Unstable States for Closed String with Massive Point

TL;DR

This paper analyzes the stability of closed relativistic strings with a point mass, revealing that most hypocycloidal rotational states are unstable due to small disturbances, impacting hadron spectroscopy models.

Contribution

It provides the first analytical and numerical demonstration of the instability of hypocycloidal rotational states in closed strings with a point mass.

Findings

Most hypocycloidal states are unstable due to positive imaginary roots in the spectrum.

Linear rotational states are confirmed to be stable.

Small disturbances can reveal instabilities not seen in previous experiments.

Abstract

The stability problem for the hypocycloidal rotational states of the closed relativistic string with a point-like mass is solved with the help of analysis of small disturbances of these states. Both analytical and numerical investigations showed an unexpected result: the mentioned states turned out to be unstable. This conclusion is based upon the presence of roots with positive imaginary parts (increments) in the spectrum of frequencies of small disturbances. But these increments were small enough, so this instability had not been detected in previous numerical experiments. For the linear rotational states (the particular case of hypocycloidal states) the stability was confirmed. These results are important for applications of this model in hadron spectroscopy.