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Perturbative determination of $c_{SW}$ for plaquette and Symanzik gauge action and stout link clover fermions

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 Added by Arwed Schiller
 Publication date 2008
  fields
and research's language is English




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Using plaquette and Symanzik improved gauge action and stout link clover fermions we determine the improvement coefficient $c_{SW}$ in one-loop lattice perturbation theory from the off-shell quark-quark-gluon three-point function. In addition, we compute the coefficients needed for the most general form of quark field improvement and present the one-loop result for the critical hopping parameter $kappa_c$. We discuss mean field improvement for $c_{SW}$ and $kappa_c$ and the choice of the mean field coupling for the actions we have considered.



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We determine the improvement factor $c_{SW}$ in one-loop lattice perturbation theory for the plaquette and Symanzik improved gauge actions. The fermionic action is ${mathcal{O}(a)}$ clover improved with one-time stout smearing. $c_{SW}$ is derived from the one-loop correction to the quark-quark-gluon vertex in the off-shell regime. We give a first numerical value for the one-loop contribution to the non gauge-invariant improvement coefficient $c_{NGI}$ for the quark field using the plaquette action. A discussion of mean field improvement is included.
We discuss a 3-flavour lattice QCD action with clover improvement in which the fermion matrix has single level stout smearing for the hopping terms together with unsmeared links for the clover term. With the (tree-level) Symanzik improved gluon action this constitutes the Stout Link Non-perturbative Clover or SLiNC action. To cancel O(a) terms the clover term coefficient has to be tuned. We present here results of a non-perturbative determination of this coefficient using the Schroedinger functional and as a by-product a determination of the critical hopping parameter. Comparisons of the results are made with lowest order perturbation theory.
For the Stout Link Non-perturbative Clover (SLiNC) action we determine in one-loop lattice perturbation theory the critical hopping parameter $kappa_c$ and the clover parameter $c_{SW}$ which is needed for $mathcal{O}(a)$ improvement. Performing this calculation off-shell we are also able to compute the non gauge invariant quark field improvement coefficient $c_{NGI}$. Additionally, we present first results for the renormalization factors of the scalar, pseudoscalar, vector and axial vector currents. We discuss mean field improvement for the SLiNC action.
We discuss an action in which the fermion matrix has single level stout smearing for the hopping terms together with unsmeared links for the clover term. With the (tree level) Symanzik improved gluon action this constitutes the Stout Link Non-perturbative Clover or SLiNC action. To cancel O(a) terms the clover coefficient, csw, has to be tuned. We present here preliminary results of a non-perturbative determination of csw using the Schrodinger functional and as a by-product also a determination of the critical hopping parameter. A determination of the renormalisation constant for the local vector current is also given. Comparisons of the results are made with lowest order perturbation theory results.
We present a fully non-perturbative determination of the $O(a)$ improvement coefficient $c_{rm SW}$ in three-flavor dynamical QCD for the RG improved as well as the plaquette gauge actions, using the Schrodinger functional scheme. Results are compared with one-loop estimates at weak gauge coupling.
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