Quenched Static force from generalized Wilson loops with gradient flow

Abstract

We compute the static force on the lattice in the quenched case directly through generalized Wilson loops. We modify the Wilson loop by inserting an $E$-field component on one of the temporal Wilson lines. However, chromo-field components prevent us from performing the continuum limit properly, hence, we use gradient flow to renormalize the field insertion. As a result, we obtain continuum results and compare them to perturbative expression to extract $\Lambda_0$, and we predict the value $\sqrt{8t_0} \Lambda_{\overline{\textrm{MS}}}^{n_f=0} =0.629^{+22}_{-26}$. This work serves as preparation for similar operators with field insertions required in nonrelativistic effective field theories.