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Register a new userHigher-loop gluon and ghost propagators in Landau gauge from numerical stochastic perturbation theory
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We present higher loop results for the gluon and ghost propagator in Landau gauge on the lattice calculated in numerical stochastic perturbation theory. We make predictions for the perturbative content of those propagators as function of the lattice momenta for finite lattices. To find out their nonperturbative contributions, the logarithmic definition of the gauge fields and the corresponding Faddeev-Popov operator have to be implemented in the Monte Carlo simulations.
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We study the ultraviolet behaviour of the ghost and gluon propagators in quenched QCD using lattice simulations. Extrapolation of the lattice data towards the continuum allows to use perturbation theory to extract $Lambda_{text{QCD}}$ - the fundamental parameter of the pure gauge theory. The values obtained from the ghost and gluon propagators are coherent. The result for pure gauge SU(3) at three loops is $Lambda_{ms}approx 320text{MeV}$. However this value does depend strongly upon the order of perturbation theory and upon the renormalisation description of the continuum propagators. Moreover, this value has been obtained without taking into account possible power corrections to the short-distance behaviour of correlation functions.
We present one- and two-loop results for the ghost propagator in Landau gauge calculated in Numerical Stochastic Perturbation Theory (NSPT). The one-loop results are compared with available standard Lattice Perturbation Theory in the infinite-volume limit. We discuss in detail how to perform the different necessary limits in the NSPT approach and discuss a recipe to treat logarithmic terms by introducing ``finite-lattice logs. We find agreement with the one-loop result from standard Lattice Perturbation Theory and estimate, from the non-logarithmic part of the ghost propagator in two-loop order, the unknown constant contribution to the ghost self-energy in the RI-MOM scheme in Landau gauge. That constant vanishes within our numerical accuracy.
We complete our high-accuracy studies of the lattice ghost propagator in Landau gauge in Numerical Stochastic Perturbation Theory up to three loops. We present a systematic strategy which allows to extract with sufficient precision the non-logarithmic parts of logarithmically divergent quantities as a function of the propagator momentum squared in the infinite-volume and $ato 0$ limits. We find accurate coincidence with the one-loop result for the ghost self-energy known from standard Lattice Perturbation Theory and improve our previous estimate for the two-loop constant contribution to the ghost self-energy in Landau gauge. Our results for the perturbative ghost propagator are compared with Monte Carlo measurements of the ghost propagator performed by the Berlin Humboldt university group which has used the exponential relation between potentials and gauge links.
In this contribution we extend our unquenched computation of the Landau gauge gluon and ghost propagators in lattice QCD at non-zero temperature. The study was aimed at providing input for investigations employing continuum functional methods. We show data which correspond to pion mass values between 300 and 500 MeV and are obtained for a lattice size 32**3 x 12. The longitudinal and transversal components of the gluon propagator turn out to change smoothly through the crossover region, while the ghost propagator exhibits only a very weak temperature dependence. For a pion mass of around 400 MeV and the intermediate temperature value of approx. 240 MeV we compare our results with additional data obtained on a lattice with smaller Euclidean time extent N_t = 8, 10 and find a reasonable scaling behavior.
Starting from the lattice Landau gauge gluon and ghost propagator data we use a sequence of Pade approximants, identify the poles and zeros for each approximant and map them into the analytic structure of the propagators. For the Landau gauge gluon propagator the Pade analysis identifies a pair of complex conjugate poles and a branch cut along the negative real axis of the Euclidean $p^2$ momenta. For the Landau gauge ghost propagator the Pade analysis shows a single pole at $p^2 = 0$ and a branch cut also along the negative real axis of the Euclidean $p^2$ momenta. The method gives precise estimates for the gluon complex poles, that agree well with other estimates found in the literature. For the branch cut the Pade analysis gives, at least, a rough estimate of the corresponding branch point.
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