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The quark confinement in QCD is achieved by concentration of the chromoelectric field between the quark-antiquark pair into a flux tube, which gives rise to a linear quark-antiquark potential. We study the structure of the flux tube created by a static quark-antiquark pair in the pure gauge SU(3) theory, using lattice Monte-Carlo simulations. We calculate the spatial distribution of all three components of the chromoelectric field and perform the “zero curl subtraction” procedure to obtain the nonperturbative part of the longitudinal component of the field, which we identify as the part responsible for the formation of the flux tube. Taking the spatial derivatives of the obtained field allows us to extract the electric charge and magnetic current densities in the flux tube. The behavior of these observables under smearing and with respect to continuum scaling is investigated. Finally, we briefly discuss the role of magnetic currents in the formation of the string tension.
The introduction of non-orthogonal electric and magnetic fields in the QCD vacuum enhances the weight of topological sectors with a nonzero topological charge. For weak fields, there is a linear response for the expectation value of the topological charge. We study this linear response and relate it to the QCD correction to the axion-photon coupling. We also analyse the magnetic field dependence of the topological susceptibility for a range of temperatures around Tc. In this work we use lattice simulations with improved staggered quarks at physical masses, including background magnetic and (imaginary) electric fields.
Attempts to extract the order of the chiral transition of QCD at zero chemical potential, with two dynamical flavors of massless quarks, from simulations with progressively decreasing pion mass, have remained inconclusive because of their increasing numerical cost. In an alternative approach to this problem, we consider the path integral as a function of continuous number Nf of degenerate quarks. If the transition in the chiral limit is first order for Nf≥3, a second-order transition for Nf=2 then requires a tricritical point in between. This, in turn, implies tricritical scaling of the critical boundary line between the first-order and crossover regions as the chiral limit is approached. Noninteger numbers of fermion flavors are easily implemented within the staggered fermion discretization. Exploratory simulations at μ=0 and Nf=2.8, 2.6, 2.4, 2.2, 2.1, on coarse Nτ=4 lattices, indeed show a smooth variation of the critical mass mapping out a critical line in the (m, Nf) plane. For the smallest masses, the line appears consistent with tricritical scaling, allowing for an extrapolation to the chiral limit.
The SU(3) pure gauge theory exhibits a first-order thermal deconfinement transition due to spontaneous breaking of its global Z3 center symmetry. When heavy dynamical quarks are added, this symmetry is broken explicitly and the transition weakens with decreasing quark mass until it disappears at a critical point. We compute the critical hopping parameter and the associated pion mass for lattice QCD with Nf=2 degenerate standard Wilson fermions on Nτ∈{6,8,10} lattices, corresponding to lattice spacings a=0.12 fm, a=0.09 fm, a=0.07 fm, respectively. Significant cutoff effects are observed, with the first-order region growing as the lattice gets finer. While current lattices are still too coarse for a continuum extrapolation, we estimate mcπ≈4 GeV with a remaining systematic error of ∼20%. Our results allow us to assess the accuracy of the leading-order and next-to-leading-order hopping expanded fermion determinant used in the literature for various purposes. We also provide a detailed investigation of the statistics required for this type of calculation, which is useful for similar investigations of the chiral transition.
The nature of the QCD chiral phase transition in the limit of vanishing quark masses has remained elusive for a long time, since it cannot be simulated directly on the lattice and is strongly cutoff-dependent. We report on a comprehensive ongoing study using unimproved staggered fermions with Nf ∈ [2, 8] mass-degenerate flavours on Nτ ∈ {4, 6, 8} lattices, in which we locate the chiral critical surface separating regions with first-order transitions from crossover regions in the bare parameter space of the lattice theory. Employing the fact that it terminates in a tricritical line, this surface can be extrapolated to the chiral limit using tricritical scaling with known exponents. Knowing the order of the transitions in the lattice parameter space, conclusions for approaching the continuum chiral limit in the proper order can be drawn. While a narrow first-order region cannot be ruled out, we find initial evidence consistent with a second-order chiral transition in all massless theories with Nf ≤ 6, and possibly up to the onset of the conformal window at 9 ≲ N∗f ≲ 12. A reanalysis of already published O(a)-improved Nf = 3 Wilson data on Nτ ∈ [4, 12] is also consistent with tricritical scaling, and the associated change from first to second-order on the way to the continuum chiral limit. We discuss a modified Columbia plot and a phase diagram for many-flavour QCD that reflect these possible features.
For large isospin asymmetries, perturbation theory predicts the quantum chromodynamic (QCD) ground state to be a superfluid phase of u and d¯ Cooper pairs. This phase, which is denoted as the Bardeen-Cooper-Schrieffer (BCS) phase, is expected to be smoothly connected to the standard phase with Bose-Einstein condensation (BEC) of charged pions at μI≥mπ/2 by an analytic crossover. A first hint for the existence of the BCS phase, which is likely characterised by the presence of both deconfinement and charged pion condensation, comes from the lattice observation that the deconfinement crossover smoothly penetrates into the BEC phase. To further scrutinize the existence of the BCS phase, in this article we investigate the complex spectrum of the massive Dirac operator in 2+1-flavor QCD at nonzero temperature and isospin chemical potential. The spectral density near the origin is related to the BCS gap via a generalization of the Banks-Casher relation to the case of complex Dirac eigenvalues (derived for the zero-temperature, high-density limits of QCD at nonzero isospin chemical potential).