Regge-like quark-antiquark excitations in the effective-action formalism

TL;DR

This paper investigates radial excitations of quark-antiquark pairs within an effective-action framework, revealing that constituent quark masses dominate energy contributions over string elongation, with specific scaling behaviors for mass and energy.

Contribution

It introduces a novel analysis of Regge-like excitations in the effective-action formalism, highlighting how these excitations affect constituent quark masses and energy scaling.

Findings

Constituent quark mass increases as the square root of excitation quantum number.

String energy increases as the fourth root of the excitation quantum number.

Energy is primarily saturated by quark masses rather than string elongation.

Abstract

Radial excitations of the quark-antiquark string sweeping the Wilson-loop area are considered in the framework of the effective-action formalism. Identifying these excitations with the daughter Regge trajectories, we find corrections which they produce to the constituent quark mass. The energy of the quark-antiquark pair turns out to be mostly saturated by the constituent quark masses, rather than by the elongation of the quark-antiquark string. Specifically, while the constituent quark mass turns out to increase as the square root of the radial-excitation quantum number, the energy of the string increases only as the fourth root of that number.