On instability of hadronic string with heavy quarks at its ends

TL;DR

This paper investigates the stability of the hadronic string model with heavy quarks at its ends, revealing potential infrared instability for large quark masses and discussing possible modifications to address this issue.

Contribution

It analyzes the quark mass dependence of the string spectrum and identifies conditions leading to instability, proposing modifications to improve the model.

Findings

First excited state approaches ground state for large quark masses

Infrared instability identified in the string spectrum

Discussion of potential model modifications

Abstract

The quark mass dependence of the energy spectrum in the Nambu--Goto string with point--like masses (quarks) at its ends is analyzed. To this end, linearized equations of motion and boundary conditions in this model are considered. It is shown that for sufficiently large quark masses, the first excited state in string spectrum may be arbitrary close to the ground state. Obviously this points to infrared instability in the system under consideration. Possible modifications of string model which could remove this drawback are discussed.