Exploring the role of the charm quark in theΔI=1/2rule

Abstract

Abstract:We study the dependence on the charm quark mass of the leading-order lowenergy constants of the ∆S = 1 effective Hamiltonian, with the aim of elucidating the role of the charm mass scale in the ∆I = 1/2 rule for K → ππ decay. To that purpose, finite- techniques are used to obtain a signal for penguin contractions in correlation functions involving four-fermion operators. The important role played by the subtractions required to construct renormalised amplitudes for m c = m u is discussed in detail. We find evidence that the moderate enhancement of the ∆I = 1/2 amplitude previously found in the GIM limit m c = m u increases only slightly as m c abandons the light quark regime. Hints of a stronger enhancement for even higher values of m c are also found, but their confirmation requires a better understanding of the subtraction terms.

Variance reduction with practical all-to-all lattice propagators

“…Our physics results are presented in a companion paper [21]; preliminary results from this study have also been reported in Ref. [22].…”

“…SVS will also be applied to propagators connecting four-fermion operators and interpolating meson operators, which are also connected to large statistical fluctuations. Physics applications are discussed in a companion paper [21]; preliminary results of our study were also presented in Ref. [22].…”

“…Using them is again sufficient for the purpose of our immediate intended applications [21], and avoids the need to set up a mixed-action approach in case an overlap valence sector is used in combination with dynamical configurations obtained e.g. using Wilson sea fermions.…”

“…The latest are however suitable enough for our present physics goals, as discussed in [21], while the smallest lattices will be mostly used for checking technical issues only indirectly related to physics. It has to be stressed that immediate applications of these techniques are intended in an environment where overlap fermions are employed; the numerically expensive character of the latter would make the use of larger lattices rapidly forbidding.…”

“…It is however worth noting that, based on our knowledge of the Dirac spectrum for low values of quark masses, quenched ensembles are expected to be worst-case scenarios for some of the variance issues we are addressing. In particular, the width of the gap in the Dirac spectrum for computations in the -regime (see [21] for details) is expected to be controlled by the parameter N f + |ν|, where N f is the number of light dynamical flavours and ν is the topological charge of the configuration. 3 The case N f = 0 is thus the one where the overlap Dirac operator is expected to be worse-conditioned.…”