BEC-BCS Crossover in the Nambu--Jona-Lasinio Model of QCD

The BEC-BCS crossover in QCD at finite baryon and isospin chemical potentials is investigated in the Nambu--Jona-Lasinio model. The diquark condensation in two color QCD and the pion condensation in real QCD would undergo a BEC-BCS crossover when the corresponding chemical potential increases. We determined the crossover chemical potential as well as the BEC and BCS regions. The crossover is not triggered by increasing the strength of attractive interaction among quarks but driven by changing the charge density. The chiral symmetry restoration at finite temperature and density plays an important role in the BEC-BCS crossover. For real QCD, strong couplings in diquark and vector meson channels can induce a diquark BEC-BCS crossover in color superconductor, and in the BEC region the chromomagnetic instability is fully cured and the ground state is a uniform phase.Comment: 18 pages, 15 figures. V2: typos corrected, references added. V3: typos in Appendix B correcte

BCS-BEC Crossover in Atomic Fermi Gases with a Narrow Resonance

We determine the effects on the BCS-BEC crossover of the energy dependence of the effective two-body interaction, which at low energies is determined by the effective range. To describe interactions with an effective range of either sign, we consider a single-channel model with a two-body interaction having an attractive square well and a repulsive square barrier. We investigate the two-body scattering properties of the model, and then solve the Eagles-Leggett equations for the zero temperature crossover, determining the momentum dependent gap and the chemical potential self-consistently. From this we investigate the dependence of the crossover on the effective range of the interaction.Comment: 12 pages, 14 figure

Universality of Phases in QCD and QCD-like Theories

We argue that the whole or the part of the phase diagrams of QCD and QCD-like theories should be universal in the large-N_c limit through the orbifold equivalence. The whole phase diagrams, including the chiral phase transitions and the BEC-BCS crossover regions, are identical between SU(N_c) QCD at finite isospin chemical potential and SO(2N_c) and Sp(2N_c) gauge theories at finite baryon chemical potential. Outside the BEC-BCS crossover region in these theories, the phase diagrams are also identical to that of SU(N_c) QCD at finite baryon chemical potential. We give examples of the universality in some solvable cases: (i) QCD and QCD-like theories at asymptotically high density where the controlled weak-coupling calculations are possible, (ii) chiral random matrix theories of different universality classes, which are solvable large-N (large volume) matrix models of QCD. Our results strongly suggest that the chiral phase transition and the QCD critical point at finite baryon chemical potential can be studied using sign-free theories, such as QCD at finite isospin chemical potential, in lattice simulations.Comment: v1: 35 pages, 6 figures; v2: 37 pages, 6 figures, minor improvements, conclusion unchanged; v3: version published in JHE

Chiral and deconfinement phase transitions of two-flavour QCD at finite temperature and chemical potential

We present results for the chiral and deconfinement transition of two flavor QCD at finite temperature and chemical potential. To this end we study the quark condensate and its dual, the dressed Polyakov loop, with functional methods using a set of Dyson-Schwinger equations. The quark-propagator is determined self-consistently within a truncation scheme including temperature and in-medium effects of the gluon propagator. For the chiral transition we find a crossover turning into a first order transition at a critical endpoint at large quark chemical potential, $\mu_{EP}/T_{EP} \approx 3$. For the deconfinement transition we find a pseudo-critical temperature above the chiral transition in the crossover region but coinciding transition temperatures close to the critical endpoint.Comment: 4 pages, 4 figures. v2: minor changes, comments adde

A simple mean field equation for condensates in the BEC-BCS crossover regime

We present a mean field approach based on pairs of fermionic atoms to describe condensates in the BEC-BCS crossover regime. By introducing an effective potential, the mean field equation allows us to calculate the chemical potential, the equation of states and the atomic correlation function. The results agree surprisingly well with recent quantum Monte Carlo calculations. We show that the smooth crossover from the bosonic mean field repulsion between molecules to the Fermi pressure among atoms is associated with the evolution of the atomic correlation function

Net Baryon Fluctuations from a Crossover Equation of State

We have constructed an equation of state which smoothly interpolates between an excluded volume hadron resonance gas at low energy density to a plasma of quarks and gluons at high energy density. This crossover equation of state agrees very well with lattice calculations at both zero and nonzero baryon chemical potential. We use it to compute the variance, skewness, and kurtosis of fluctuations of baryon number, and compare to measurements of proton number fluctuations in central Au-Au collisions as measured by the STAR collaboration in a beam energy scan at the Relativistic Heavy Ion Collider. The crossover equation of state can reproduce the data if the fluctuations are frozen out at temperatures well below than the average chemical freeze-out.Comment: 5 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1506.0340