On the neutrality issue in the Polyakov-loop NJL model

We elucidate how the color neutrality is harmed in the Polyakov Nambu-Jona Lasinio (PNJL) model at finite density within the adopted mean field approximation. Also we point out how usual assumption about the diagonal form of the Wilson loop may fail in the presence of the diquark condensate on several grounds.Comment: 8 pages, 1 figure. Introduction enlarged, several comments about the adopted mean field approximation and the relation with Elitzur's theorem added. Version to appear on Phys. Rev.

Chiral crossover, deconfinement and quarkyonic matter within a Nambu-Jona Lasinio model with the Polyakov loop

We study the interplay between the chiral and the deconfinement transitions, both at high temperature and high quark chemical potential, by a non local Nambu-Jona Lasinio model with the Polyakov loop in the mean field approximation and requiring neutrality of the ground state. We consider three forms of the effective potential of the Polyakov loop: two of them with a fixed deconfinement scale, cases I and II, and the third one with a $\mu$ dependent scale, case III. In the cases I and II, at high chemical potential $\mu$ and low temperature $T$ the main contribution to the free energy is due to the Z(3)-neutral three-quark states, mimicking the quarkyonic phase of the large $N_c$ phase diagram. On the other hand in the case III the quarkyonic window is shrunk to a small region. Finally we comment on the relations of these results to lattice studies and on possible common prospects. We also briefly comment on the coexistence of quarkyonic and color superconductive phases.Comment: 16 pages, 7 figures, RevTeX4. Some typos corrected, references adde

Strange mass dependence of the tricritical point in the U(3)_L x U(3)_R chiral sigma model

We study the strange quark mass dependence of the tricritical point of the U(3)_L x U(3)_R linear sigma model in the chiral limit. Assuming that the tricritical point is at a large strange mass value, the strange sector as well as the \eta-a_0 sector decouples from the light degrees of freedom which determines the thermodynamics. By tracing this decoupling we arrive from the original U(3)_L x U(3)_R symmetric model, going through the U(2)_L x U(2)_R symmetric one, at the SU(2)_L x SU(2)_R linear sigma model. One-loop level beta functions for the running of the parameters in each of these models and tree-level matching of the coupling of these models performed at intermediate scales are used to determine the influence of the heavy sector on the parameters of the SU(2)_L x SU(2)_R linear sigma model. By investigating the thermodynamics of this latter model we identified the tricritical surface of the U(3)_L x U(3)_R linear sigma model in the chiral limit. To apply the results for QCD we used different scenarios for the m_s and \mu_q dependence of the effective model parameters, then the \mu_q^TCP(m_s) function can be determined. Depending on the details, a curve bending upwards or downwards near \mu_q=0 can be obtained, while with explicit chemical potential dependence of the parameters the direction of the curve can change with m_s, too.Comment: 17 pages, 6 figures, uses revtex4-

The deconfinement transition of finite density QCD with heavy quarks from strong coupling series

Starting from Wilson's action, we calculate strong coupling series for the Polyakov loop susceptibility in lattice gauge theories for various small N_\tau in the thermodynamic limit. Analysing the series with Pad\'e approximants, we estimate critical couplings and exponents for the deconfinement phase transition. For SU(2) pure gauge theory our results agree with those from Monte-Carlo simulations within errors, which for the coarser N_\tau=1,2 lattices are at the percent level. For QCD we include dynamical fermions via a hopping parameter expansion. On a N_\tau=1 lattice with N_f=1,2,3, we locate the second order critical point where the deconfinement transition turns into a crossover. We furthermore determine the behaviour of the critical parameters with finite chemical potential and find the first order region to shrink with growing \mu. Our series moreover correctly reflects the known Z(N) transition at imaginary chemical potential.Comment: 18 pages, 7 figures, typos corrected, version published in JHE

Monopole clusters, center vortices, and confinement in a Z(2) gauge-Higgs system

We propose to use the different kinds of vacua of the gauge theories coupled to matter as a laboratory to test confinement ideas of pure Yang-Mills theories. In particular, the very poor overlap of the Wilson loop with the broken string states supports the 't Hooft and Mandelstam confinement criteria. However in the Z(2) gauge-Higgs model we use as a guide we find that the condensation of monopoles and center vortices is a necessary, but not sufficient condition for confinement.Comment: 13 pages, 6 figures, minor changes, version to be published on Phys. Rev.

Assessing the Performance of Recent Density Functionals for Bulk Solids

We assess the performance of recent density functionals for the exchange-correlation energy of a nonmolecular solid, by applying accurate calculations with the GAUSSIAN, BAND, and VASP codes to a test set of 24 solid metals and non-metals. The functionals tested are the modified Perdew-Burke-Ernzerhof generalized gradient approximation (PBEsol GGA), the second-order GGA (SOGGA), and the Armiento-Mattsson 2005 (AM05) GGA. For completeness, we also test more-standard functionals: the local density approximation, the original PBE GGA, and the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA. We find that the recent density functionals for solids reach a high accuracy for bulk properties (lattice constant and bulk modulus). For the cohesive energy, PBE is better than PBEsol overall, as expected, but PBEsol is actually better for the alkali metals and alkali halides. For fair comparison of calculated and experimental results, we consider the zero-point phonon and finite-temperature effects ignored by many workers. We show how Gaussian basis sets and inaccurate experimental reference data may affect the rating of the quality of the functionals. The results show that PBEsol and AM05 perform somewhat differently from each other for alkali metal, alkaline earth metal and alkali halide crystals (where the maximum value of the reduced density gradient is about 2), but perform very similarly for most of the other solids (where it is often about 1). Our explanation for this is consistent with the importance of exchange-correlation nonlocality in regions of core-valence overlap.Comment: 32 pages, single pdf fil

Heavy Quark Free Energies and Screening in SU(2) Gauge Theory

We investigate the singlet, triplet and colour average heavy quark free energies in SU(2) pure gauge theory at various temperatures T. We focus on the long distance behaviour of the free energies, studying in particular the temperature dependence of the string tension and the screening masses. The results are qualitatively similar to the SU(3) scenario, except near the critical temperature Tc of the deconfining transition. Finally we test a recently proposed method to renormalize the Polyakov loop.Comment: 5 pages, 4 figures, contribution to the Proceedings of SEWM 2002 (Heidelberg

Information-anchored sensitivity analysis: theory and application

Analysis of longitudinal randomised controlled trials is frequently complicated because patients deviate from the protocol. Where such deviations are relevant for the estimand, we are typically required to make an untestable assumption about post-deviation behaviour in order to perform our primary analysis and estimate the treatment effect. In such settings, it is now widely recognised that we should follow this with sensitivity analyses to explore the robustness of our inferences to alternative assumptions about post-deviation behaviour. Although there has been a lot of work on how to conduct such sensitivity analyses, little attention has been given to the appropriate loss of information due to missing data within sensitivity analysis. We argue more attention needs to be given to this issue, showing it is quite possible for sensitivity analysis to decrease and increase the information about the treatment effect. To address this critical issue, we introduce the concept of information-anchored sensitivity analysis. By this we mean sensitivity analysis in which the proportion of information about the treatment estimate lost due to missing data is the same as the proportion of information about the treatment estimate lost due to missing data in the primary analysis. We argue this forms a transparent, practical starting point for interpretation of sensitivity analysis. We then derive results showing that, for longitudinal continuous data, a broad class of controlled and reference-based sensitivity analyses performed by multiple imputation are information-anchored. We illustrate the theory with simulations and an analysis of a peer review trial, then discuss our work in the context of other recent work in this area. Our results give a theoretical basis for the use of controlled multiple imputation procedures for sensitivity analysis