in physics, ranging from the behaviour of particles in neutron stars to the conditions of the early universe. However, classical simulations of QCD face significant computational barriers, such as the sign problem at finite matter densities. Quantum computing offers a promising solution to overcome these challenges. Here, we take an important step toward exploring the QCD phase diagram with quantum devices by preparing thermal states in one-dimensional non-Abelian gauge theories. We experimentally simulate the thermal states of SU(2) and SU(3) gauge theories at finite densities on a trapped-ion quantum computer using a variational method. This is achieved by introducing two features: Firstly, we add motional ancillae to the existing qubit register to efficiently prepare thermal probability distributions. Secondly, we introduce charge-singlet measurements to enforce colour-neutrality constraints. This work pioneers the quantum simulation of QCD at finite density and temperature for two and three colours, laying the foundation to explore QCD phenomena on quantum platforms.

We suggest the idea, supported by concrete calculations within chiral models, that the critical endpoint of the phase diagram of Quantum Chromodynamics with three colors can be detected, by means of Lattice simulations of grand-canonical ensembles with a chiral chemical potential, $\mu_5$, conjugated to chiral charge density. In fact, we show that a continuation of the critical endpoint of the phase diagram of Quantum Chromodynamics at finite chemical potential, $\mu$, to a critical end point in the temperature-chiral chemical potential plane, is possible. This study paves the way of the mapping of the phases of Quantum Chromodynamics at finite $\mu$, by means of the phases of a fictitious theory in which $\mu$ is replaced by $\mu_5$.

Critical phenomena emerging from the critical end point of a first-order transition are ubiquitous in nature. Here we bring the concept of a supercritical crossover, the Widom line, initially developed in the context of fluids, into the interacting matter described by quantum chromodynamics (QCD). We show that the existence of the putative critical end point between hadron gas and quark-gluon plasma in the temperature versus chemical potential of the QCD phase diagram implies the existence of a Widom line emerging from it in the supercritical region. We survey the thermodynamic anomalies already identified in simplified theoretical models of QCD exhibiting a critical end point, to show that they can be interpreted in terms of a Widom line. Then we suggest possible directions where the Widom line concept could provide new light on the QCD phase diagram. Published by the American Physical Society 2024

Two measurements related to the proton and antiproton production near midrapidity in \(\sqrt {s_{{NN}}} = 7.7\), 11.5, 19.6, 27, 39, 62.4 and 200 GeV Au+Au collisions using the STAR detector at the Relativistic Heavy Ion Collider (RHIC) are discussed. At intermediate impact parameters, the net-proton midrapidity dv1/dy, where v1 and y are directed flow and rapidity, respectively, shows non-monotonic variation as a function of beam energy. This non-monotonic variation is characterized by the presence of a minimum in dv1/dy between \(\sqrt {s_{NN}} = 11.5\) and 19.6 GeV and a change in the sign of dv1/dy twice between \(\sqrt {s_{{NN}}}\) = 7.7 and 39 GeV. At small impact parameters the product of the moments of net-proton distribution, kurtosis × variance (κσ2) and skewness × standard deviation (Sσ) are observed to be significantly below the corresponding measurements at large impact parameter collisions for \(\sqrt {s_{{NN}}}\) = 19.6 and 27 GeV. The κσ2 and Sσ values at these beam energies deviate from the expectations from Poisson statistics and that from a hadron resonance gas model. Both these measurements have implications towards understanding the quantum chromodynamics (QCD) phase structures, the first-order phase transition and the critical point in the high baryonic chemical potential region of the phase diagram.

The majority of the phase diagram of quantum chromodynamics (QCD), especially at non- vanishing baryon densities, is not explored from the theoretical side. This is caused by the non-applicability of perturbative methods, due to the strong coupling at all temperatures T and quark chemical potentials μ, which are not asymptotically large, and numerical lattice methods, which are valid only for μ/T < 1. A deeper theoretical understanding of the QCD phase structure at intermediate baryon densities has direct implications for the study of matter under extreme conditions, such as in heavy-ion-collisions and the interior of neutron stars. In the absence of first-principle methods, investigations of the phase structure at intermediate chemical potentials and temperature are carried out mostly using effective models, that capture certain, essential features of QCD but not all of them. This thesis explores mechanisms for the formation of regimes with spatially modulated, chiral observables in QCD at non-vanishing μ using QCD-inspired theories. In particular, we focus on two such regimes: a crystalline phase, the inhomogeneous phase (IP), where the chiral condensate is non-uniform and periodically varying in space, and a liquid-like phase, the quantum pion liquid (QπL), characterized by spatially oscillatory, intermediate- range correlations of mesonic fields. Hints in the literature imply the possible existence of spatially modulated regimes in QCD around the expected critical point (CP), which marks the end of the chiral crossover transition at low and zero μ. To incorporate new, relevant features of QCD in model studies, we employ renormal- izable 2 + 1-dimensional four-fermion models and investigate the effects of these features on the phase structure within the mean-field approximation, where bosonic quantum fluc- tuations are suppressed. In a complementary approach, the influence of bosonic quantum fluctuations on inhomogeneous condensates is investigated with lattice field theory (LFT) simulations of a scalar O(N ) model. A key finding of this thesis is that the novel inclusion of scalar-vector meson mixing induces spatially oscillating, exponentially damped mesonic correlation functions, i.e., a QπL is observed in the phase diagram of the studied four-fermion model. This result aligns with arguments in the literature expecting spatially modulated regimes from the emergent combined symmetry of the model under charge conjugation and complex conjugation, which is also present in QCD at μ̸ = 0. Moreover, the stability of homogeneous ground states is proven within the phase diagram of all four-fermion models in two spatial dimensions. We argue that this finding suggests the absence of IPs in these models with the mean- field approximation and in the full quantum theories. Further, Monte-Carlo simulations of a scalar O(N ) model, which classically features an IP, reveal that bosonic quantum fluctuations disorder inhomogeneous condensates in finite spatial volumes and, instead, a QπL is observed. The findings suggest that the scenario of a QπL is more likely to be realized in QCD than an IP, since the presence of bosonic quantum fluctuations, mixing effects between scalar and vector mesons, and emergent symmetries at μ̸ = 0 seem to favor the formation of QπLs. A crucial next step to provide quantitative, theoretical predictions for the QCD phase diagram is to incorporate the above mentioned effects in more sophisticated model approaches as well as in functional computations.

A significant goal of high-energy nuclear collisions is to determine the Quantum Chromodynamics (QCD) phase diagram for the strongly interacting matter. The most experimentally accessible way to characterize the QCD phase diagram is to scan in temperature (T) and the baryon chemical potential ($\mu_B$). The hadronic matter exists in a state where the fundamental constituents, quarks and gluons, are confined in composite particles. At high energy densities, QCD predicts a phase transition from a hadronic gas to a state of deconfined matter - the quark-gluon plasma (QGP). In a hot and dense state QCD matter is melted into its constituent quarks, and the strong interaction becomes dominant. In addition, a chiral phase transition is predicted. QCD-based models predict a first-order phase transition and the existence of a critical point (CP) at higher $\mu_B$. However, the exact locations of the first-order phase transition and the CP are still unknown. Experiments at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) have provided compelling evidences of the formation of a QGP matter close to $\mu_B$ = 0. In order to study the QCD phase structure experimentally as a function of T and $\mu_B$, the Beam Energy Scan (BES) program at RHIC was proposed. Several collision energies are used to create systems described by various initial coordinates of T and $\mu_B$. The experimental goals of the BES program are the following: search for threshold energies for the QGP signatures, search for signatures of a first-order phase transition, search for a CP, and search for possible signatures of chiral symmetry restoration. In these proceedings, we present the current status of the BES program at the STAR experiment.