ON THE CASIMIR ENERGY OF A SKYRMION

We evaluate the leading correction to the classical skyrmion mass, that is, the Casimir energy. We use a method which is well defined in the chiral limit. The main ultraviolet divergence is cancelled by the counterterms of Gasser and Leutwyler. We show that the result is controlled by the low energy behavior of the phase-shifts which are large and positive due to the presence of two normalizable zero-modes. As a consequence, the sign and order of magnitude do not depend on the truncation of the chiral lagrangian. The correction is found to be negative and rather large, of the order of 1 GeV.