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Register a new userTowards 4-loop NSPT result for a 3-dimensional condensate-contribution to hot QCD pressure
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Thanks to dimensional reduction, the contributions to the hot QCD pressure coming from so-called soft modes can be studied via an effective three-dimensional theory named Electrostatic QCD (spatial Yang-Mills fields plus an adjoint Higgs scalar). The poor convergence of the perturbative series within EQCD suggests to perform lattice measurements of some of the associated gluon condensates. These turn out, however, to be plagued by large discretization artifacts. We discuss how Numerical Stochastic Perturbation Theory can be exploited to determine the full lattice spacing dependence of one of these condensates up to 4-loop order, and sharpen our tools on a concrete 2-loop example.
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We update Monte Carlo simulations of the three-dimensional SU(3) + adjoint Higgs theory, by extrapolating carefully to the infinite volume and continuum limits, in order to estimate the contribution of the infrared modes to the pressure of hot QCD. The sum of infrared contributions beyond the known 4-loop order turns out to be a smooth function, of a reasonable magnitude and specific sign. Unfortunately, adding this function to the known 4-loop terms does not improve the match to four-dimensional lattice data, in spite of the fact that other quantities, such as correlation lengths, spatial string tension, or quark number susceptibilities, work well within the same setup. We outline possible ways to reduce the mismatch.
In SU(2) gluodynamics, the Debye gluon contribution W_D(A_0) to the effective action of the temporal gauge field component, A_0 = const, at high temperature is calculated in the background R^{xi} gauge. It is shown that at nonzero A_0 the standard definition k_0 = 0, |k| -> 0 corresponds to long distance correlations for the longitudinal in internal space gluons. The transversal gluons become screened by the A_0 background field. Therefore they give zero contributions and have to be excluded from the correlation corrections. The total effective action accounting for the one-loop, two-loop and correct W_D(A_0) satisfies Nielsens identity that proves gauge invariance of the A_0 condensation phenomenon.
We study the electroweak phase transition by lattice simulations of an effective 3-dimensional theory, for a Higgs mass of about $70$ GeV. Exploiting a variant of the equal weight criterion of phase equilibrium, we obtain transition temperature, latent heat and surface tension and compare with $M_H approx 35$ GeV. For the symmetric phase, bound state masses and the static force are determined and compared with results for pure $SU(2)$ theory.
By means of Numerical Stochastic Perturbation Theory (NSPT), we calculate the lattice gluon propagator up to three loops of perturbation theory in the limits of infinite volume and vanishing lattice spacing. Based on known anomalous dimensions and a parametrization of both the hypercubic symmetry group H(4) and finite-size effects, we calculate the non-leading-log and non-logarithmic contributions iteratively, starting with the first-loop expression.
We conclude our investigations on the QCD cross-over transition temperatures with 2+1 staggered flavours and one-link stout improvement. We extend our previous two studies [Phys. Lett. B643 (2006) 46, JHEP 0906:088 (2009)] by choosing even finer lattices (N_t=16) and we work again with physical quark masses. These new results [for details see JHEP 1009:073,2010] support our earlier findings. We compare them with the published results of the hotQCD collaboration. All these results are confronted with the predictions of the Hadron Resonance Gas model and Chiral Perturbation Theory for temperatures below the transition region. Our results can be reproduced by using the physical spectrum. The findings of the hotQCD collaboration can be recovered only by using a distorted spectrum. This analysis provides a simple explanation for the observed discrepancy in the transition T between our and the hotQCD collaborations.
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