Unquenched Numerical Stochastic Perturbation Theory

The inclusion of fermionic loops contribution in Numerical Stochastic Perturbation Theory (NSPT) has a nice feature: it does not cost so much (provided only that an FFT can be implemented in a fairly efficient way). Focusing on Lattice SU(3), we report on the performance of the current implementation of the algorithm and the status of first computations undertaken.Comment: 3 pages, 3 figures, Lattice2002(algor

Two and three loops computations of renormalization constants for lattice QCD

Renormalization constants can be computed by means of Numerical Stochastic Perturbation Theory to two/three loops in lattice perturbation theory, both in the quenched approximation and in the full (unquenched) theory. As a case of study we report on the computation of renormalization constants of the propagator for Wilson fermions. We present our unquenched (N_f=2) computations and compare the results with non perturbative determinations.Comment: Lattice2004(improv), 3 pages, 4 figure

3-d lattice SU(3) free energy to four loops

We report on the perturbative computation of the 3d lattice Yang-Mills free energy to four loops by means of Numerical Stochastic Perturbation Theory. The known first and second orders have been correctly reproduced; the third and fourth order coefficients are new results and the known logarithmic IR divergence in the fourth order has been correctly identified. Progress is being made in switching to the gluon mass IR regularization and the related inclusion of the Faddeev-Popov determinant.Comment: Lattice2004(non-zero), 3 pages, 2 figure

The leading non-perturbative coefficient in the weak-coupling expansion of hot QCD pressure

Using Numerical Stochastic Perturbation Theory within three-dimensional pure SU(3) gauge theory, we estimate the last unknown renormalization constant that is needed for converting the vacuum energy density of this model from lattice regularization to the MSbar scheme. Making use of a previous non-perturbative lattice measurement of the plaquette expectation value in three dimensions, this allows us to approximate the first non-perturbative coefficient that appears in the weak-coupling expansion of hot QCD pressure.Comment: 16 pages. v2: published versio

Four loop stochastic perturbation theory in 3d SU(3)

Dimensional reduction is a key issue in finite temperature field theory. For example, when following the QCD Free Energy from low to high scales across the critical temperature, ultrasoft degrees of freedom can be captured by a 3d SU(3) pure gauge theory. For such a theory a complete perturbative matching requires four loop computations, which we undertook by means of Numerical Stochastic Perturbation Theory. We report on the computation of the pure gauge plaquette in 3d, and in particular on the extraction of the logarithmic divergence at order g^8, which had already been computed in the continuum.Comment: 3 pages, 2 figure, Lattice2003(nonzero

3-d Lattice QCD Free Energy to Four Loops

We compute the expansion of the 3-d Lattice QCD free energy to four loop order by means of Numerical Stochastic Perturbation Theory. The first and second order are already known and are correctly reproduced. The third and fourth order coefficients are new results. The known logarithmic divergence in the fourth order is correctly identified. We comment on the relevance of our computation in the context of dimensionally reduced finite temperature QCD.Comment: 8 pages, 3 figures, latex typeset with JHEP3.cl

B Physics on the Lattice: Λ‾\overline{\Lambda}, λ1\lambda_{1}, m‾b(m‾b)\overline{m}_{b}(\overline{m}_{b}), λ2\lambda_2, B0−Bˉ0B^{0}-\bar{B}^{0} mixing, \fb and all that

We present a short review of our most recent high statistics lattice determinations in the HQET of the following important parameters in B physics: the B--meson binding energy, $\overline{\Lambda}$ and the kinetic energy of the b quark in the B meson, $\lambda_1$, which due to the presence of power divergences require a non--perturbative renormalization to be defined; the $\overline{MS}$ running mass of the b quark, $\overline{m}_{b}(\overline{m}_{b})$; the $B^{*}$--$B$ mass splitting, whose value in the HQET is determined by the matrix element of the chromo--magnetic operator between B meson states, $\lambda_2$; the B parameter of the $B^{0}$--$\bar{B}^{0}$ mixing, $B_{B}$, and the decay constant of the B meson, $f_{B}$. All these quantities have been computed using a sample of $600$ gauge field configurations on a $24^{3}\times 40$ lattice at $\beta=6.0$. For $\overline{\Lambda}$ and $\overline{m}_{b}(\overline{m}_{b})$, we obtain our estimates by combining results from three independent lattice simulations at $\beta=6.0$, $6.2$ and $6.4$ on the same volume.Comment: 3 latex pages, uses espcrc2.sty (included). Talk presented at LATTICE96(heavy quarks

Renormalization of infrared contributions to the QCD pressure

Thanks to dimensional reduction, the infrared contributions to the QCD pressure can be obtained from two different three-dimensional effective field theories, called the Electrostatic QCD (Yang-Mills plus adjoint Higgs) and the Magnetostatic QCD (pure Yang-Mills theory). Lattice measurements have been carried out within these theories, but a proper interpretation of the results requires renormalization, and in some cases also improvement, i.e. the removal of terms of O(a) or O(a^2). We discuss how these computations can be implemented and carried out up to 4-loop level with the help of Numerical Stochastic Perturbation Theory.Comment: 7 pages, 4 figures, talk presented at Lattice 2006 (High temperature and density

A High Statistics Lattice Calculation of The B-meson Binding Energy

We present a high statistics lattice calculation of the B--meson binding energy $\overline{\Lambda}$ of the heavy--quark inside the pseudoscalar B--meson. Our numerical results have been obtained from several independent numerical simulations at $\beta=6.0$, $6.2$ and $6.4$, and using, for the meson correlators, the results obtained by the APE group at the same values of $\beta$. Our best estimate, obtained by combining results at different values of $\beta$, is $\overline{\Lambda}=180^{+30}_{-20}$ MeV. For the $\overline{MS}$ running mass, we obtain $\overline{m}_{b}(\overline{m}_{b})=4.15 \pm 0.05 \pm 0.20$ GeV, in reasonable agreement with previous determinations. The systematic error is the truncation of the perturbative series in the matching condition of the relevant operator of the Heavy Quark Effective Theory.Comment: Latex, 13 pages, 1 figure appended in uuencoded gzip.tar.fil

High density QCD on a Lefschetz thimble?

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.Comment: Misleading footnote 1 corrected: locality deserves better investigations. Formula (31) corrected (we thank Giovanni Eruzzi for this observation). Note different title in journal versio