ar X iv : h ep - l at / 9 90 90 92 v 2 2 3 Se p 19 99 Non - perturbative improvement of bilinears in unquenched QCD ∗

We describe how the improvement of quark bilinears generalizes from quenched to unquenched QCD, and discuss which of the additional improvement constants can be determined using Ward Identities. A major motivation for undertaking the improvement program is to facilitate unquenched calculations by allowing simulations at larger lattice spacings. Thus it is important to study the application of the improvement program to un-quenched theories. This has been done for the action itself, and for certain operators in the chi-ral limit [1,2]. Here we take a further step by considering the theory of on-shell improvement of quark bilinears in unquenched QCD with non-zero quark masses. We enumerate the additional improvement coefficients that are required, and discuss which of them can be determined non-perturbatively using Ward Identities (WI). The analysis depends on the number of dynam-ical flavors, and we consider here the physically relevant theories with N f ≥ 3 non-degenerate flavors. The two flavor theory is more complicated and will be discussed elsewhere [3]. We use an abbreviated notation for flavor traces A µ = Tr(A µ) = j=1,N f A (jj) µ , λA µ = Tr(λA µ), with λ an SU (N f) generator. Note that we consider both flavor singlets and non-singlets, with the latter being both off-diagonal and diagonal. All three are needed for phenomenology. For example , the flavor off-diagonal operator A (23) µ = ¯ dγ µ γ 5 s is needed to determine f K , and the nu-cleon matrix elements of the flavor diagonal operators A jj µ and T jj µν (which, with j an unsummed flavor index, are linear combinations of flavor singlet and non-singlet) give information on the structure functions. We begin by reviewing previous work on non-perturbative O(a) improvement of unquenched QCD. The ALPHA collaboration [1] has shown how on-shell improvement of the action can be accomplished by adding the Sheikholeslami-Wohlert or " clover " term, with appropriately chosen coefficient c SW. On-shell matrix elements of flavor non-singlet axial, vector and tensor bilin-ears are then improved, in the chiral limit, by adding dimension four operators: λA µ