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Non-Perturbative Renormalisation of the Lattice $Δs=2$ Four-Fermion Operator

A. Donini·G. Martinelli·C. T. Sachrajda·M. Talevi·A. Vladikas
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Abstract

We compute the renormalised four-fermion operator $O^{ΔS=2}$ using a non-perturbative method recently introduced for determining the renormalisation constants of generic lattice composite operators. Because of the presence of the Wilson term, $O^{ΔS=2}$ mixes with operators of different chiralities. A projection method to determine the mixing coefficients is implemented. The numerical results for the renormalisation constants have been obtained from a simulation performed using the SW-Clover quark action, on a $16^3 \times 32$ lattice, at $β=6.0$. We show that the use of the constants determined non-perturbatively improves the chiral behaviour of the lattice kaon matrix element $\<\bar K^0| O^{ΔS=2} | K^0\>_{\latt}$.

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A. Donini, G. Martinelli, C. T. Sachrajda, M. Talevi, A. Vladikas. 1995-08-22. Non-Perturbative Renormalisation of the Lattice $Δs=2$ Four-Fermion Operator. https://doi.org/10.1016/0370-2693(95)01124-9

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