We propose a new method to investigate the thermal properties of QCD with a small quark chemical potential . Derivatives of quark and gluonic observables with respect to are computed at ϭ0 for two flavors of p4 improved staggered fermions with maϭ0.1,0.2 on a 16 3 ϫ4 lattice, and used to calculate the leading order Taylor expansion in of the location of the pseudocritical point about ϭ0. This expansion should be well behaved for the small values of q /T c ϳ0.1 relevant for BNL RHIC phenomenology, and predicts a critical curve T c () in reasonable agreement with estimates obtained using exact reweighting. In addition, we contrast the case of isoscalar and isovector chemical potentials, quantify the effect of 0 on the equation of state, and comment on the complex phase of the fermion determinant in QCD with 0.

We present a lattice QCD calculation of the up, down, strange and charm quark masses performed using the gauge configurations produced by the European Twisted Mass Collaboration with N f = 2 + 1 + 1 dynamical quarks, which include in the sea, besides two light mass degenerate quarks, also the strange and charm quarks with masses close to their physical values. The simulations are based on a unitary setup for the two light quarks and on a mixed action approach for the strange and charm quarks. The analysis uses data at three values of the lattice spacing and pion masses in the range 210 ÷ 450 MeV, allowing for accurate continuum limit and controlled chiral extrapolation. The quark mass renormalization is carried out non-perturbatively using the RI -MOM method. The results for the quark masses converted to the MS scheme are: m ud (2 GeV) = 3.70(17) MeV, m s (2 GeV) = 99.6(4.3) MeV and m c (m c ) = 1.348(46) GeV. We obtain also the quark mass ratios m s /m ud = 26.66(32) and m c /m s = 11.62(16). By studying the mass splitting between the neutral and charged kaons and using available lattice results for the electromagnetic contributions, we evaluate m u /m d = 0.470(56), leading to m u = 2.36(24) MeV and m d = 5.03(26) MeV.

It is sometimes speculated that the sign problem that afflicts many quantum field theories might be reduced or even eliminated by choosing an alternative domain of integration within a complexified extension of the path integral (in the spirit of the stationary phase integration method). In this paper we start to explore this possibility somewhat systematically. A first inspection reveals the presence of many difficulties but-quite surprisingly-most of them have an interesting solution. In particular, it is possible to regularize the lattice theory on a Lefschetz thimble, where the imaginary part of the action is constant and disappears from all observables. This regularization can be justified in terms of symmetries and perturbation theory. Moreover, it is possible to design a Monte Carlo algorithm that samples the configurations in the thimble. This is done by simulating, effectively, a five dimensional system. We describe the algorithm in detail and analyze its expected cost and stability. Unfortunately, the measure term also produces a phase which is not constant and it is currently very expensive to compute. This residual sign problem is expected to be much milder, as the dominant part of the integral is not affected, but we have still no convincing evidence of this. However, the main goal of this paper is to introduce a new approach to the sign problem, that seems to offer much room for improvements. An appealing feature of this approach is its generality. It is illustrated first in the simple case of a scalar field theory with chemical potential, and then extended to the more challenging case of QCD at finite baryonic density.

We identify the global symmetries of SU(2) lattice gauge theory with N flavors of staggered fermion in the presence of a quark chemical potential µ, for fermions in both fundamental and adjoint representations, and anticipate likely patterns of symmetry breaking at both low and high densities. Results from numerical simulations of the model with N = 1 adjoint flavor on a 4 3 × 8 lattice are presented, using both hybrid Monte Carlo and Two-Step Multi-Boson algorithms. It is shown that the sign of the fermion determinant starts to fluctuate once the model enters a phase with non-zero baryon charge density. HMC simulations are not ergodic in this regime, but TSMB simulations retain ergodicity even in the dense phase, and in addition appear to show superior decorrelation. The HMC results for the equation of state and the pion mass show good quantitative agreement with the predictions of chiral perturbation theory, which should hold only for N ≥ 2. The TSMB results incorporating the sign of the determinant support a delayed onset transition, consistent with the pattern of symmetry breaking expected for N = 1.