A Correction to the Hamiltonian of the QCD String with Quarks due to the Rigidity Term

TL;DR

This paper derives a correction to the Hamiltonian of the quark-antiquark system caused by the rigidity term in the gluodynamics string, affecting orbital momentum and higher derivatives, with applications to large-mass quark systems.

Contribution

It introduces a new correction to the Hamiltonian due to the rigidity term, including additional orbital and higher derivative contributions, and evaluates its effect in the relativistic quark model.

Findings

Derived a correction to the Hamiltonian from the rigidity term.

Identified additional contributions to orbital momentum.

Evaluated the correction for large quark masses.

Abstract

A correction to the Hamiltonian of the quark-antiquark system, arising due to the rigidity term in the gluodynamics string effective action, is obtained. This correction contains additional contributions to the orbital momentum of the system and several higher derivative operators. With the help of the derived Hamiltonian a rigid string-induced term in the Hamiltonian of the relativistic quark model is evaluated for the case of large masses of a quark and antiquark.