Two-pion decays of mesons and confinement singularities

TL;DR

This paper analyzes the two-pion decay of the rho meson to understand confinement interactions, highlighting the roles of bremsstrahlung and direct transitions, and emphasizing the need for more experimental data.

Contribution

It demonstrates how quark confinement influences decay amplitudes and estimates the contributions of different transition processes in rho meson decay.

Findings

Direct transition processes are essential but not fully determined by current data.

Quark singularities must vanish in decay amplitudes, revealing confinement effects.

More comprehensive decay data are needed for precise understanding.

Abstract

We consider the two-pion decay of the $\rho$-meson, the $^3S_1q\bar q$-state of the constituent quarks -- the decay being determined by the transition $q\bar q\to \pi\pi$ contains information about confinement interactions. One can specify in this decay two types of transitions: ({\bf i}) the bremsstrahlung radiation of a pion $q\to q+\pi$ (or $\bar q\to\bar q+\pi$) with the subsequent fusion $q\bar q\to \pi$, and ({\bf ii}) the direct transition $q\bar q\to \pi\pi$. We demonstrate how in the amplitudes of the corresponding transitions the quark singularities have to disappear, {\it i.e.} what is the way the quark confinement at relatively short distances can be realized. We calculate and estimate the contributions of processes with bremsstrahlung radiation of the pion and of the direct transition $q\bar q\to \pi\pi$. The estimates demonstrate that the processes involving the direct transition $q\bar q\to \pi\pi$ are necessary, but they cannot be determined unambiguously by the decay $\rho(775)\to \pi\pi$. We conclude that for the determination of the $q\bar q\to \pi\pi$ transition more complete data on the resonance decays into the $\pi\pi$ channels are required than those available at the moment.