Low-energy gluon contributions to the vacuum polarization of heavy quarks

Abstract

We calculate a correction to the electromagnetic current induced by a heavy quark loop. The contribution of this correction to the vacuum polarization function appears at the O(alpha_s^3) order of perturbation theory and has a qualitatively new feature -- its absorptive part starts at zero energy in contrast to other contributions where the absorptive parts start at the two-particle threshold. Our result imposes a constraint on the order n of the moments used in the heavy-quark sum rules, n<4.

Comments: 8 pages in LaTeX, 1 PostScript figure included in the text