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The running coupling constant is calculated using the imaginary time formalism (ITF) of thermal field theory under the self-energy approximation. In the process, each Feynman diagram in thermal field theory is rewritten as the summation of non-thermal diagrams with coefficients that are functions of mass and temperature. By employing the same mass scale and coupling constant for both the non-thermal QFT and ITF, we derive a relation between them. Also, we calculate the self-energy using ITF, which is equated to the same as that of non-thermal QFT under the zero external momentum limit. This can provide a new expression for the coupling constant. Combining this result with the $\beta(g)$ and $\gamma_m(g)$ function relations of the renormalization group equations gives rise to a thermal-dependent coupling constant and running mass. Using these results, the free energy density is evaluated for two-loop order and compared with quasiparticle model.

In this review, we present the key aspects of modern thermal perturbation theory based on the hard thermal loop (HTL) approximation, including its theoretical foundations and applications within quantum electrodynamics (QED) and quantum chromodynamics (QCD) plasmas. To maintain conciseness, we focus on scenarios in thermal equilibrium, examining a variety of physical quantities and settings. Specifically, we explore both bulk thermodynamic properties and real-time observables in high-temperature domains relevant to heavy-ion physics., Comment: Review article; An invited review in "Progress in Particle and Nuclear Physics", Elsevier

In this article an introduction to the thermal field theory within imaginary time has been discussed in details. The imaginary time formalism has been introduced through both the operatorial and the functional integration method. The prescription to perform frequency sum for boson and fermion has been discussed. Green's function both in Minkowski time as well as in Euclidean time has been derived. The tadpole diagram in $\phi^4$ theory and the self-energy in $\phi^3$ theory have been computed. The basic features of general two point functions for both fermions and bosons in presence of a heat bath have been discussed. Then the free partition functions for scalar, fermion and gauge field, and interacting scalar field have been obtained. The quantum electrodynamics (QED) and gauge fixing have been discussed in details. The one-loop self-energy for electron and photon in QED have been obtained in hard thermal loop (HTL) approximation. The dispersion properties and collective excitations of both electron and photon in a thermal medium have been presented. The spectral representation of fermion and gauge boson propagators have been obtained. In HTL approximation, the generalisation of QED results of two point functions to quantum chromodynamics (QCD) have been outlined that mostly involve group theoretical factors. As an effective field theory approach the HTL resummation and the HTL perturbation theory have been introduced. The leading order, next-to-leading order and next-to-next-leading order free energy and pressure for deconfined QCD medium created in heavy-ion collisions have been computed within HTLpt. The general features of the deconfined QCD medium have also been outlined with non-perturbative effects like gluon condensate and Gribov-Zwanziger action. The dilepton production rates from quark-gluon plasma with these non-perturbative effects have been computed., Comment: An invited review published in "The European Physical Journal Special Topics" and this version matches with the published one

We discuss a novel approach to estimate the partition function in effective model frameworks when the effective potentials have multiple extrema, so that ascertaining a mean field becomes difficult. Using this approach we present a consistent model to study the thermodynamic properties of gluon quasi-particles as a function of temperature, both in the color confined and the color deconfined phases., Comment: 8 pages, 9 captioned figures, matches with the published version

We propose a beyond mean field approach to evaluate Yang-Mills thermodynamics from the partition function with n-body gluon contribution, in the presence of a uniform background Polyakov field. Using a path integral based formalism, we obtain, unlike the previous mean field studies within this model framework, physically consistent results with good agreement to the lattice data throughout the temperature range., Comment: 4 pages, 3 captioned figures, Proceedings of the contributory talk at XXIV DAE-BNRS High Energy Physics Symposium 2020 held at NISER, Bhubaneswar, Odisha

In this work, we compute the hard thermal loop pressure of quark-gluon plasma within strong magnetic field approximation at one-loop order. Magnetic field breaks the rotational symmetry of the system. As a result, the pressure of QGP becomes anisotropic and one finds two different pressures along the longitudinal (along the magnetic field direction) and transverse direction. Similarly, the second-order quark number susceptibility, which represents the fluctuation of the net quark number density, also becomes anisotropic. We compute the second order QNS of deconfined QCD matter in strong field approximation considering same chemical potential for two quark flavors., Comment: 4 pages, 1 figure, XXIV DAE-BRNS High Energy Physics Symposium 2020 Proceedings

We have systematically constructed the general structure of the gauge boson self-energy and the effective propagator in presence of a nontrivial background like hot magnetized material medium. Based on this as well as the general structure of fermion propagator in weakly magnetized medium we have calculated pressure of deconfined QCD matter within HTL approximation., Comment: 4 pages, 2 figures, XXIII DAE High Energy Physics Symposium Proceedings

In this article, there are 18 sections discussing various current topics in the field of relativistic heavy-ion collisions and related phenomena, which will serve as a snapshot of the current state of the art. Section 1 reviews experimental results of some recent light-flavored particle production data from ALICE collaboration. Other sections are mostly theoretical in nature. Very strong but transient magnetic field created in relativistic heavy-ion collisions could have important observational consequences. This has generated a lot of theoretical activity in the last decade. Sections 2, 7, 9, 10 and 11 deal with the effects of the magnetic field on the properties of the QCD matter. There are several unanswered questions about the QCD phase diagram. Sections 3, 11 and 18 discuss various aspects of the QCD phase diagram and phase transitions. Recent years have witnessed interesting developments in foundational aspects of hydrodynamics and their application to heavy-ion collisions. Sections 12, 15, 16 and 17 of this article probe some aspects of this exciting field. Transport coefficients together with their temperature- and density-dependence, are essential inputs in hydrodynamical calculations. Sections 5, 8 and 14 deal with calculation/estimation of various transport coefficients (shear and bulk viscosity, thermal conductivity, relaxation times, etc.) of quark matter and hadronic matter. Sections 4, 6 and 13 deals with interesting new developments in the field. Section 4 discusses color dipole gluon distribution function at small transverse momentum in the form of a series of Bells polynomials. Section 6 discusses the properties of Higgs boson in the quark gluon plasma using Higgs-quark interaction. Section 13 discusses modification of coalescence model to incorporate viscous corrections and application of this model., Comment: 109 pages, 49 captioned figures, compilation of the contributions as presented in the `Workshop on Dynamics of QCD Matter', 15th to 17th August 2019, NISER Bhubaneswar, India, published version

Considering the strong field approximation we compute the hard thermal loop pressure at finite temperature and chemical potential of hot and dense deconfined QCD matter in lowest Landau level in one-loop order. We consider the anisotropic pressure in the presence of the strong magnetic field i.e., longitudinal and transverse pressure along parallel and perpendicular to the magnetic field direction. As a first effort, we compute and discuss the anisotropic quark number susceptibility of deconfined QCD matter in lowest Landau level. The longitudinal quark number susceptibility is found to increase with the temperature whereas the transverse one decreases with the temperature. We also compute the quark number susceptibility in the weak field approximation. We find that the thermomagnetic correction to the quark number susceptibility is very marginal in the weak field approximation., Comment: 31 pages, 9 figures, Version published in PRD

We consider weakly magnetized hot QED plasma comprising electrons and positrons. There are three distinct dispersive (longitudinal and two transverse) modes of a photon in a thermo-magnetic medium. At lowest order in coupling constant, photon is damped in this medium via Compton scattering and pair creation process. We evaluate the damping rate of hard photon by calculating the imaginary part of the each transverse dispersive modes in a thermo-magnetic QED medium. We note that one of the fermions in the loop of one-loop photon self-energy is considered as soft and the other one is hard. Considering the resummed fermion propagator in a weakly magnetized medium for the soft fermion and the Schwinger propagator for hard fermion, we calculate the soft contribution to the damping rate of hard photon. In weak field approximation the thermal and thermo-magnetic contributions to damping rate get separated out for each transverse dispersive mode. The total damping rate for each dispersive mode in presence of magnetic field is found to be reduced than that of the thermal one. This formalism can easily be extended to QCD plasma., Comment: 32 pages, 7 figures

We have computed the hard dilepton production rate from a weakly magnetized deconfined QCD medium within one-loop photon self-energy by considering one hard and one thermomagnetic resummed quark propagator in the loop. In the presence of the magnetic field, the resummed propagator leads to four quasiparticle modes. The production of hard dileptons consists of rates when all four quasiquarks originating from the poles of the propagator individually annihilate with a hard quark coming from a bare propagator in the loop. Besides these, there are also contributions from a mixture of pole and Landau cut part. In weak field approximation, the magnetic field appears as a perturbative correction to the thermal contribution. Since the calculation is very involved, for a first effort as well as for simplicity, we obtained the rate up to first order in the magnetic field, i.e., ${\cal O}[(eB)]$, which causes a marginal improvement over that in the absence of magnetic field., Comment: 21 pages, 7 figures, published version

Considering the general structure of the two point functions of quarks and gluons, we compute the free energy and pressure of a strongly magnetized hot and dense QCD matter created in heavy-ion collisions. In presence of strong magnetic field we found that the deconfined QCD matter exhibits a paramagnetic nature. One gets different pressure in a direction parallel and perpendicular to magnetic field due to the magnetization acquired by the system. We obtain both longitudinal and transverse pressure, and magnetization of a hot deconfined QCD matter in presence of magnetic field. We have used hard thermal loop approximation (HTL) for heat bath. We obtained completely analytic expression for pressure and magnetization under certain approximation. Various divergences appearing in free energy are regulated using appropriate counter terms. The obtained anisotropic pressure may be useful for magnetohydrodynamics description of a hot and dense deconfined QCD matter produced in heavy-ion collisions., Comment: 37 pages, 8 figures

Based on transversality condition of gauge boson self-energy we have systematically constructed the general structure of the gauge boson two-point functions using four linearly independent basis tensors in presence of a nontrivial background, i.e., hot magnetized material medium. The hard thermal loop approximation has been used for the heat bath to compute various form factors associated with the gauge boson's two point functions both in strong and weak field approximation. We have also analyzed the dispersion of a gauge boson (e.g., gluon) using the effective propagator both in strong and weak magnetic field approximation. The formalism is also applicable to QED. The presence of only thermal background leads to a longitudinal (plasmon) mode and a two-fold degenerate transverse mode. In presence of a hot magnetized background medium the degeneracy of the two transverse modes is lifted and one gets three quasiparticle modes. In weak field approximation one gets two transverse modes and one plasmon mode. On the other hand, in strong field approximation also one gets the three modes in Lowest Landau Level. The general structure of two-point function may be useful for computing the thermo-magnetic correction of various quantities associated with a gauge boson., Comment: 39 pages, 7 figures

We consider the effect of the chromo-electromagnetic field fluctuations in addition to the collisional as well as the radiative energy loss suffered by heavy quarks while propagating through the hot and densed deconfined medium of quarks and gluons created in relativistic heavy ion collisions. The chromo-electromagnetic field fluctuations play an important role as it leads to an energy gain of heavy quarks of all momentum, significantly effective at the lower momentum region. With this, we have computed, for the first time, the nuclear modification factor (R_{AA}) of heavy mesons, viz., D-mesons and B-mesons and compared with the those experimental measurements in Pb-Pb collisions at \sqrt{s_{NN}} = 2.76 TeV and \sqrt{s_{NN}} = 5.02 TeV by the CMS and ALICE experiments at the LHC. Our results are found to be in very good agreement with those available data measured by CMS and ALICE experiments.

We have systematically constructed the general structure of the fermion self-energy and the effective quark propagator in presence of a nontrivial background like hot magnetised medium. This is applicable to both QED and QCD. The hard thermal loop approximation has been used for the heat bath. We have also examined transformation properties of the effective fermion propagator under some of the discrete symmetries of the system. Using the effective fermion propagator we have analysed the fermion dispersion spectra in a hot magnetised medium along with the spinor for each fermion mode obtained by solving the modified Dirac equation. The fermion spectra is found to reflect the discrete symmetries of the two-point functions. We note that for a chirally symmetric theory the degenerate left and right handed chiral modes in vacuum or in a heat bath get separated and become asymmetric in presence of magnetic field without disturbing the chiral invariance. The obtained general structure of the two-point functions is verified by computing the three-point function, which agrees with the existing results in one-loop order. Finally, we have computed explicitly the spectral representation of the two-point functions which would be very important to study the spectral properties of the hot magnetised medium corresponding to QED and QCD with background magnetic field., Comment: 31 pages, 7 figures; Version accepted in Phys. Rev. D

We consider our recently obtained general structure of two point (self-energy and propagator) functions of quarks and gluons in a nontrivial background like a heat bath and an external magnetic field. Based on this, here we have computed free energy and pressure of quarks and gluons for a magnetized hot and dense deconfined QCD matter in weak field approximation. For heat bath we have used hard thermal loop perturbation theory (HTLpt) in presence of finite chemical potential. For weak field approximations we have obtained the pressure of QCD matter, both with and without the high temperature expansion. The results with high $T$ expansions are completely analytic and gauge independent but depends on the renormalization scale in addition to the temperature, chemical potential and the external magnetic field. We also discuss the modification of QCD Debye mass of such matter for an arbitrary magnetic field. Analytic expressions for Debye mass are also obtained for both strong and weak field approximation. It is found to exhibit some interesting features depending upon the three different scales, i.e, the quark mass, temperature and the strength of the magnetic field. The various divergences appearing in the quark and gluon free energies are regulated through appropriate counter terms. In weak field approximation, the low temperature behavior of the pressure is found to strongly depend on the magnetic field than that at high temperature. We also discuss the specific problem with one-loop HTLpt associated with the over-counting of certain orders in coupling., Comment: 65 pages, 8 figures; Published version

We evaluate the electromagnetic spectral function in QCD plasma in a nonperturbative background of in-medium quark and gluon condensates by incorporating the leading order power corrections in a systematic framework within the ambit of the operator product expansion in D=4 dimension. We explicitly show that the mixing of the composite operators removes mass singularities and renders Wilson coefficients finite and well defined. As a spectral property, we then obtain the nonperturbative dilepton production rate from QCD plasma. The operator product expansion automatically restricts the dilepton rate to the intermediate mass range, which is found to be enhanced due to the power corrections. We also compare our result with those from nonperturbative calculations, e.g., lattice QCD and effective QCD models based on Polyakov loop., Comment: 24 pages, 8 figures; Discussion added on OPE scales, version accepted in JHEP

We emphasize that a knowledge of energy and entropy densities of quark gluon plasma - a thermalized de-confined matter, formed in relativistic heavy ion collisions fixes the formation temperature and the product of gluon fugacity and formation time uniquely, {\em provided} we know the relative fugacities of quarks and gluons. This also provides that a smaller formation time would imply larger fugacities for partons. Next we explore the limits of chemical equilibration of partons during the initial stages in relativistic collision of heavy nuclei. The experimentally measured rapidity densities of transverse energy and charged particle multiplicity at RHIC and LHC energies are used to estimate the energy and number densities with the assumption of formation of a thermally equilibrated quark gluon plasma which may be chemically equilibrated to the same or differing extents for quarks and gluons. The estimates are found to be very sensitive to the correction factor used for the Bj\"{o}rken energy density for identifying it with the initial energy density. The extent of chemical equilibration near the end of the QGP phase is inferred by solving master equations by including the processes $gg \leftrightarrow ggg$ and $gg \leftrightarrow q\overline{q}$ along with expansion and cooling of the plasma. The possible consequences for invariant mass distribution of intermediate mass dileptons radiated from the plasma are discussed which could distinguish between different scenarios., Comment: 13 page, 13 figures, 2 tables

We have evaluated the electromagnetic spectral function and its spectral properties by computing the one-loop photon polarization tensor in presence of magnetic field, particularly in a strong field approximation compared to the thermal scale. When the magnetic scale is higher than the thermal scale the lowest Landau level (LLL) becomes effectively (1+1) dimensional strongly correlated system that provides a kinematical threshold based on the mass scale. Beyond this threshold the photon strikes the LLL and the spectral strength starts with a high value due to the dimensional reduction and then falls off with increase of the photon energy due to LLL dynamics in a strong field approximation. This strongly enhances the dilepton rate over the thermal perturbative leading order (Born) rate at very low invariant mass. We have also investigated the electromagnetic screening by computing the Debye screening mass and it depends distinctively on three different scales (mass of the quasiquark, temperature and the magnetic field strength) of a hot magnetized system. The mass dependence of the Debye screening supports the occurrence of a magnetic catalysis effect in the strong field approximation., Comment: 18 pages, 8 figures; Matches with the published version

In a previous paper (JHEP {\bf 05} (2014) 27), we calculated the three-loop thermodynamic potential of QCD at finite temperature $T$ and quark chemical potentials $\mu_q$ using the hard-thermal-loop perturbation theory (HTLpt) reorganization of finite temperature and density QCD. The result allows us to study the thermodynamics of QCD at finite temperature and isospin chemical potential $\mu_I$. We calculate the pressure, energy density, and entropy density, the trace anomaly, and the speed of sound at zero and nonzero $\mu_I$. The second, fourth, and sixth-order isospin susceptibilities are calculated at zero $\mu_I$. Our results can be directly compared to lattice QCD without Taylor expansions around $\mu_q=0$ since QCD has no sign problem at finite isospin chemical potential., Comment: 19 pages, 9 figs. Updated version matches published version in PRD including changes of title

We use a recently obtained resummed quark propagator at finite temperature which takes into account both the chromoelectric scale gT and the chromomagnetic scale g^2T through the Gribov action. The electric scale generates two massive modes whereas the magnetic scale produces a new massless spacelike mode in the medium. Moreover, the non-perturbative quark propagator is found to contain no discontinuity in contrast to the standard perturbative hard thermal loop approach. Using this non-perturbative quark propagator and self-consistent vertices, we compute the non-perturbative dilepton rate at vanishing three-momentum at one-loop order. The resulting rate has a rich structure at low energies due to the inclusion of the non-perturbative magnetic scale. We also calculate the quark number susceptibility, which is related to the conserved quark number density fluctuation in the deconfined state. Both the dilepton rate and quark number susceptibility are compared with results from lattice quantum chromodynamics and the standard hard thermal loop approach. Finally, we discuss how the absence of a discontinuity in the imaginary part of the non-perturbative quark propagator makes the results for both dilepton production and quark number susceptibility dramatically different from those in perturbative approaches and seemingly in conflict with known lattice data., Comment: 30 pages, 7 figures; v2 - version accepted for publication in PRD

In this proceedings we present a state-of-the-art method of calculating thermodynamic potential at finite temperature and finite chemical potential, using Hard Thermal Loop perturbation theory (HTLpt) up to next-to-next-leading-order (NNLO). The resulting thermodynamic potential enables us to evaluate different thermodynamic quantities including pressure and various quark number susceptibilities (QNS). Comparison between our analytic results for those thermodynamic quantities with the available lattice data shows a good agreement., Comment: 5 pages, 6 figures, conference proceedings of XXI DAE-BRNS HEP Symposium, IIT Guwahati, December 2014; to appear in 'Springer Proceedings in Physics Series'

We have studied the vector meson spectral function (VMSF) in a hot and dense medium within an effective QCD model namely the Nambu-Jona-Lasinio (NJL) and its Polyakov Loop extended version (PNJL) with and without the effect of isoscalar vector interaction (IVI). The effect of the IVI has been taken into account using the ring approximation. We obtained the dilepton production rate (DPR) using the VMSF and observed that at moderate temperature it is enhanced in the PNJL model as compared to the NJL and Born rate due to the suppression of color degrees of freedom., Comment: 5 pages, 7 figures, conference proceedings of the XXI DAE-BRNS HEP Symposium, IIT Guwahati, December 2014; to appear in 'Springer Proceedings in Physics Series'

In this work we have re-explored our earlier study on the vector meson spectral function and its spectral property in the form of dilepton rate in a two-flavour Polyakov loop extended Nambu-Jona-Lasinio (PNJL) model in presence of a strong entanglement between the chiral and Polyakov loop dynamics. The entanglement considered here is generated through the four-quark scalar type interaction in which the coupling strength depends on the Polyakov loop and runs with temperature and chemical potential. The entanglement effect is also considered for the four-quark vector type interaction in the same manner. We observe that the entanglement effect relatively enhances the color degrees of freedom due to the running of the both scalar and vector couplings. This modifies the vector meson spectral function and thus the spectral property such as the dilepton production rate in low invariant mass also gets modified., Comment: 12 Pages, 18 figures

The properties of the vector meson current-current correlation function and its spectral representation are investigated in details with and without isoscalar-vector interaction within the framework of effective QCD approach, namely Nambu-Jona-Lasinio (NJL) model and its Polyakov Loop extended version (PNJL), at finite temperature and finite density. The influence of the isoscalarvector interaction on the vector meson correlator is obtained using the ring resummation known as the Random Phase Approximation (RPA). The spectral as well as the correlation function in PNJL model show that the vector meson retains its bound property up to a moderate value of temperature above the phase transition. Using the vector meson spectral function we, for the first time, obtained the dilepton production rate from a hot and dense medium within the framework of PNJL model that takes into account the nonperturbative effect through the Polyakov Loop fields. The dilepton production rate in PNJL model is enhanced compared to NJL and Born rate in the deconfined phase due to the suppression of color degrees of freedom at moderate temperature. The presence of isoscalar-vector interaction further enhances the dileption rate over the Born rate in the low mass region. Further, we also have computed the Euclidean correlation function in vector channel and the conserved density fluctuation associated with temporal correlation function appropriate for a hot and dense medium. The dilepton rate and the Euclidean correlator are also compared with available lattice data and those quantities in PNJL model are found to agree well in certain domain., Comment: 30 pages, 16 figures, typos corrected, references added, to appear in JHEP

The perturbative series for finite-temperature field theories has very poor convergence properties and one needs a way to reorganize it. In this talk, I review two ways of reorganizing the perturbative series for field theories at finite temperature and chemical potential, namely hard-thermal-loop perturbation theory (HTLpt) and dimensional reduction (DR). I will present results for the pressure, trace anomaly, speed of sound and the quark susceptibilities from a 3-loop HTLpt calculation and for the quark susceptibilities using DR at four loops. A careful comparison with available lattice data shows good agreement for a number of physical quantities., Comment: Invited talk at 1th Quark Confinement and the Hadron Spectrum, September 8-12 2014, Saint Petersburg, Russia. 12 pages. 18 figs

Fluctuations of conserved quantum numbers are associated with the corresponding susceptibilities because of the symmetry of the system. The underlying fact is that these fluctuations as defined through the static correlators become identical to the direct calculation of these susceptibilities defined through the thermodynamic derivatives, due to the fluctuation-dissipation theorem. Through a rigorous exercise we explicitly show that a diagrammatic calculation of the static correlators associated with the conserved quark number fluctuations and the corresponding susceptibilities are possible in case of mean field theories, if the implicit dependence of the mean fields on the quark chemical potential are taken into account appropriately. As an aside we also give an analytical prescription for obtaining the implicit dependence of the mean fields on the quark chemical potential.

In this proceedings contribution we present a recent three-loop hard-thermal-loop perturbation theory (HTLpt) calculation of the thermodynamic potential for a finite temperature and chemical potential system of quarks and gluons. We compare the resulting pressure, trace anomaly, and diagonal/off-diagonal quark susceptibilities with lattice data. We show that there is good agreement between the three-loop HTLpt analytic result and available lattice data., Comment: 4 pages, 4 figures

We calculate the three-loop thermodynamic potential of QCD at finite temperature and chemical potential(s) using the hard-thermal-loop perturbation theory (HTLpt) reorganization of finite temperature and density QCD. The resulting analytic thermodynamic potential allows us to compute the pressure, energy density, and entropy density of the quark-gluon plasma. Using these we calculate the trace anomaly, speed of sound, and second-, fourth-, and sixth-order quark number susceptibilities. For all observables considered we find good agreement between our three-loop HTLpt calculations and available lattice data for temperatures above approximately 300 MeV., Comment: 48 pages, 14 figures; v2 - published version

We present results of a three-loop hard-thermal-loop perturbation theory calculation of the thermodynamical potential of a finite temperature and baryon chemical potential system of quarks and gluons. We compare the resulting pressure and diagonal quark susceptibilities with available lattice data. We find reasonable agreement between our analytic results and lattice data at both zero and finite chemical potential., Comment: 5 pages, 5 figures; v4 - small typo fixes; published version

We use the recently obtained two-loop hard thermal loop perturbation theory thermodynamics functions of a plasma of quarks and gluons to compute the diagonal second- and fourth-order quark number susceptibilities. The two-loop hard thermal loop perturbation theory thermodynamic functions used are reliable in the limit that the ratio of the quark chemical potential to temperature is small. Using this result, we are able to obtain (semi-)analytic expressions for the quark number susceptibilities at leading- and next-to-leading-order in hard thermal loop perturbation theory. We compare the hard thermal loop perturbation theory results with perturbative quantum chromodynamics calculations, a Polyakov-loop Nambu-Jona-Lasinio model calculation, and lattice quantum chromodynamics results., Comment: 14 pages, 2 figures; v3 - version accepted for publication in JHEP

We calculate the two-loop pressure of a plasma of quarks and gluons at finite temperature and chemical potential using the hard thermal loop perturbation theory (HTLpt) reorganization of finite temperature/density quantum chromodynamics. The computation utilizes a high temperature expansion through fourth order in the ratio of the chemical potential to temperature. This allows us to reliably access the region of high temperature and small chemical potential. We compare our final result for the two-loop HTLpt pressure at finite temperature and chemical potential with perturbative quantum chromodynamics (QCD) calculations and available lattice QCD results., Comment: 23 pages, 5 figures; published version

Based on quantum statistical mechanics we show that the $SU(3)$ color singlet ensemble of a quark-gluon gas exhibits a $Z(3)$ symmetry through the normaized character in fundamental representation and also becomes equivalent, within a stationary point approximation, to the ensemble given by Polyakov Loop. Also Polyakov Loop gauge potential is obtained by considering spatial gluons along with the invariant Haar measure at each space point. The probability of the normalized character in $SU(3)$ vis-a-vis Polyakov Loop is found to be maximum at a particular value exhibiting a strong color correlation. This clearly indicates a transition from a color correlated to uncorrelated phase or vise-versa. When quarks are included to the gauge fields, a metastable state appears in the temperature range $145\le T({\rm{MeV}}) \le 170$ due to the explicit $Z(3)$ symmetry breaking in the quark-gluon system. Beyond $T\ge 170$ MeV the metastable state disappears and stable domains appear. At low temperature a dynamical recombination of ionized $Z(3)$ color charges to a color singlet $Z(3)$ confined phase is evident along with a confining background that originates due to circulation of two virtual spatial gluons but with conjugate $Z(3)$ phases in a closed loop. We also discuss other possible consequences of the center domains in the color deconfined phase at high temperature., Comment: Version published in J. Phys. G

We obtain the radiative energy loss of a heavy quark in a deconfined medium due to radiation of gluons off them using a recently derived generalised gluon emission spectrum. We find that the heavy flavour loses energy almost in a similar fashion like light quarks through this process. With this, we further analyse the nuclear modification factor for D-meson at LHC and RHIC energies. In particular, the obtained result is found to be in close agreement with the most recent data from ALICE collaboration at 2.76 ATeV Pb-Pb collisions. We also discuss the nuclear modification factor due to the collisional energy loss. Furthermore, the result of non-photonic single electron from the decay of both D and B mesons is compared with the RHIC data at 200 AGeV Au-Au collisions, which is also in close agreement., Comment: Non-photonic single electron results included, title changed a bit, version accepted in Phys. Lett. B

We calculate the dimension two gluon condensate contribution to quark, gluon and ghost propagators at finite temperature., Comment: Minor modifications. Accepted in PLB

An improved generalized suppression factor for gluon emission off a heavy quark is derived within perturbative QCD, which is valid for the full range of rapidity of the radiated gluon and also has no restriction on the scaled mass of the quark with its energy. In the appropriate limit it correctly reproduces the usual dead cone factor in the forward rapidity region. On the other hand, this improved suppression factor becomes close to unity in the backward direction. This indicates a small suppression of gluon emission in the backward region, which should have an impact on the phenomenology of heavy quark energy loss in the hot and dense matter produced in ultra-relativistic heavy-ion collisions., Comment: A portion of the discussion and Fig. 3 changed in the text; A little change in the abstract; Version accepted in PRD

Both electric and magnetic screening masses in a nonperturbative gluonic background are investigated using operator product expansion. The magnetic screening mass is found to agree with lattice results whereas the electric screening mass is somewhat smaller than the one found on the lattice., Comment: Accepted in PRD

In HTL perturbation theory we obtain leading order quark number susceptibility as a response to an external disturbance, viz., chemical potential (\mu) that generates density fluctuation, which is related to the correlation function through the thermodynamic sum rule associated with the symmetry of the system. We also obtain various thermodynamic quantities in leading order., Comment: 4 pages, 2 figures, Talk given at the 6th ICPAQGP-2010, Goa, India, December 6-10, 2010

Considering recently developed Hard Thermal Loop perturbation theory that takes into account the effect of the variation of the external field through the fluctuations of a conserved quantity we calculate the temporal component of the Euclidian correlation function in the vector channel. The results are found to be in good agreement with the very recent results obtained within the quenched approximation of QCD and small values of the quark mass ($\sim 0.1T$) on improved lattices of size $128^3\times N_\tau$ at ($N_\tau=40, \ T=1.2T_C$), ($N_\tau=48, \ T=1.45T_C$), and ($N_\tau=16, \ T=2.98T_C$), where $N_\tau$ is the temporal extent of the lattice. This suggests that the results from lattice QCD and Hard Thermal Loop perturbation theory are in close proximity for a quantity associated with the conserved density fluctuation., Comment: 16 pages, 4 figures; One para added in introduction, Fig 1 modified; Accepted in Phys. Rev. D

We generalise the most extensively used Gunion-Bertsch formula for the soft gluon emission in a perturbative QCD, which could be very important for the phenomenology of the hot and dense matter produced in the heavy-ion collisions., Comment: 4 pages, 3 figures. Improved discussion. Accepted in PRD (Rapid Communication)

We discuss low mass dilepton rates ($\le 1$ GeV) from the deconfined phase of QCD using both perturbative and non-perturbative models and compare with those from lattice gauge theory and in-medium hadron gas. Our analysis suggests that the rate at very low invariant mass ($ M\le 200$ MeV) using the nonperturbative gluon condensate in a semiempirical way within the Green function dominates over the Born-rate and independent of any uncertainty associated with the choice of the strong coupling in perturbation theory. On the other hand the rate from $\rho-q$ interaction in the deconfined phase is important between 200 MeV $\le M \le 1 GeV as it is almost of same order of the Born-rate as well as in-medium hadron gas rate. Also the higher order perturbative rate, leaving aside its various uncertainties, from HTL approximation becomes reliable at $M\ge 200$ MeV and also becomes comparable with the Born-rate and the lattice-rate for $M\ge 500$ MeV, constraining on the broad resonance structures in the dilepton rate at large invariant mass. We also discuss the lattice constraints on the low mass dilepton rate. Furthermore, we discuss a more realistic way to advocate the quark-hadron duality hypothesis based on the dilepton rates from QGP and hadron gas than it is done in the literature., Comment: 24 pages, 9 figures; Discussion added, Accepted in Phys. Rev. C

The expansion dynamics of hot electron-positron-photon plasma droplets is dealt with within relativistic hydrodynamics. Such droplets, envisaged to be created in future experiments by irradiating thin foils with counter-propagating ultra-intense laser beams, are sources of flashes of gamma radiation. Warm electron-positron plasma droplets may be identified and characterized by a broadened 511 keV line.

Based on the external perturbation that disturbs the system only slightly from its equilibrium position we make the Taylor expansion of the pressure of a quark gas. It turns out that the first term was used in the literature to construct a Hard Thermal Loop perturbation theory (HTLpt) within the variation principle of the lowest order of the thermal mass parameter. Various thermodynamic quantities within the 1-loop HTLpt encountered overcounting of the leading order (LO) contribution and also required a separation scale for soft and hard momenta. Using same variational principle we reconstruct the HTLpt at the first derivative level of the pressure that takes into account the effect of the variation of the external source through the conserved density fluctuation. This modification markedly improves those quantities in 1-loop HTLpt in a simple way instead of pushing the calculation to a considerably more complicated 2-loop HTLpt. Moreover, the results also agree with those obtained in the 2-loop approximately self-consistent \Phi-derivable Hard Thermal Loop resummation. We also discuss how this formalism can be extended for the higher order contributions, Comment: Paper revised; a sec. deleted and title changed

We discuss on the critical exponent of $\eta/s$ for a fluid, and propose a new exponent-less measure of fluidity based on a mode-mode coupling theory. This exhibits a remarkable universality for fluids obeying a liquid-gas phase transition both in hydrodynamic as well as in nonhydrodynamic region. We show that this result is independent of the choice of the fluid dynamics, {\em viz.}, relativistic or nonrelativistic. Quark-Gluon Plasma, being a hot relativistic and a nearly perfect fluid produced in relativistic heavy-ion collisions, is expected to obey the same universality constrained by both the viscous and the thermal flow modes in it. We also show that if the elliptic flow data in RHIC puts a constraint on $\eta/s$ then the new fluidity measure for Quark-Gluon Plasma in turn also restricts the other transport coefficient, {\it viz.}, the thermal conductivity., Comment: 4 pages and 2 figures; Title and abstract changed; discussion added

$SU(N_c)$ colour-singlet restriction, along with flavour and spin symmetry, on thermal partonic ensemble is shown to recombine the partons with internal colour structure into colour-singlet multi-quark clusters which can be identified with various hadronic modes at a given temperature. This provides a possible basis for recombination model for hadronization of quark-gluon plasma. This also leads to a natural explanation for the ratio of (anti)protons to pions and the quark number scaling of the elliptic flow coefficient in relativistic heavy-ion collisions., Comment: 5 pages; version accepted as a Rapid Communication in Phys. Rev. C