Curved QCD string dynamics

TL;DR

This paper investigates the dynamics of curved QCD strings in mesons using a flexible flux tube model, revealing that curved strings behave similarly to straight strings with minor differences, especially at high velocities.

Contribution

It introduces a dynamic curved string model for mesons, extending beyond the traditional straight string approximation, and provides numerical solutions without non-relativistic assumptions.

Findings

Curved strings are dynamically similar to straight strings with small radial momentum differences.

Numerical solutions for equal and fixed quark ends demonstrate the model's applicability.

Small deviations from straight string behavior are observed at high velocities.

Abstract

We consider the effects of going beyond the approximation of a straight string in mesons by using a flexible flux tube model wherein a Nambu-Goto string bends in response to quark accelerations. The curved string is dynamically identical to the straight string even for ultra-relativistic mesons except for a small additional radial momentum. We numerically solve the curved string model in the case where both ends have equal mass quarks and also the case where one end is fixed. No approximation of non-relativistic motion is made. We note some small but interesting difference from the straight string.