Perturbative Wilson loops with massive sea quarks on the lattice

Abstract

We present O(g^4) calculations of both planar and non-planar Wilson loops for various actions in the presence of sea quarks. In particular, the plaquette, the static potential and the static self energy are calculated to this order for massive Wilson, Sheikholeslami-Wohlert and Kogut-Susskind fermions, including the mass and n_f dependence. The results can be used to obtain alpha_{MS} and m_b(m_b) from lattice simulations. We compare our perturbative calculations to simulation data of the static potential and report excellent qualitative agreement with boosted perturbation theory predictions for distances r<1/GeV. We are also able to resolve differences in the running of the coupling between n_f=2 and n_f=0 static potentials. We compute perturbative estimates of the ``beta-shifts'' of QCD with sea quarks, relative to the quenched theory, which we find to agree within 10 % with non-perturbative simulations. This is done by matching the respective static potentials at large distances. The prospects of determining the QCD running coupling from low energy hadron phenomenology in the near future are assessed. We obtain the result ${\Lambda }_{\overline{MS}}^{(2)}{r}_0=0.69(15)$ for the two flavour QCD Lambda-parameter from presently available lattice data where $r_0^{-1}\approx 400$ MeV and estimate ${\alpha }_{\overline{MS}}^{(5)}(m_Z)=0.1133(59)$.

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