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Particles and Fields
Eur. Phys. J. C 10, 121-142
DOI 10.1007/s100529900097

Non-perturbative renormalization of lattice four-fermion operators without power subtractions

A. Donini1 - V. Giménez2 - G. Martinelli1 - M. Talevi3 - A. Vladikas4

1 Dipartimento di Fisica, Università di Roma "La Sapienza'' and INFN, Sezione di Roma, P.le A. Moro 2, I-00185 Roma, Italy
2 Dep. de Fisica Teorica and IFIC, Universitat de Valencia, Dr. Moliner 50, E-46100, Burjassot, Valencia, Spain
3 Department of Physics & Astronomy, University of Edinburgh, The King's Buildings, Edinburgh EH9 3JZ, UK
4 INFN, Sezione di Roma II, and Dip. di Fisica, Università di Roma "Tor Vergata'', Via della Ricerca Scientifica 1,
I-00133 Roma, Italy

Received: 26 February 1999 / Published online: 15 July 1999

A general nonperturbative analysis of the renormalization properties of $\Delta I=3/2$ four-fermion operators in the framework of lattice regularization with Wilson fermions is presented. We discuss the nonperturbative determination of the operator renormalization constants in the lattice regularization independent (RI or MOM) scheme. We also discuss the determination of the finite lattice subtraction coefficients from Ward identities. We prove that, at large external virtualities, the determination of the lattice mixing coefficients, obtained using the RI renormalization scheme, is equivalent to that based on Ward identities, in the continuum and chiral limits. As a feasibility study of our method, we compute the mixing matrix at several renormalization scales, for three values of the lattice coupling $\beta$, using the Wilson and tree-level improved SW-Clover actions.

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