String Models, Stability and Regge Trajectories for Hadron States

TL;DR

This paper compares various string models of hadrons, finds classical instabilities in some, and advocates for a stable string with massive ends to accurately describe Regge trajectories across different hadron types.

Contribution

It introduces a stability analysis of rotational states in different string models and supports a specific stable string model for hadron spectroscopy.

Findings

Y string baryon model rotations are classically unstable.

Linear growth of disturbances in Y model contrasts with exponential in linear models.

Stable string with massive ends effectively describes Regge trajectories for various hadrons.

Abstract

Various string models of mesons and baryons include a string carrying 2 or 3 massive points (quarks or antiquarks). Rotational states (planar uniform rotations) of these systems generate quasilinear Regge trajectories and may be used for describing excited hadron states on these trajectories. For different string models of baryon we are to solve the problem of choice between them and the stability problem for their rotational states. An unexpected result is that for the Y string baryon model these rotations are unstable with respect to small disturbances on the classical level. This instability has specific feature, disturbances grow linearly, whereas for the linear string baryon model they grow exponentially and may increase predictions for baryon's width $\Gamma$. The classical instability of rotational states and nonstandard Regge slope are the arguments in favor of the stable simplest model of string with massive ends both for baryons and mesons. Rotational states of this model with two types of spin-orbit correction are used to describe Regge trajectories for light, strange, charmed, bottom mesons and for $N$, $\Delta$, $\Sigma$, $\Lambda$ and $\Lambda_c$ baryons.