WHY PADE APPROXIMANTS REDUCE THE RENORMALIZATION-SCALE DEPENDENCE IN QFT

We prove that in the limit where the beta function is dominated by the one-loop contribution (''large beta(0) limit'') diagonal Pade approxi mants (PA's) of perturbative series become exactly renormalization-sca le (RS) independent. This symmetry suggests that diagonal PA's are cor rectly resumming contributions from higher-order diagrams that an resp onsible for the renormalization of the coupling constant. Nondiagonal PX's are not exactly invariant, but generally reduce the RS dependence as compared to partial sums. In physical eases, higher-order correcti ons in the beta function break the symmetry softly, introducing a smal l scale and scheme dependence. We also compare the Pade resummation wi th the Brodsky-Lepage-Mackenzie (BLM) method, We find that in the larg e-N-f limit using the BLM scale is identical to resumming the series b y an x[0/n] nondiagonal PA.