Universality of the $N_f=2$ Running Coupling in the Schödinger Functional Scheme.

Abstract

We investigate universality of the Nf = 2 running coupling in the Schodinger functional scheme, by calculating the step scaling function in lattice QCD with the renormalization group (RG) improved gauge action at both weak(u = 0.9796) and strong(u = 3.3340) couplings, where u = ¯ g 2 with ¯ gSF being the running coupling in this scheme. In our main calculations, we use the treelevel value for O(a) improvement coefficients of boundary gauge fields. In additi on we employ the 1-loop value for them in order to see how scaling behaviours are affected by them. In the continuum limit, the step scaling function obtained from the RG improved gauge actions agrees with the previous result obtained from the plaquette action within errors at both couplings, though errors of our result are larger. Combined fits using all data w ith the RG improved action as well as the plaquette action reduce errors in the continuum limit by 2% at the weak coupling and 22% at the strong coupling.