Confining potential under the gauge field condensation in the SU(2) Yang–Mills theory

Abstract

$Q\bar{Q}$ potential is studied in the SU(2) gauge theory. Based on the nonlinear gauge of the Curci–Ferrari type, the possibility of a gluon condensation $\langle A_{\mu}^+A_{\mu}^-\rangle$ in a low-energy region has been considered at the one-loop level. Instead of the magnetic monopole condensation, this condensation makes classical gluons massive, and can yield a linear potential. We show that this potential consists of the Coulomb plus linear part and an additional part. Comparing with the Cornell potential, we study this confining potential in detail, and find that the potential has two implicit scales: $r_c$ and $\tilde{R}_0$. The meanings of these scales are clarified. We also show that the Cornell potential that fits well to this confining potential is obtained by taking these scales into account.