Gauge-invariant field-strength correlators for QCD in a magnetic background

We consider the properties of the gauge-invariant two-point correlation functions of the gauge-field strengths for QCD in the presence of a magnetic background field. We discuss the general structure of the correlators in this case and provide the results of an exploratory lattice study for $N_f = 2$ QCD discretized with unimproved staggered fermions. Our analysis provides evidence for the emergence of anisotropies in the non-perturbative part of the correlators and for an increase of the gluon condensate as a function of the external magnetic field.Comment: Published version. Added table with perturbative parameters values. 8 pages, 5 figure

Theta dependence of the deconfinement temperature in Yang-Mills theories

We determine the theta dependence of the deconfinement temperature of SU(3) pure gauge theory, finding that it decreases in presence of a topological theta term. We do that by performing lattice simulations at imaginary theta, then exploiting analytic continuation. We also give an estimate of such dependence in the limit of a large number of colors N, and compare it with our numerical results.Comment: 5 pages, 4 figures, 1 table. Discussion and references added. Final version published in Phys. Rev. Let

Phase diagram of Yang-Mills theories in the presence of a theta term

We study the phase diagram of non-Abelian pure gauge theories in the presence of a topological theta term. The dependence of the deconfinement temperature on theta is determined on the lattice both by analytic continuation and by reweighting, obtaining consistent results. The general structure of the diagram is discussed on the basis of large-N considerations and of the possible analogies and dualities existing with the phase diagram of QCD in presence of an imaginary baryon chemical potential.Comment: 14 pages, 3 tables, 13 figures. Final version published in Physical Review

Magnetic susceptibility and equation of state of N_f = 2+1 QCD with physical quark masses

We determine the free energy of strongly interacting matter as a function of an applied constant and uniform magnetic field. We consider N_f = 2+1 QCD with physical quark masses, discretized on a lattice by stout improved staggered fermions and a tree level improved Symanzik pure gauge action, and explore three different lattice spacings. For magnetic fields of the order of those produced in non-central heavy ion collisions (eB ~ 0.1 GeV^2) strongly interacting matter behaves like a medium with a linear response, and is paramagnetic both above and below the deconfinement transition, with a susceptibility which steeply rises in the deconfined phase. We compute the equation of state, showing that the relative increase in the pressure due to the magnetic field gets larger around the transition, and of the order of 10 % for eB ~ 0.1 GeV^2.Comment: 11 pages, 10 figures, 3 tables. Final version published in Physical Review

The curvature of the chiral pseudocritical line from LQCD: analytic continuation and Taylor expansion compared

We present a determination of the curvature $\kappa$ of the chiral pseudocritical line from $N_f=2+1$ lattice QCD at the physical point obtained by adopting the Taylor expansion approach. Numerical simulations performed at three lattice spacings lead to a continuum extrapolated curvature $\kappa = 0.0145(25)$, a value that is in excellent agreement with continuum limit estimates obtained via analytic continuation within the same discretization scheme, $\kappa = 0.0135(20)$. The agreement between the two calculations is a solid consistency check for both methods.Comment: Quark Matter 201

Magnetic Susceptibility of Strongly Interacting Matter across the Deconfinement Transition

We propose a method to determine the total magnetic susceptibility of strongly interacting matter by lattice QCD simulations, and present first numerical results for the theory with two light flavors, which suggest a weak magnetic activity in the confined phase and the emergence of strong paramagnetism in the deconfined, Quark-Gluon Plasma phase.Comment: 6 pages, 6 figures, 2 tables. Final version published in Physical Review Letter

Susceptibility of the QCD vacuum to CP-odd electromagnetic background fields

We investigate two flavor QCD in presence of CP-odd electromagnetic background fields and determine, by means of lattice QCD simulations, the induced effective theta term to the first order in the scalar product of E and B. We employ a rooted staggered discretization and study lattice spacings down to 0.1 fm and Goldstone pion masses around 480 MeV. In order to deal with a positive measure, we consider purely imaginary electric fields and real magnetic fields, then exploiting analytic continuation. Our results are relevant to a description of the effective pseudoscalar QED-QCD interactions.Comment: 5 pages, 4 figures, 1 table. New data and references added. Matches the published versio

Roberge-Weiss endpoint at the physical point of Nf=2+1N_f = 2+1 QCD

We study the phase diagram of $N_f = 2+1$ QCD in the $T - \mu_B$ plane and investigate the critical point corresponding to the onset of the Roberge-Weiss transition, which is found for imaginary values of $\mu_B$. We make use of stout improved staggered fermions and of the tree level Symanzik gauge action, and explore four different sets of lattice spacings, corresponding to $N_t = 4,6,8,10$, and different spatial sizes, in order to assess the universality class of the critical point. The continuum extrapolated value of the endpoint temperature is found to be $T_{\rm RW} = 208(5)$ MeV, i.e. $T_{\rm RW}/T_c \sim 1.34(7)$, where $T_c$ is the chiral pseudocritical temperature at zero chemical potential, while our finite size scaling analysis, performed on $N_t = 4$ and $N_t = 6$ lattices, provides evidence for a critical point in the $3d$ Ising universality class.Comment: 10 pages, 14 eps figures, 2 tables, final version published in Physical Review

Topology in full QCD at high temperature: a multicanonical approach

We investigate the topological properties of $N_f = 2+1$ QCD with physical quark masses, at temperatures around 500 MeV. With the aim of obtaining a reliable sampling of topological modes in a regime where the fluctuations of the topological charge $Q$ are very rare, we adopt a multicanonical approach, adding a bias potential to the action which enhances the probability of suppressed topological sectors. This method permits to gain up to three orders of magnitude in computational power in the explored temperature regime. Results at different lattice spacings and physical spatial volumes reveal no significant finite size effects and the presence, instead, of large finite cut-off effects, with the topological susceptibility which decreases by 3-4 orders of magnitude while moving from $a \simeq 0.06$ fm towards the continuum limit. The continuum extrapolation is in agreeement with previous lattice determinations with smaller uncertainties but obtained based on ansatzes justified by several theoretical assumptions. The parameter $b_2$, related to the fourth order coefficient in the Taylor expansion of the free energy density $f(\theta)$, has instead a smooth continuum extrapolation which is in agreement with the dilute instanton gas approximation (DIGA); moreover, a direct measurement of the relative weights of the different topological sectors gives an even stronger support to the validity of DIGA.Comment: 23 pages, 13 figure