Quark mass correction to the string potential

TL;DR

This paper develops a method to calculate the interquark potential for a relativistic string with massive ends, revealing how quark mass influences the deconfinement distance and providing a renormalization procedure for the model.

Contribution

It introduces a consistent calculation approach for the interquark potential in the Nambu-Goto string model with massive ends, including a unique mode-by-mode subtraction for renormalization.

Findings

Quark mass decreases the critical deconfinement distance.

A mode-by-mode subtraction method ensures finite eigenfrequency sums.

The approach extends to the relativistic string with rigidity.

Abstract

A consistent method for calculating the interquark potential generated by the relativistic string with massive ends is proposed. In this approach the interquark potential in the model of the Nambu--Goto string with point--like masses at its ends is calculated. At first the calculation is done in the one--loop approximation and then the variational estimation is performed. The quark mass correction results in decreasing the critical distance (deconfinement radius). When quark mass decreases the critical distance also decreases. For obtaining a finite result under summation over eigenfrequencies of the Nambu--Goto string with massive ends a suitable mode--by--mode subtraction is proposed. This renormalization procedure proves to be completely unique. In the framework of the developed approach the one--loop interquark potential in the model of the relativistic string with rigidity is also calculated.