The QCD phase diagram is studied in the presence of an isospin asymmetry using continuum extrapolated staggered quarks with physical masses. In particular, we investigate the phase boundary between the normal and the pion condensation phases and the chiral/deconfinement transition. The simulations are performed with a small explicit breaking parameter in order to avoid the accumulation of zero modes and thereby stabilize the algorithm. The limit of vanishing explicit breaking is obtained by means of an extrapolation, which is facilitated by a novel improvement program employing the singular value representation of the Dirac operator. Our findings indicate that no pion condensation takes place above T ≈ 160 MeV and also suggest that the deconfinement crossover continuously connects to the BEC-BCS crossover at high isospin asymmetries. The results may be directly compared to effective theories and model approaches to QCD.

We determine the light meson spectrum in QCD in the presence of background magnetic fields using quenched Wilson fermions. Our continuum extrapolated results indicate a monotonous reduction of the connected neutral pion mass as the magnetic field grows. The vector meson mass is found to remain nonzero, a finding relevant for the conjectured ρ-meson condensation at strong magnetic fields. The continuum extrapolation was facilitated by adding a novel magnetic field-dependent improvement term to the additive quark mass renormalization. Without this term, sizable lattice artifacts that would deceptively indicate an unphysical rise of the connected neutral pion mass for strong magnetic fields are present. We also investigate the impact of these lattice artifacts on further observables like magnetic polarizabilities and discuss the magnetic field-induced mixing between ρmesons and pions. We also derive Ward-Takashi identities for QCD+QED both in the continuum formulation and for (order a-improved) Wilson fermions. 1 In fact, the above mentioned lattice results are based on the connected contribution to the pion correlator, which corresponds to a hypothetic meson with exclusivelyūu ordd flavor content. We get back to this point in Sec. II B below. 2 Note that this is the simplest scenario for the superconductivity of the QCD vacuum when exposed to external magnetic fields. In fact, when coupled to the photon field that exhibits gauge fluctuations, the would-be massless ρ mode is absorbed by the photon field in accordance with the Higgs mechanism [18] so that no massless mode remains. For constant background magnetic fields -like the one we are working with here -this mechanism is absent. Also note that the proposed superconducting phase was suggested to exhibit several unusual features like anisotropy and inhomogeneity [17,19], and we do not attempt to capture these subtle characteristics here, which would require dynamical QCD+QED simulations and is much more involved.arXiv:1707.05600v3 [hep-lat]

We investigate the viability of a new type of compact star whose main constituent is a Bose-Einstein condensate of charged pions. Several different setups are considered, where a gas of charged leptons and neutrinos is also present. The pionic equation of state is obtained from lattice QCD simulations in the presence of an isospin chemical potential and requires no modeling of the nuclear force. The gravitationally bound configurations of these systems are found by solving the Tolman-Oppenheimer-Volkoff equations. We discuss weak decays within the pion condensed phase and elaborate on the generation mechanism of such objects.

We compute and analyze correlation functions in the isovector vector channel at vanishing spatial momentum across the deconfinement phase transition in lattice QCD. The simulations are carried out at temperatures T /T c = 0.156, 0.8, 1.0, 1.25 and 1.67 with T c 203MeV for two flavors of Wilson-Clover fermions with a zero-temperature pion mass of 270 MeV. Exploiting exact sum rules and applying a phenomenologically motivated ansatz allows us to determine the spectral function ρ(ω, T ) via a fit to the lattice correlation function data. From these results we estimate the electrical conductivity across the deconfinement phase transition via a Kubo formula and find evidence for the dissociation of the ρ meson by resolving its spectral weight at the available temperatures. We also apply the Backus-Gilbert method as a model-independent approach to this problem. At any given frequency, it yields a local weighted average of the true spectral function. We use this method to compare kinetic theory predictions and previously published phenomenological spectral functions to our lattice study.

We present a lattice QCD calculation with two dynamical flavors of the isovector vector correlator in the high-temperature phase. We analyze the correlator in terms of the associated spectral function, for which we review the theoretical expectations. In our main analysis, we perform a fit for the difference of the thermal and vacuum spectral functions, and we use an exact sum rule that constrains this difference. We also perform a direct fit for the thermal spectral function, and obtain good agreement between the two analyses for frequencies below the two-pion threshold. Under the assumption that the spectral function is smooth in that region, we give an estimate of the electrical conductivity.