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Register a new userOn high-order perturbative calculations at finite density
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We discuss the prospects of performing high-order perturbative calculations in systems characterized by a vanishing temperature but finite density. In particular, we show that the determination of generic Feynman integrals containing fermionic chemical potentials can be reduced to the evaluation of three-dimensional phase space integrals over vacuum on-shell amplitudes - a result reminiscent of a previously proposed naive real-time formalism for vacuum diagrams. Applications of these rules are discussed in the context of the thermodynamics of cold and dense QCD, where it is argued that they facilitate an extension of the Equation of State of cold quark matter to higher perturbative orders.
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Fluctuations of conserved charges are sensitive to the QCD phase transition and a possible critical endpoint in the phase diagram at finite density. In this work, we compute the baryon number fluctuations up to tenth order at finite temperature and density. This is done in a QCD-assisted effective theory that accurately captures the quantum- and in-medium effects of QCD at low energies. A direct computation at finite density allows us to assess the applicability of expansions around vanishing density. By using different freeze-out scenarios in heavy-ion collisions, we translate these results into baryon number fluctuations as a function of collision energy. We show that a non-monotonic energy dependence of baryon number fluctuations can arise in the non-critical crossover region of the phase diagram. Our results compare well with recent experimental measurements of the kurtosis and the sixth-order cumulant of the net-proton distribution from the STAR collaboration. They indicate that the experimentally observed non-monotonic energy dependence of fourth-order net-proton fluctuations is highly non-trivial. It could be an experimental signature of an increasingly sharp chiral crossover and may indicate a QCD critical point. The physics implications and necessary upgrades of our analysis are discussed in detail.
In this paper, we study two-color, two-flavor QCD using chiral perturbation theory at next-to-leading order when the diquark chemical potential ($mu_{B}$) is equal to the isospin chemical potential ($mu_{I}$). For chemical potentials larger than the physical pion mass, the system is in a multicomponent superfluid phase with both pions and diquarks. We construct the one-loop effective potential using $chi$PT in the presence of an external multicomponent superfluid source and use the effective potential to calculate the chiral condensate, the multicomponent superfluid condensate and the (multicomponent) superfluid density. We also find the critical chemical potential and the order of the phase transition from the normal phase to the multicomponent condensed phase at next-to-leading order. The phase transition remains second order (as at tree-level) and the critical chemical potential is equal to the one-loop renormalized diquark (or pion) mass.
We present a program for the reduction of large systems of integrals to master integrals. The algorithm was first proposed by Laporta; in this paper, we implement it in MAPLE. We also develop two new features which keep the size of intermediate expressions relatively small throughout the calculation. The program requires modest input information from the user and can be used for generic calculations in perturbation theory.
We demonstrate that the complex Langevin method (CLM) enables calculations in QCD at finite density in a parameter regime in which conventional methods, such as the density of states method and the Taylor expansion method, are not applicable due to the severe sign problem. Here we use the plaquette gauge action with $beta = 5.7$ and four-flavor staggered fermions with degenerate quark mass $m a = 0.01$ and nonzero quark chemical potential $mu$. We confirm that a sufficient condition for correct convergence is satisfied for $mu /T = 5.2 - 7.2$ on a $8^3 times 16$ lattice and $mu /T = 1.6 - 9.6$ on a $16^3 times 32$ lattice. In particular, the expectation value of the quark number is found to have a plateau with respect to $mu$ with the height of 24 for both lattices. This plateau can be understood from the Fermi distribution of quarks, and its height coincides with the degrees of freedom of a single quark with zero momentum, which is 3 (color) $times$ 4 (flavor) $times$ 2 (spin) $=24$. Our results may be viewed as the first step towards the formation of the Fermi sphere, which plays a crucial role in color superconductivity conjectured from effective theories.
We introduce an effective quark-meson-nucleon model for the QCD phase transitions at finite baryon density. The nucleon and the quark degrees of freedom are described within a unified framework of a chiral linear sigma model. The deconfinement transition is modeled through a simple modification of the distribution functions of nucleons and quarks, where an additional auxiliary field, the bag field, is introduced. The bag field plays a key role in converting between the nucleon and the quark degrees of freedom. The model predicts that the chiral and the deconfinement phase transitions are always separated. Depending on the model parameters, the chiral transition occurs in the baryon density range of $(1.5-15.5)n_0$, while the deconfinement transition occurs above $5 n_0$, where $n_0$ is the saturation density.
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