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Register a new userOn-shell and off-shell improvement for Ginsparg-Wilson fermions
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We discuss the improvement of bilinear fermionic operators for Ginsparg-Wilson fermions. We present explicit formulae for improved Greens functions, which apply both on-shell and off-shell.
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The improvement of fermionic operators for Ginsparg-Wilson fermions is investigated. We present explicit formulae for improved Greens functions, which apply both on-shell and off-shell.
We review a relativistic approach to the heavy quark physics in lattice QCD by applying a relativistic $O(a)$ improvement to the massive Wilson quark action on the lattice. After explaining how power corrections of $m_Q a$ can be avoided and remaining uncertainties are reduced to be of order $(aLambda_{rm QCD})^2$, we demonstrate a determination of four improvement coefficients in the action up to one-loop level in a mass dependent way. We also show a perturbative determination of mass dependent renormalization factors and $O(a)$ improvement coefficients for the vector and axial vector currents. Some preliminary results of numerical simulations are also presented.
We discuss the improvement of flavour non-singlet point and one-link lattice quark operators, which describe the quark currents and the first moment of the DIS structure functions respectively. Suitable bases of improved operators are given, and the corresponding renormalisation factors and improvement coefficients are calculated in one-loop lattice perturbation theory, using the Sheikholeslami-Wohlert (clover) action. To this order we achieve off-shell improvement by eliminating the effect of contact terms. We use massive fermions, and our calculations are done keeping all terms up to first order in the lattice spacing, for arbitrary m^2/p^2, in a general covariant gauge. We also compare clover fermions with fermions satisfying the Ginsparg-Wilson relation, and show how to remove O(a) effects off-shell in this case too, and how this is in many aspects simpler than for clover fermions. Finally, tadpole improvement is also considered.
We briefly describe some of our recent results for the mass spectrum and matrix elements using $O(a)$ improved fermions for quenched QCD. Where possible a comparison is made between improved and Wilson fermions.
We show that, under certain general assumptions, any sensible lattice Dirac operator satisfies a generalized form of the Ginsparg-Wilson relation (GWR). Those assumptions, on the other hand, are mostly dictated by large momentum behaviour considerations. We also show that all the desirable properties often deduced from the standard GWR hold true of the general case as well; hence one has, in fact, more freedom to modify the form of the lattice Dirac operator, without spoiling its nice properties. Our construction, a generalized Ginsparg-Wilson relation (GGWR), is satisfied by some known proposals for the lattice Dirac operator. We discuss some of these examples, and also present a derivation of the GGWR in terms of a renormalization group transformation with a blocking which is not diagonal in momentum space, but nevertheless commutes with the Dirac operator.
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