On quark mass correction to the string potential

TL;DR

This paper investigates how quark mass corrections influence the string potential in the Nambu-Goto model, providing exact solutions and discussing the universality of the Lüscher term.

Contribution

It offers exact solutions for the interquark potential with massive endpoints in the Nambu-Goto string, extending previous work and analyzing the Lüscher term's universality.

Findings

Exact solutions for gap equations obtained

Interquark potential determined without simplifying assumptions

Lüscher term remains universal

Abstract

Following recent work by Lambiase and Nesterenko we study in detail the interquark potential for a Nambu-Goto string with point masses attached to its ends. We obtain exact solutions to the gap equations for the Lagrange multipliers and metric components and determine the potential without simplifying assumptions. We also discuss L\"{u}scher term and argue that it remains universal.