Decay of Pseudoscalars into Lepton Pairs and Large-NcQCD

Abstract

The counterterm combination that describes the decay of pseudoscalar mesons into charged lepton pairs at lowest order in chiral perturbation theory is considered within the framework of QCD in the limit of a large number of colors N c . When further restricted to the lowest meson dominance approximation to large-N c QCD, our results agree well with the available experimental data.

Zweig rule violation in the scalar sector and values of low-energy constants

“…But we consider T -matrix models fitting experimental data, with up and down quarks with their physical masses. The limit m → 0 sets the ππ-threshold to zero 5 , changes ππ phase shifts near the threshold and shifts 5 For m → 0, the cut along the real axis starts at s = 0. However, the integral …”

Matrix elements of light quarks

“…In this paper, a value of Q 8 much lower than in refs. [60,61] was found, although still about a factor of two larger than lattice determinations. The very low value of Q 7 found from the lattice K → ππ calculation originates from large cancellations occuring in the renormalization of the relevant operator and requires further investigation.…”

BK in the chiral limit within the 1/Nc expansion

“…We have no proof that these infinite sums have to behave as if they were finite but we know that, if this is so, a successful framework such as Vector Meson Dominance then becomes the leading term in the approximation to large N c that we propose, instead of a phenomenological ansatz [9]. Besides, our approximation works well in those cases where we can compare with the experiment [10,11].…”

“…For the L i couplings we use lowest meson dominance, as explained in ref. [10,9]. This also works phenomenologically.…”