Contribution to Hadrons' Width from Classical Instability of Y Configuration and Other String Hadron Models

TL;DR

This paper investigates the classical rotational stability of various string-based hadron models, revealing instabilities that contribute to the width of excited hadron states, especially in linear and closed string models.

Contribution

It demonstrates that all examined string hadron models exhibit classical rotational instability, with different mechanisms, impacting the understanding of hadron widths.

Findings

All models show instability under small disturbances.

Y configuration's instability arises from real frequency spectrum.

Linear and closed string models have complex frequencies leading to exponential growth.

Abstract

We consider various hadron models with a string carrying $n=3$ massive points (quarks): Y configuration, linear baryon model $q$-$q$-$q$ and the closed string. For these models classical rotational states (planar uniform rotations) are tested for stability with respect to small disturbances. It is shown that rotations of all mentioned models are unstable, but nature of this instability is different. For the model Y the instability results from existence of multiple real frequencies in the spectrum of small disturbances, but for the linear model and the closed string the similar spectra contain complex frequencies, corresponding to exponentially growing modes of disturbances. This classical rotational instability is important for describing excited hadrons, in particular, for the linear model and the closed string it results in additional contribution in width of hadron states.