Estimates for parameters and characteristics of the confining SU(3)-gluonic field in charged pions and kaons from leptonic decays and chiral symmetry breaking

TL;DR

This paper estimates parameters of the confining SU(3)-gluonic field in charged pions and kaons, computes decay constants, and explores implications for chiral symmetry breaking in QCD, linking theoretical models with experimental decay data.

Contribution

It provides nonperturbative calculations of the weak axial form factor and estimates of gluon field parameters in pions and kaons, offering insights into confinement and chiral symmetry breaking.

Findings

Decay constants computed for pions and kaons match experimental data.

Gluon concentrations and field strengths are quantitatively estimated.

Chiral symmetry breaking is explained without additional mechanisms, solely via the confining SU(3)-gluonic field.

Abstract

The confinement mechanism proposed earlier by the author is employed for to compute the decay constants $f_P$ corresponding to leptonic decays $P\to l^\pm+\nu_l$, $l=\mu, e$, where $P$ stands for any meson from $\pi^\pm$, $K^\pm$. For this aim the weak axial form factor of $P$-meson is nonperturbatively calculated. The study entails estimates for parameters of the confining SU(3)-gluonic field in charged pions and kaons. The corresponding estimates of the gluon concentrations, electric and magnetic colour field strengths are also adduced for the mentioned field at the scales of the mesons under consideration. Further the obtained results are applied to the problem of chiral symmetry breaking in quantum chromodynamics (QCD). It is shown that in chirally symmetric world masses of pions and kaons are fully determined by the confining SU(3)-gluonic field among (massless) $u$, $d$ and $s$ quarks and not equal to zero. Accordingly chiral symmetry is sufficiently rough approximate one holding true only when neglecting the mentioned SU(3)-gluonic field between quarks and no additional mechanism of the spontaneous chiral symmetry breaking connected to the so-called Goldstone bosons is required. Finally, a possible relation of the results obtained with a phenomenological string-like picture of confinement is discussed too.