O(a^2) corrections to the propagator and bilinears of Wilson / clover fermions
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We present the corrections to the fermion propagator, to second order in the lattice spacing, O(a^2), in 1-loop perturbation theory. The fermions are described by the clover action and for the gluons we use a 3-parameter family of Symanzik improved actions. Our calculation has been carried out in a general covariant gauge. The results are provided as a polynomial of the clover parameter, and are tabulated for 10 popular sets of the Symanzik coefficients (Plaquette, Tree-level Symanzik, Iwasaki, TILW and DBW2 action).
We also study the O(a^2) corrections to matrix elements of fermion bilinear operators that have the form $\barΨΓΨ$, where $Γ$ denotes all possible distinct products of Dirac matrices. These correction terms are essential ingredients for improving, to O(a^2), the matrix elements of the fermion operators.
Our results are applicable also to the case of twisted mass fermions.
A longer write-up of this work, including non-perturbative results, is in preparation together with V. Gimenez, V. Lubicz and D. Palao.
7 pages, 1 figure. Talk presented at the XXVI International Symposium on Lattice Field Theory, July 14-19, 2008, Williamsburg, VA, USA
7 pages, 1 figure. Talk presented at the XXVI International Symposium on Lattice Field Theory, July 14-19, 2008, Williamsburg, VA, USA