Are three flavors special?

TL;DR

This paper investigates the special role of three flavors in scalar meson mixing within chiral Lagrangian frameworks, revealing that such mixing is only feasible for three flavors before symmetry breaking, impacting models with charm and technicolor theories.

Contribution

It demonstrates that scalar meson mixing via two nonets is only possible for three flavors prior to chiral symmetry breaking, providing a new criterion for flavor structure in meson models.

Findings

Mixing of two nonets is only possible for three flavors before symmetry breaking.

Scalar and pseudoscalar states with charm likely lack four-quark components.

Implications for constructing chiral Lagrangians and technicolor theories.

Abstract

It has become clearer recently that the regular pattern of three flavor nonets describing the low spin meson multiplets seems to require some modification for the case of the spin 0 scalar mesons. One picture which has had some success, treats the scalars in a chiral Lagrangian framework and considers them to populate two nonets. These are, in turn, taken to result from the mixing of two "bare" nonets, one of which is of quark- antiquark type and the other of two quark- two antiquark type. Here we show that such a mixing is, before chiral symmetry breaking terms are included, only possible for three flavors. In other cases, the two types of structure can not have the same chiral symmetry transformation property. Specifically, our criterion would lead one to believe that scalar and pseudoscalar states containing charm would not have "four quark" admixtures. This work is of potential interest for constructing chiral Lagrangians based on exact chiral symmetry which is then broken by well known specific terms. It may also be of interest in studying some kinds of technicolor theories.