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

• Published in: Physical review. D, Particles, fields, gravitation, and cosmology Particles, fields, gravitation, and cosmology, 2014-11, Vol.90 (9), Article 094504
• Main Authors: Endress, E., Pena, C.
• Format: Article
• Language: English
• Subjects: Amplitudes; Constants; Decay; Fermions; Low energy; Quarks; Reduction; Subtraction
• ISSN: 1550-7998; 1550-2368
• DOI: 10.1103/PhysRevD.90.094504

We study the dependence on the charm quark mass of the leading-order low-energy constants of the Delta S = 1 effective Hamiltonian, with the aim of elucidating the role of the charm mass scale in the Delta I = 1/2 rule for K arrow right [pi][pi] decay. To that purpose, finite-volume chiral perturbation theory predictions are matched to QCD simulations, performed in the quenched approximation with overlap fermions and mu = md = ms. Light quark masses range between a few MeV up to around one third of the physical strange mass, while charm masses range between mu and a few hundred MeV. Novel variance reduction 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 renormalized amplitudes for mc [not =] mu is discussed in detail. We find evidence that the moderate enhancement of the Delta I = 1/2 amplitude previously found in the GIM limit mc = mu increases only slightly as mc abandons the light quark regime. Hints of a stronger enhancement for even higher values of mc are also found, but their confirmation requires a better understanding of the subtraction terms.