1 research outputs found
Dissecting the rule at large
We study the scaling of kaon decay amplitudes with the number of colours,
, in a theory with four degenerate flavours, . In this scenario,
two current-current operators, , mediate transitions, such
as the two isospin amplitudes of non-leptonic kaon decays for , and . In particular, we concentrate on the
simpler amplitudes, , mediated by these two operators. A
diagrammatic analysis of the large- scaling of these observables is
presented, which demonstrates the anticorrelation of the leading and corrections in both amplitudes. Using
our new and previous quenched data, we confirm this expectation and
show that these corrections are large and may be at the origin of
the rule. The evidence for the latter is indirect, based on the
matching of the amplitudes to their prediction in Chiral Perturbation Theory,
from which the LO low-energy couplings of the chiral weak Hamiltonian, ,
can be determined. A NLO estimate of the isospin
amplitudes can then be derived, which is in good agreement with the
experimental value.Comment: 12 pages, 7 figures. Minor change