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Experimental investigations of the phase diagram of strongly interacting matter involve collisions of heavy ions at ultrarelativistic velocities. The medium created in such a collision is often of dimensions a few fermi, in particular in the Beam Energy Scan experiments. An understanding of the effect of the finite volume and the boundary is important for connecting the experimental results to the phase diagram. Using the Nambu Jona-Lasinio model, an effective theory for the chiral transition of quantum chromodynamics (QCD), we have studied the effect of the finite volume of the fireball on the transition line at finite temperature and density using the MIT boundary condition to mimic the condition that the system is deconfined inside. The shift of the transition temperature for finite volume and finite volume effect on number density and its susceptibilities are studied. The volume effects should be considered when looking for signatures of the phase diagram in experiments., Comment: 14 pages, 11 figures. Minor changes in text, one figure updated

The discovery and characterization of hot and dense QCD matter, known as Quark Gluon Plasma (QGP), remains the most international collaborative effort and synergy between theorists and experimentalists in modern nuclear physics to date. The experimentalists around the world not only collect an unprecedented amount of data in heavy-ion collisions, at Relativistic Heavy Ion Collider (RHIC), at Brookhaven National Laboratory (BNL) in New York, USA, and the Large Hadron Collider (LHC), at CERN in Geneva, Switzerland but also analyze these data to unravel the mystery of this new phase of matter that filled a few microseconds old universe, just after the Big Bang. In the meantime, advancements in theoretical works and computing capability extend our wisdom about the hot-dense QCD matter and its dynamics through mathematical equations. The exchange of ideas between experimentalists and theoreticians is crucial for the progress of our knowledge. The motivation of this first conference named "HOT QCD Matter 2022" is to bring the community together to have a discourse on this topic. In this article, there are 36 sections discussing various topics in the field of relativistic heavy-ion collisions and related phenomena that cover a snapshot of the current experimental observations and theoretical progress. This article begins with the theoretical overview of relativistic spin-hydrodynamics in the presence of the external magnetic field, followed by the Lattice QCD results on heavy quarks in QGP, and finally, it ends with an overview of experiment results., Comment: Compilation of the contributions (148 pages) as presented in the `Hot QCD Matter 2022 conference', held from May 12 to 14, 2022, jointly organized by IIT Goa & Goa University, Goa, India

The energy loss pattern of a low momentum heavy quark in a deconfined quark-gluon plasma can be understood in terms of a Langevin description. In thermal equilibrium, the motion can then be parametrized in terms of a single heavy quark momentum diffusion coefficient kappa, which needs to be determined nonperturbatively. In this work, we study the temperature dependence of kappa for a static quark in a gluonic plasma, with a particular emphasis on the temperature range of interest for heavy ion collision experiments., Comment: 12 pages, 9 figures. The discussion section and the appendix substantially modified, two figures added, typos fixed

In our world the standard model of particle physics contains within it the fairly intractable theory called QCD. A toy version with two colours is often studied as a model confining and chiral symmetry breaking field theory. Here we investigate the cascade of changes at various distance scales if we make this change within the standard model. It is possible to limit the changes at the hadronic scale. However, the minor changes that occur actually cascade down to the far infrared, into nuclear and atomic physics, and chemistry. Through this it also possibly affects the evolution of stars and galaxies. We remark on this unexpected sensitivity of the universe to physics at the scale of quarks., Comment: Submitted to Indian Journal of Physics memorial issue for Pushan Majumdar

We investigate the interaction between a heavy quark-antiquark pair in color octet configuration in gluon plasma. We calculate nonperturbatively an effective thermal potential for such a pair through the study of the correlation function of a hybrid state with $Q \bar{Q}$ octet and an adjoint gluon source in the static limit. We discuss the extraction of an octet potential, and present results for the effective thermal potential between octet $Q \bar{Q}$ pair in gluon plasma for moderately high temperatures $\lesssim 2 T_c$. The implications of our result are discussed., Comment: 17 pages, 13 figures. Figures 8, 9 and two figures in appendix modified. Some minor notational changes. No change of conclusion

A non-perturbative calculation of the effective thermal potential between heavy $Q$ and $\bar Q$ from lattice QCD is difficult, and usually involves a Bayesian analysis. Here we present a simple method to obtain the potential from smeared Wilson loop, using the structure of the thermal Wilson loop. We present results for the $Q \bar Q$ thermal potential in a gluonic plasma for temperatures $\lesssim 2 T_c$. We also present preliminary results for the effective potential when the $Q$ and $\bar Q$ are in octet color configuration., Comment: 7 pages, 5 figures, contribution to Lattice 2019

A thermal potential can be defined to facilitate understanding the behavior of quarkonia in quark-gluon plasma. A nonperturbative evaluation of this potential from lattice QCD is difficult, as it involves real-time corelation function, and has often involved the use of Bayesian analysis, with its associated systematics. In this work we show that using the properties of the static quarkonia thermal correlation functions, one can directly extract a thermal potential for quarkonia from Euclidean Wilson loop data. This leads to a controlled extraction, and allows us to judge the suitability of various model potentials. We also discuss the phenomenology of quarkonia in the gluonic plasma., Comment: 17 pages, 14 figures. Argument extended in appendix, minor changes in figure label, caption, and text. No change in results

Quarkonia are some of the most important probes of the medium created in relativistic heavy ion collision experiments, but it is still difficult to get quantitative results for its behavior in the plasma. Here I discuss the decay width of a heavy quarkonium system, and calculate the gluodissociation width of bottomonia. In the end I comment on study of quarkonia as open quantum systems.

Wilson flow is an effective tool for constructing renormalized composite operators. We explore use of the Wilson flow to construct renormalized order parameters for the deconfinement transition in SU(3) gauge theory. We discuss renormalization of the Polyakov loop, and of gluon condensates., Comment: 7 pages, contribution to Lattice 2016, held in Southampton, UK

We report the measurement of quark number susceptibilities (QNS) and their temperature dependence from simulations of QCD with two flavours of light dynamical staggered quarks at finite temperature on 8 * 32^3 lattices. From the radius of convergence of the Taylor expansion we estimate the critical end point. We use a Pade approximant to resum the series expansion and compute the equation of state at finite chemical potential, namely the baryon number density and its contribution to the pressure. We also report the isothermal compressibility of QCD matter at finite baryon density. Finally we explore the freezeout conditions for a measure of fluctuations. We examine some sources of systematic and statistical errors in all of these measurements., Comment: 12 pages, 10 figures

We compare lattice scales determined from the vector meson mass and the Wilson flow scale w_0 in QCD with two-flavours of rooted naive staggered fermions over a wide range of lattice spacing and quark mass. We find that the distributions of meson correlation functions are non-Gaussian. We modify the statistical analysis to take care of the non-Gaussianity. Current day improvements in the statistical quality of data on hadron correlations further allow us to simplify certain aspects of the analysis of masses. We examine these changes through the analysis of pions and apply them to the vector meson. We compare the flow scale determined using the rho mass with that using Lambda_{MSbar}., Comment: 10 pages, 6 figures, reference added

We explore the use of Wilson flow to study the deconfinement transition in SU(3) gauge theory. We use the flowed Polyakov loop as a renormalized order parameter for the transition, and use it to renormalize the Polyakov loop. We also study the flow properties of the electric and magnetic gluon condensates, and demonstrate that the difference of the flowed operators shows rapid change across the transition point., Comment: 13 pages, 10 figures. Small changes in figures and discussion, results unchanged. Published version

Scale setting for QCD with two flavours of staggered quarks is examined using Wilson flow over a factor of four change in both the lattice spacing and the pion mass. The statistics needed to keep the errors in the flow scale fixed is found to increase approximately as the inverse square of the lattice spacing. Tree level improvement of the scales t_0 and w_0 is found to be useful in most of the range of lattice spacings we explore. The scale uncertainty due to remaining lattice spacing effects is found to be about 3%. The ratio w_0/\sqrt{t_0} is N_f dependent and we find its continuum limit to be 1.106 \pm 0.007 (stat) \pm 0.005 (syst) for m_\pi w_0 \simeq 0.3.

The behavior of quarkonia in relativistic heavy ion collisions is reviewed. After a detailed discussion of the current theoretical understanding of quarkonia in a static equilibriated plasma, we discuss quarkonia yield from the fireball created in ultrarelativistic heavy ion collision experiments. We end with a brief discussion of the experimental results and outlook., Comment: Review article for Pramana. 17 pages. Discussion in Sec. 2.2 extended, one error corrected, references updated and some typos corrected. Published version

Using non-perturbative lattice method we studied hadronic screening correlators above and immediately below the deconfinement transition temperature, Tc, in the quenched approximation with lattice spacing of 1/(8T) using clover improved Wilson fermions. Simulations were performed at temperatures T /Tc = 0, 0.95 and 1.5. Mesonic screening correlators show no statistically significant thermal effects below Tc, and clear evidence for weakly interacting quarks above Tc . Baryon screening correlators yield similar physics above Tc, but show precursor effects for chiral symmetry restoration below Tc ., Comment: 12 pages, 8 figures, typos corrected

We calculate the momentum diffusion coefficient for heavy quarks in SU(3) gluon plasma at temperatures 1-2 times the deconfinement temperature. The momentum diffusion coefficient is extracted from a Monte Carlo calculation of the correlation function of color electric fields, in the leading order of expansion in heavy quark mass. Systematics of the calculation are examined, and compared with perturbtion theory and other estimates., Comment: 7 pages, 4 figures. Proceedings of the 30th International Symposium on Lattice Field Theory, June 24 - 29, 2012, Cairns, Australia

We present results of our simulations of QCD with two light dynamical quarks on a 32^3 X 8 lattice at a current quark mass tuned to have the Goldstone pion mass of about 230 MeV. Employing the Taylor expansion method we proposed earlier, we estimate the radius of convergence of the series for the baryonic susceptibility by using terms up to eighth order. Together with our earlier results, corresponding to the same physical parameters but on coarser lattices at respectively 1.33 times and twice the lattice cut-off (a), we were able to attempt a march towards the continuum limit., Comment: 4 pages, 4 figures, To appear in the proceedings of the 23rd International Conference on Ultrarelativistic Nucleus-Nucleus Collisions, Quark Matter 2012, August 13-18, 2012, Washington DC

The momentum diffusion coefficient for heavy quarks is studied in a deconfined gluon plasma in the static approximation by investigating a correlation function of the color electric field using Monte Carlo techniques. The diffusion coefficient is extracted from the long distance behavior of such a correlator. For temperatures Tc < T <~ 2 Tc, our nonperturbative estimate of the diffusion coefficient is found to be very different from the leading order perturbation theory, and is in the right ballpark to explain the heavy quark flow seen by PHENIX at RHIC., Comment: Minor changes, version to appear in Physical Review D

The thermodynamics of the deconfined phase of the SU(N) gauge theory is studied. Careful study is made of the approach to the continuum limit. The latent heat of the deconfinement transition is studied, for the theories with 3, 4 and 6 colors. Continuum estimates of various thermodynamic quantities are studied, and the approach to conformality investigated. The bulk thermodynamic quantities at different N are compared, to investigate the validity of 't Hooft scaling at these values of N., Comment: 7 pages, 4 figures. Contribution to the XXVIII International Symposium on Lattice Field Theory (Lattice 2010), June 2010, Villasimius, Italy

We study the thermodynamics of SU(N_c) pure gauge theories for N_c=3, 4 and 6. The continuum and thermodynamic limits of bulk quantities such as the pressure, energy density and the entropy density are taken by using several different lattice spacings and volumes. There is no window of temperature in which a non-trivial conformal theory describes bulk thermodynamics. We extract the latent heat of the first-order deconfinement phase transitions and observe good scaling with N_c. For all quantities that we measure, strong N_c scaling holds, except, possibly, very close to the transition temperature, T_c; however we are unable to find strong evidence for scaling with the 't Hooft coupling in thermal quantities at the small values of N_c which we study.

We investigate the deconfinement transition in SU(Nc) gauge theories, and properties of the deconfined phase. A detailed lattice study of SU(4) and SU(6) gauge theories are conducted, and finite volume and cutoff effects on thermodynamic observables are studied. The scaling of the deconfinement transition point with lattice spacing is used to calculate the scale, Lambda_MSbar. The continuum estimates of the thermodynamic quantities are used to study properties of the gluon plasma. In particular, the approach to conformal limit is studied. We do not find any evidence of a strongly coupled, conformal phase in these theories., Comment: 7 pages, 5 figures, talk presented at The XXVII International Symposium on Lattice Field Theory, July 26-31, 2009, Peking University, Beijing, China

We investigated the finite temperature (T) phase transition for SU(Nc) gauge theory with Nc=4, 6, 8 and 10 at lattice spacing, a, of 1/(6T) or less. We found that these theories have first order transitions at such small a. In many cases we were able to find the critical couplings with precision as good as a few parts in 10^4. We also investigated the use of two-loop renormalization group equations in extrapolating the lattice results to the continuum, thus fixing the temperature scale in units of the phase transition temperature, Tc. We found that when a \le 1/(8Tc) the two-loop extrapolation was accurate to about 1--2%. However, we found that trading Tc for the QCD scale, Lambda_MSbar, increases uncertainties significantly, to the level of about 5--10%., Comment: Small corrections

We report lattice computations in SU(N_c) pure gauge theory, where N_c is increased beyond the physical value of 3. We demonstrate two-loop scaling of T_c, thus obtaining the variation of T_c/Lambda_MSbar with N_c, and fixing the temperature scale. We study the equation of state of the gluoN_c plasma, the conformal anomaly, and the approach to the weak coupling theory. We find that the weak-coupling prediction is always closer to the lattice data than the conformal field theory is., Comment: 4 pages, 4 figures - To appear in the conference proceedings for Quark Matter 2009, March 30 - April 4, Knoxville, Tennessee

We study the correlations between quark-antiquark pairs in different quantum number channels in a deconfined plasma by using an effective model of QCD. Using the three flavour PNJL model, the finite temperature spectral functions for different mesonic states are studied at zero and nonzero quark chemical potentials. It is found that in the $\eta$ channel resonance structures survive above the chiral transition temperature $\tc$, while the kaonic states seem to get washed off just above $\tc$. The sensitivity of the structures to the anomaly term are carefully investigated., Comment: 15pages

In this work we consider the 1-component real scalar $\phi^4$ theory in 4 space-time dimensions on the lattice and investigate the finite size scaling of thermodynamic quantities to study whether the thermodynamic limit is attained. The results are obtained for the symmetric phase of the theory., Comment: To be published in the Proceedings of the 18th DAE-BRNS High Energy Physics Symposium,India (3 pages, 3 figures, revtex4)

We calculate the low energy contribution to quarkonium correlators in Euclidean time in lattice QCD. This contribution was found to give the dominant source of the temperature dependence of the correlators. We have found that the low energy contribution is well described by a quasi-particle model and have determined the effective temperature dependent heavy quark mass., Comment: Contribution to QM2008, 4 pages, LaTeX, uses iopart.cls, corrected typos

Lattice studies of charmonium systems have indicated that in a deconfined gluonic plasma ground state charmonia survive as bound states upto temperatures \~ 2 Tc. After surveying the methodologies used in reaching these results, we examine the behavior of these systems when the bound state is in motion with respect to the heatbath frame. We find that the finite momenta charmonia show medium modifications when the medium is deconfined; in particular, a modification of the energy-momentum dispersion relation is indicated., Comment: 5 pages including 6 eps figures. Contribution to Strong and Electroweak Matter 2004, Helsinki, Finland, June 2004

The behavior of charmonia after the deconfinement transition is investigated on quenched lattices. Analysis of temporal correlators on fine lattices at temperatures upto 3 T_c show that the J/psi and eta_c survive the deconfinement transition with little significant changes, and survive as bound states at least upto 2.25 T_c. The spatially excited chi_c states suffer serious system modifications, maybe dissolution, already a little above T_c., Comment: Contribution to Quark Matter 2004. 4 pages

We present a study of charmonia in hot gluonic plasma, for temperatures upto three times the deconfinement transition temperature Tc. q \bar{q} systems with quark masses close to the charm mass and different spin-parity quantum numbers were studied on very fine isotropic lattices. The analysis of temporal correlators, and spectral functions constructed from them, shows that the J/psi and eta_c survive up to quite high temperatures, with little observable change up to 1.5 Tc, and then gradually weakening and disappearing by 3 Tc. For the scalar and axial vector channels, serious modifications are induced by the hot medium already close to Tc, possibly dissociating the mesons by 1.1 Tc., Comment: 18 pages, 31 eps figures

We present results from lattice studies of charmonium systems near the deconfinement transition temperature. On quenched isotropic lattices with lattice spacings between 0.02 and 0.05 fm, bar{q} q systems with quark masses close to the charm mass and with different spin-parity quantum numbers are studied in the temperature range 0.9 Tc - 3 Tc. Results for temporal correlators of local operators, and the spectral functions constructed from them, are discussed. For the pseudoscalar and vector channels, the correlators are observed to change very little across the deconfinement transition, unlike in the case of the light quarks., Comment: 3 pages, 4 figures, Lattice2002(nonzerot)

Comparison of two appropriately chosen screening masses of colour singlet operators in the pure glue QCD plasma indicates that at sufficiently high temperature it contains a weakly-interacting massive quasi-particle with the quantum numbers of the electric gluon. Still in the deconfined phase, but closer to T_c, the same mass ratio is similar to that at zero temperature, indicating that the propagating modes are more glueball-like, albeit with a lower scale for the masses. We observe a continuity between these two regimes., Comment: 4 pages, 3 figures

We present results from a lattice hadron spectrum calculation using three flavors of dynamical quarks - two light and one strange, and quenched simulations for comparison. These simulations were done using a one-loop Symanzik improved gauge action and an improved Kogut-Susskind quark action. The lattice spacings, and hence also the physical volumes, were tuned to be the same in all the runs to better expose differences due to flavor number. Lattice spacings were tuned using the static quark potential, so as a byproduct we obtain updated results for the effect of sea quarks on the static quark potential. We find indications that the full QCD meson spectrum is in better agreement with experiment than the quenched spectrum. For the 0++ (a0) meson we see a coupling to two pseudoscalar mesons, or a meson decay on the lattice., Comment: 38 pages, 20 figures, uses epsf. 5/29/01 revision responds to referee's Comments, changes pion fits and tables, and corrects Fig. 10 and some minor errors

Adding separate chemical potentials lambda and gamma for Z2 monopoles and vortices respectively in the Villain form of the mixed fundamental-adjoint action for the SU(2) lattice gauge theory, we investigate their role in the interplay between the deconfinement and bulk phase transitions using Monte Carlo techniques. Setting lambda to be nonzero, we find that the line of deconfinement transitions is shifted in the coupling plane but it behaves curiously also like the bulk transition line for large enough adjoint coupling, as for lambda=0. In a narrow range of couplings, however, we find separate deconfinement and bulk phase transitions on the same lattice for nonzero and large lambda, suggesting the two to be indeed coincident in the region where a first order deconfinement phase transition is seen. In the limit of large lambda and gamma, we obtain only lines of second order deconfinement phase transitions, as expected from universality., Comment: 18 pages, 10 figures included

The impact of Z_2-monopoles and vortices on the bulk and the deconfinement phase transitions of the SU(2) lattice gauge theory with a mixed Villain form of action is investigated by varying their numbers with appropriate chemical potentials. Suppressing the former shifts the line of deconfinement transitions in the coupling plane but it continues to behave also like the bulk transition line. We find separate deconfinement and bulk phase transitions on the same lattice, suggesting the two to be indeed coincident at higher adjoint couplings. Universality is restored when both monopoles and vortices are suppressed., Comment: LATTICE99(Finite Temp I), 3 pages, 3 eps figures, LaTeX, espcrc2.sty

We perform a systematic scaling study of screening masses in pure gauge SU(2) theory at temperatures above the phase transition temperature. The major finite volume effect is seen to be spatial deconfinement. We extract the screening masses in the infinite volume and zero lattice spacing limit. We find that these physical results can be deduced from runs on rather coarse lattices. Dimensional reduction is clearly seen in the spectrum., Comment: 14 pages, 3 figures. Minor change in Figs. 2 & 3 and discussion. Main results unchanged

The SO(3) lattice gauge theory with a Villain form of action was investigated by Monte Carlo techniques on asymmetric lattices with Nt = 2 and 4, where Nt is the number of sites in the temporal extent. Unlike the results for higher Nt, only one transition of second order was found for Nt = 2 . An extended action with an irrelevant term to suppress Z_2 monopoles enabled us to get a better view of the deconfinement transition as the effects of bulk transition could be suppressed as well. Although the action has no global Z_2 symmetry for the SO(3) theory, unlike the SU(2) theory at finite temperature, our study revealed a second order deconfinement transition, with properties similar to the deconfinement transition of SU(2)., Comment: 19 pages latex, incl. figures

Screening masses in the equilibrium thermodynamics of gauge theories were measured. The spectroscopy of these screening masses gives strong evidence for dimensional reduction at $T\ge2T_c$. A perturbative explanation of these masses is ruled out. The mass ratios in the high temperature phase are consistent with those in the pure gauge theory in three dimensions., Comment: Talk given at the 5th International Workshop on Thermal Field Theories and their Applications, Regensburg, Germany, August 1998