A strategy to study the role of the charm quark in explaining the Delta{I}=1/2 rule

Giusti, Leonardo; Hernández, P.; Laine, M.; Weisz, Peter; Wittig, Hartmut

doi:10.1088/1126-6708/2004/11/016

Cited by 41 publications

(138 citation statements)

References 90 publications

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“…It turns out [20], however, that in the normalised observable [C 27 ] ab norm (x 0 , y 0 ) that we have considered here, the contributions from the Goldstone zeromodes cancel out at this order. Therefore the result can in fact formally be expanded as a Taylor-series in (M L) 2 , with the zeroth order term agreeing with the result of the ǫ-regime (see below).…”

Section: P-regimementioning

confidence: 83%

“…Considering, in particular, the operators 20) which appear in the computations of Fig. 2, and choosing the indices that appear in the physical operators O 27 and O 8 , we obtain …”

Section: Appendix a Irreducible Representations Of The Valence Groupmentioning

confidence: 99%

“…N v = N f = 4 [20]. We discuss here how our predictions can be converted to apply to that situation.…”

Section: Appendix D Correlation Functions For N V =mentioning

confidence: 99%

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Probing the chiral weak Hamiltonian at finite volumes

Hernández¹,

Laine²

2006

J. High Energy Phys.

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Non-leptonic kaon decays are often described through an effective chiral weak Hamiltonian, whose couplings ("low-energy constants") encode all non-perturbative QCD physics. It has recently been suggested that these low-energy constants could be determined at finite volumes by matching the non-perturbatively measured three-point correlation functions between the weak Hamiltonian and two left-handed flavour currents, to analytic predictions following from chiral perturbation theory. Here we complete the analytic side in two respects: by inspecting how small ("ǫ-regime") and intermediate or large ("p-regime") quark masses connect to each other, and by including in the discussion the two leading ∆I = 1/2 operators. We show that the ǫ-regime offers a straightforward strategy for disentangling the coefficients of the ∆I = 1/2 operators, and that in the p-regime finite-volume effects are significant in these observables once the pseudoscalar mass M and the box length L are in the regime M L < ∼ 5.0. July 20061 pilar.hernandez@ific.uv.es 2

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Section: P-regimementioning

confidence: 83%

“…Considering, in particular, the operators 20) which appear in the computations of Fig. 2, and choosing the indices that appear in the physical operators O 27 and O 8 , we obtain …”

Section: Appendix a Irreducible Representations Of The Valence Groupmentioning

confidence: 99%

See 1 more Smart Citation

Probing the chiral weak Hamiltonian at finite volumes

Hernández¹,

Laine²

2006

J. High Energy Phys.

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“…In this section the propagator techniques are applied to an ongoing project to study the role of the charm quark in the explanation of the ∆I = 1/2 rule [18,19,20]. Our physics results are presented in a companion paper [21]; preliminary results from this study have also been reported in Ref.…”

Section: Eye Diagrams For K → πmentioning

confidence: 99%

Variance reduction with practical all-to-all lattice propagators

Endress¹,

Peña²,

Sivalingam³

2015

Computer Physics Communications

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Abstract:We discuss all-to-all quark propagator techniques in two (related) contexts within Lattice QCD: the computation of closed quark propagators, and applications to the so-called "eye diagrams" appearing in the computation of non-leptonic kaon decay amplitudes. Combinations of low-mode averaging and diluted stochastic volume sources that yield optimal signal-to-noise ratios for the latter problem are developed. We also apply a recently proposed probing algorithm to compute directly the diagonal of the inverse Dirac operator, and compare its performance with that of stochastic methods. At fixed computational cost the two procedures yield comparable signal-to-noise ratios, but probing has practical advantages which make it a promising tool for a wide range of applications in Lattice

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“…This procedure complements for the case of the chiral condensate the low-mode averaging (LMA) technique proposed in ref. [49]. The latter has been successfully applied already to meson two-point functions [49 -51], baryon two-point functions [52] and more recently to three-point functions for the extraction of low-energy constants of the ∆S = 1 chiral effective Hamiltonian [53].…”

Section: Numerical Estimatormentioning

confidence: 99%

Spontaneous chiral symmetry breaking in QCD: a finite-size scaling study on the lattice

Giusti¹,

Necco²

2007

J. High Energy Phys.

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Spontaneous chiral symmetry breaking in QCD with massless quarks at infinite volume can be seen in a finite box by studying, for instance, the dependence of the chiral condensate from the volume and the quark mass. We perform a feasibility study of this program by computing the quark condensate on the lattice in the quenched approximation of QCD at small quark masses. We carry out simulations in various topological sectors of the theory at several volumes, quark masses and lattice spacings by employing fermions with an exact chiral symmetry, and we focus on observables which are infrared stable and free from mass-dependent ultraviolet divergences. The numerical calculation is carried out with an exact variance-reduction technique, which is designed to be particularly efficient when spontaneous symmetry breaking is at work in generating a few very small low-lying eigenvalues of the Dirac operator. The finite-size scaling behaviour of the condensate in the topological sectors considered agrees, within our statistical accuracy, with the expectations of the chiral effective theory. Close to the chiral limit we observe a detailed agreement with the first Leutwyler-Smilga sum rule. By comparing the mass, the volume and the topology dependence of our results with the predictions of the chiral effective theory, we extract the corresponding low-energy constant.

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A strategy to study the role of the charm quark in explaining the Delta{I}=1/2 rule

Cited by 41 publications

References 90 publications

Probing the chiral weak Hamiltonian at finite volumes

Probing the chiral weak Hamiltonian at finite volumes

Variance reduction with practical all-to-all lattice propagators

Spontaneous chiral symmetry breaking in QCD: a finite-size scaling study on the lattice

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