Quark mass correction to the string potential

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 pointlike masses at its ends is calculated. At first the calculation is done in the one-loop approximation. For obtaining a finite result under summation over eigenfrequencies of the Nambu-Goto string with massive ends, an appropriate renormalization procedure is suggested. It is shown that in this case the Lüscher term in the string potential acquires a dependence on the quark mass which results in the reduction of the absolute value of this term. Then the interquark potential in the string model with new boundary conditions is calculated by making use of the variational estimation of the corresponding functional integral. In this case the quark mass correction results in decreasing the critical distance (deconfinement radius) in the string potential. In the framework of the developed approach, the one-loop interquark potential in the model of the relativistic string with rigidity is also calculated.