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O(a^2) corrections to the one-loop propagator and bilinears of clover fermions with Symanzik improved gluons

Wed, 31 Dec 2008 23:00:00 GMT

O(a^2) corrections to the one-loop propagator and bilinears of clover fermions with Symanzik improved gluons Constantinou, Martha; Lubicz, Vittorio; Panagopoulos, Haralambos; Stylianou, Fotos 2009 Journal of High Energy Physics 10 1-28 We calculate corrections to the fermion propagator and to the Green's functions of all fermion bilinear operators of the form PsibarGammaPsi, to one-loop in perturbation theory. We employ the Wilson/clover action for fermions and the Symanzik improved action for gluons. The novel aspect of our calculations is that they are carried out to second order in the lattice spacing, O(a^2). Consequently, they have addressed a number of new issues, most notably the appearance of loop integrands with strong IR divergences (convergent only beyond 6 dimensions). Such integrands are not present in O(a^1) improvement calculations; there, IR divergent terms are seen to have the same structure as in the O(a^0) case, by virtue of parity under integration, and they can thus be handled by well-known techniques. We explain how to correctly extract the full O(a^2) dependence; in fact, our method is generalizable to any order in a. The O(a^2) corrections to the quark propagator and Green's functions computed in this paper are useful to improve the nonperturbative RI-MOM determination of renormalization constants for quark bilinear operators. Our results depend on a large number of parameters: coupling constant, number of colors, lattice spacing, external momentum, clover parameter, Symanzik coefficients, gauge parameter. To make these results most easily accessible to the reader, we have included them in the distribution package of this paper, as an ASCII file named: Oa2results.m; the file is best perused as Mathematica input.

O (a(2)) corrections to the one-loop propagator and bilinears of cloverfermions with Symanzik improved gluons

Wed, 30 Sep 2009 22:00:00 GMT

O (a(2)) corrections to the one-loop propagator and bilinears of cloverfermions with Symanzik improved gluons Constantinou, Martha; Lubicz, Vittorio; Panagopoulos, H.; Stylianou, F. 2009-10 Journal of high energy physics 12 001-067 We calculate corrections to the fermion propagator and to the Green'sfunctions of all fermion bilinear operators of the form (Psi) over barGamma Psi, to one-loop in perturbation theory.We employ the Wilson/clover action for fermions and the Symanzikimproved action for gluons.The novel aspect of our calculations is that they are carried out tosecond order in the lattice spacing, O (a(2)). Consequently, they haveaddressed a number of new issues, most notably the appearance of loopintegrands with strong IR divergences (convergent only beyond 6dimensions). Such integrands are not present in O (a(1)) improvementcalculations; there, IR divergent terms are seen to have the samestructure as in the O (a(0)) case, by virtue of parity underintegration, and they can thus be handled by well-known techniques. Weexplain how to correctly extract the full O (a(2)) dependence; in fact,our method is generalizable to any order in a.The O (a(2)) corrections to the quark propagator and Green's functionscomputed in this paper are useful to improve the nonperturbative RI-MOMdetermination of renormalization constants for quark bilinear operators.Our results depend on a large number of parameters: coupling constant,number of colors, lattice spacing, external momentum, clover parameter,Symanzik coefficients, gauge parameter. To make these results mosteasily accessible to the reader, we have included them in thedistribution package of this paper, as an ASCII file named: Oa2results.m; the file is best perused as Mathematica input.

O(a^2) corrections to 1-loop matrix elements of 4-fermion operators with improved fermion/gluon actions

Wed, 31 Dec 2008 23:00:00 GMT

O(a^2) corrections to 1-loop matrix elements of 4-fermion operators with improved fermion/gluon actions Constantinou, Martha; Lubicz, Vittorio; Panagopoulos, Haralambos; Skouroupathis, Apostolos; Stylianou, Fotos 2009 260 We calculate the corrections to the amputated Green's functions of 4-fermion operators, in 1-loop Lattice Perturbation theory. The novel aspect of our calculations is that they are carried out to second order in the lattice spacing, O(a^2). We employ the Wilson/clover action for massless fermions (also applicable for the twisted mass action in the chiral limit) and the Symanzik improved action for gluons. Our calculations have been carried out in a general covariant gauge. Results have been obtained for several popular choices of values for the Symanzik coefficients (Plaquette, Tree-level Symanzik, Iwasaki, TILW and DBW2 action). We pay particular attention to Delta F=2 operators, both Parity Conserving and Parity Violating (F stands for flavour: S, C, B). We study the mixing pattern of these operators, to O(a^2), using the appropriate projectors. Our results for the corresponding renormalization matrices are given as a function of a large number of parameters: coupling constant, clover parameter, number of colors, lattice spacing, external momentum and gauge parameter. The O(a^2) correction terms (along with our previous O(a^2) calculation of Z_Psi) are essential ingredients for minimizing the lattice artifacts which are present in non-perturbative evaluations of renormalization constants with the RI'-MOM method. A longer write-up of this work, including non-perturbative results, is in preparation together with members of the ETM Collaboration.