The static force from generalized Wilson loops on the lattice using gradient flow

The static QCD force from the lattice can be used to extract Λ_MS, which determines the running of the strong coupling. Usually, this is done with a numerical derivative of the static potential. However, this introduces additional systematic uncertainties; thus, we use another observable to measure the static force directly. This observable consists of a Wilson loop with a chromoelectric field insertion. We work in the pure SU(3) gauge theory. We use gradient flow to improve the signal-to-noise ratio and to address the field insertion. We extract Λ_MS^n_f=0 from the data by exploring different methods to perform the zero flow time limit. We obtain the value √(8t_0)Λ_MS^n_f=0 =0.629^+23_-34, where t_0 is a flow time reference scale. We also obtain precise determinations of several scales: r_0/r_1, √(8 t_0)/r_0, √(8 t_0)/r_1 and we compare to the literature. The gradient flow appears to be a promising method for calculations of Wilson loops with chromolectric and chromomagnetic insertions in quenched and unquenched configurations.