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Register a new userEquation of state of cold and dense QCD matter in resummed perturbation theory
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We discuss the Hard Dense Loop resummation at finite quark mass and evaluate the equation of state (EoS) of cold and dense QCD matter in $beta$ equilibrium. The resummation in the quark sector has an effect of lowering the baryon number density and the EoS turns out to have much smaller uncertainty than the perturbative QCD estimate. Our numerical results favor smooth matching between the EoS from the resummed QCD calculation at high density and the extrapolated EoS from the nuclear matter density region. We also point out that the speed of sound in our EoS slightly exceeds the conformal limit.
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We perform a detailed analysis of the predictions of resummed perturbation theory for the pressure and the second-, fourth-, and sixth-order diagonal quark number susceptibilities in a hot and dense quark-gluon plasma. First, we present an exact one-loop calculation of the equation of state within hard-thermal-loop perturbation theory (HTLpt) and compare it to a previous one-loop HTLpt calculation that employed an expansion in the ratios of thermal masses and the temperature. We find that this expansion converges reasonably fast. We then perform a resummation of the existing four-loop weak coupling expression for the pressure, motivated by dimensional reduction. Finally, we compare the exact one-loop HTLpt and resummed dimensional reduction results with state-of-the-art lattice calculations and a recent mass-expanded three-loop HTLpt calculation.
In this Ph.D. thesis, the primary goal is to present a recent investigation of the finite density thermodynamics of hot and dense quark-gluon plasma. As we are interested in a temperature regime, in which naive perturbation theory is known to lose its predictive power, we clearly need to use a refined approach. To this end, we adopt a resummed perturbation theory point of view and employ two different frameworks. We first use hard-thermal-loop perturbation theory (HLTpt) at leading order to obtain the pressure for nonvanishing quark chemical potentials, and next, inspired by dimensional reduction, resum the known four-loop weak coupling expansion for the quantity. We present and analyze our findings for various cumulants of conserved charges. This provides us with information, through correlations and fluctuations, on the degrees of freedom effectively present in the quark-gluon plasma right above the deconfinement transition. Moreover, we compare our results with state-of-the-art lattice Monte Carlo simulations as well as with a recent three-loop mass truncated HTLpt calculation. We obtain very good agreement between the two different perturbative schemes, as well as between them and lattice data, down to surprisingly low temperatures right above the phase transition. We also quantitatively test the convergence of an approximation, which is used in higher order loop calculations in HTLpt. This method based on expansions in mass parameters, is unavoidable beyond leading order, thus motivating our investigation. We find the ensuing convergence to be very fast, validating its use in higher order computations.
A previously derived three-dimensional effective lattice theory describing the thermodynamics of QCD with heavy quarks in the cold and dense region is extended through order $sim u^5kappa^8$ in the combined character and hopping expansion of the original four-dimensional Wilson action. The systematics of the effective theory is investigated to determine its range of validity in parameter space. We demonstrate the severe cut-off effects due to lattice saturation, which afflict any lattice results at finite baryon density independent of the sign problem or the quality of effective theories, and which have to be removed by continuum extrapolation. We then show how the effective theory can be solved analytically by means of a linked cluster expansion, which is completely unaffected by the sign problem, in quantitative agreement with numerical simulations. As an application, we compute the cold nuclear equation of state of heavy QCD. Our continuum extrapolated result is consistent with a polytropic equation of state for non-relativistic fermions.
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.
Cumulants of conserved charges provide important information about the physics of the quark-gluon plasma around the phase transition region, as they are by construction sensitive to changes in the degrees of freedom of the system. In this brief proceedings contribution, I report on recent results for two such quantities from two different improved perturbative frameworks, as well as discuss their relevance for heavy ion experiments.
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