NUCLEAR Nuclear Physics B 373 (1992) 781—794 P H VS I CS B North-Holland _________________ Four-fermion operators with improved nearest-neighbour action R. Frezzotti a E. Gabrielli h C. Pittori b and G.C. Rossi a a Dipartimento di Fisica, II Unit’ersità di Roma “Tor Vergata ‘~ 1-00185 Rome, Italy and INFN Sezione di Roma II, Italy h Dipartimento di Fisica, Unir’ersitâ di Roma, “La Sapienza‘~ 1-00185 Rome, Italy and JNFN Sezione di Roma, Italy Received 17 July 1991 Accepted for publication 28 October 1991 We discuss the improvement of local four-fermion operators and we present the one-loop perturbative calculation of their renormalization constants and mixing coefficients in the theory defined by a nearest-neighbour improved lattice action. This calculation is a necessary ingredient for improved Monte Carlo computations of hadronic matrix elements relevant for weak interac- tions. 1. Introduction In this paper we extend the improvement program presented in refs. [1,21to the local four-fermion operators which are relevant for the construction of the effec- tive weak hamiltonian [31. We consider here only the mixing with operators having the same dimension as the bare ones. The base of scalar operators of dimension six which are eigenvectors of the anomalous dimension matrix is given by o~= ~[(~IY 2)(~’ 3Y~4) ± (2 *-* ~)I~ (1) 01 (N 2_ 1 )(~ 1~ 2)(~3~~P4) + (~iTay2)(~3T0y~4), (2) 02= ~(~lY 2)(~3Y~4) + (~iTay~2)(~3Tay~4). (3) In eqs. (1)—(3) we have generically denoted by ~Ji. the quark field of flavour i; we have also defined 1 + Ys YRLY( -). (4) 0550-3213/92/$05.OO © 1992 — Elsevier Science Publishers B.V. All rights reserved