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Register a new userStochastic Perturbation Theory and the Gluon Condensate
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Authors
P. E. L. Rakow
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On the lattice searching for the gluon condensate is difficult because a large perturbative contribution to the expectation value of the action has to be subtracted before looking for a small contribution from a possible gluon condensate. The perturbative calculation therefore has to be very precise. We use a modified version of stochastic perturbation theory to calculate a perturbative series in a boosted coupling, which converges more rapidly than the series with the usual lattice coupling, reducing the uncertainties in our results. We do not see any condensate of dimension two, as suggested by some earlier lattice studies, but we do find a contribution from a dimension four condensate. The value of this condensate is approximately 0.04(1) GeV^4, but with large uncertainties.
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We calculate loop contributions up to four loops to the Landau gauge gluon propagator in numerical stochastic perturbation theory. For different lattice volumes we carefully extrapolate the Euler time step to zero for the Langevin dynamics derived from the Wilson action. The one-loop result for the gluon propagator is compared to the infinite volume limit of standard lattice perturbation theory.
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.
In this contribution we present an exploratory study of several novel methods for numerical stochastic perturbation theory. For the investigation we consider observables defined through the gradient flow in the simple {phi}^4 theory.
We present the results of our perturbative calculations of the static quark potential, small Wilson loops, the static quark self energy, and the mean link in Landau gauge. These calculations are done for the one loop Symanzik improved gluon action, and the improved staggered quark action.
This is the second of two papers devoted to the perturbative computation of the ghost and gluon propagators in SU(3) Lattice Gauge Theory. Such a computation should enable a comparison with results from lattice simulations in order to reveal the genuinely non-perturbative content of the latter. The gluon propagator is computed by means of Numerical Stochastic Perturbation Theory: results range from two up to four loops, depending on the different lattice sizes. The non-logarithmic constants for one, two and three loops are extrapolated to the lattice spacing $a to 0$ continuum and infinite volume $V to infty$ limits.
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