Approximating chiral $${SU}(3)$$ S U ( 3 ) amplitudes

Abstract

We construct large-N c motivated approximate chiral SU (3) amplitudes of next-to-next-to-leading order. The amplitudes are independent of the renormalisation scale. Fitting lattice data with those amplitudes allows for the extraction of chiral coupling constants with the correct scale dependence. The differences between approximate and full amplitudes are required to be at most of the order of N 3 LO contributions numerically. Applying the approximate expressions to recent lattice data for meson decay constants, we determine several chiral couplings with good precision. In particular, we obtain a value for F 0 , the meson decay constant in the chiral SU (3) limit, that is more precise than all presently available determinations.

Resonance effects in pion and kaon decay constants

“…In this work we discuss the SU (3) chiral dynamics and the effect of vector loops, in addition to the scalar ones. The outcomes in the present article are not expected to provide an improved version of the already very precise χPT computations present in the market, which are known now up to next-to-next-to-leading order (NNLO) in the chiral expansion [21,22] and incorporate specific lattice simulation subtleties (twisted boundary conditions [23], finite volume effects [24], etc.). The central aim of this article is to show how it is possible to study the dynamics of the lightest resonances through the analysis of these observables in the lattice.…”

“…for µ = 770 MeV [22,61]). This effect cannot be attributed to an inappropriate description of the kaon and pion masses in Eqs.…”

Constraints on low energy QCD parameters from $$\eta \rightarrow 3\pi $$ η → 3 π and $$\pi \pi $$ π π scattering

“…This is consistent with the large N c picture assumed in this paper, but quite far away from other determinations and in tension with our limit (10.2). In fact, a large part of the region covered by the fit [13] is excluded by our prior for Z , namely by the constraint stemming from the paramagnetic inequality Z < Z (2) (7.5).…”

“…Reference [13], which is based on a large N c motivated approximation of the standard O p 6 χ PT calculations, used on lattice data, reports a very large value of the chiral decay constant and a very low value of L 4 . This is consistent with the large N c picture assumed in this paper, but quite far away from other determinations and in tension with our limit (10.2).…”

$\eta$-$\eta\prime$ mixing in Large-Nc ChPT: discussion, phenomenology, and prospects

“…Refs. [27,28]) and also within the NNLO, namely, the different contributions show a hierarchy loop > C i ∼ L i L j . A similar pattern is also observed within SU(3) ChPT [23],…”