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.

Abstract:We study the thermal transition of QCD with two degenerate light flavours by lattice simulations using O(a)-improved Wilson quarks. Temperature scans are performed at a fixed value of N t = (aT ) −1 = 16, where a is the lattice spacing and T the temperature, at three fixed zero-temperature pion masses between 200 MeV and 540 MeV. In this range we find that the transition is consistent with a broad crossover. As a probe of the restoration of chiral symmetry, we study the static screening spectrum. We observe a degeneracy between the transverse isovector vector and axial-vector channels starting from the transition temperature. Particularly striking is the strong reduction of the splitting between isovector scalar and pseudoscalar screening masses around the chiral phase transition by at least a factor of three compared to its value at zero temperature. In fact, the splitting is consistent with zero within our uncertainties. This disfavours a chiral phase transition in the O(4) universality class.

We perform a high precision measurement of the static qq potential in threedimensional SU(N ) gauge theory with N = 2, 3 and compare the results to the potential obtained from the effective string theory. In particular, we show that the exponent of the leading order correction in 1/R is 4, as predicted, and obtain accurate results for the continuum limits of the string tension and the non-universal boundary coefficientb 2 , including an extensive analysis of all types of systematic uncertainties. We find that the magnitude ofb 2 decreases with increasing N , leading to the possibility of a vanishingb 2 in the large N limit. In the standard form of the effective string theory possible massive modes and the presence of a rigidity term are usually not considered, even though they might give a contribution to the energy levels. To investigate the effect of these terms, we perform a second analysis, including these contributions. We find that the associated expression for the potential also provides a good description of the data. The resulting continuum values forb 2 are about a factor of 2 smaller than in the standard analysis, due to contaminations from an additional 1/R 4 term. However,b 2 shows a similar decrease in magnitude with increasing N . In the course of this extended analysis we also obtain continuum results for the masses appearing in the additional terms and we find that they are around twice as large as the square root of the string tension in the continuum and compatible between SU(2) and SU(3) gauge theory. In the follow up papers we will extend our investigations to the large N limit and excited states of the open flux tube.

Abstract. We investigate the properties of QCD at finite isospin chemical potential at zero and non-zero temperatures. This theory is not affected by the sign problem and can be simulated using Monte-Carlo techniques. With increasing isospin chemical potential and temperatures below the deconfinement transition the system changes into a phase where charged pions condense, accompanied by an accumulation of low modes of the Dirac operator. The simulations are enabled by the introduction of a pionic source into the action, acting as an infrared regulator for the theory, and physical results are obtained by removing the regulator via an extrapolation. We present an update of our study concerning the associated phase diagram using 2+1 flavours of staggered fermions with physical quark masses and the comparison to Taylor expansion. We also present first results for our determination of the equation of state at finite isospin chemical potential and give an example for a cosmological application. The results can also be used to gain information about QCD at small baryon chemical potentials using reweighting with respect to the pionic source parameter and the chemical potential and we present first steps in this direction.