On the determination of lowenergy constants for $\Delta S=1$ transitions
Abstract
We present our preliminary results for threepoint correlation functions involving the operators entering the $\Delta{S}=1$ effective Hamiltonian with an active charm quark, obtained using overlap fermions in the quenched approximation. This is the first computation carried out for valence quark masses small enough so as to permit a matching to Quenched Chiral Perturbation Theory in the $\epsilon$regime. The commonly observed large statistical fluctuations are tamed by means of lowmode averaging techniques, combined with restrictions to individual topological sectors. We also discuss the matching of the resulting hadronic matrix elements to the effective lowenergy constants for $\Delta{S}=1$ transitions. This involves (a) finitevolume corrections which can be evaluated at NLO in Quenched Chiral Perturbation Theory, and (b) the shortdistance renormalization of the relevant fourquark operators in discretizations based on the overlap operator. We discuss perturbative estimates for the renormalization factors and possible strategies for their nonperturbative evaluation. Our results can be used to isolate the longdistance contributions to the $\Delta I=1/2$ rule, coming from physics effects around the intrinsic QCD scale.
 Publication:

arXiv eprints
 Pub Date:
 October 2005
 arXiv:
 arXiv:heplat/0510033
 Bibcode:
 2005hep.lat..10033G
 Keywords:

 High Energy Physics  Lattice
 EPrint:
 11 pages, 2 figures, talks presented at Lattice 2005 (Weak matrix elements)