  A sum rule due to Das et al. is reanalyzed using a euclidian space approach
and a Pad\'e resummation procedure. It is shown that the result is essentially
determined by the matrix elements of dimension six and dimension eight
operators which have recently been measured by the ALEPH collaboration. The
result is further improved by using the vector spectral function which must be
extrapolated to the chiral limit. This extrapolation is shown to be reliably
performed under the constraint of a set of sum rules. The sum rule is employed
not as an approximation to $M_{\pi^+}-M_{\pi^0}$ but as an exact result for a
chiral low-energy parameter. A sufficiently precise evaluation provides also an
estimate for a combination of subleading electromagnetic low-energy parameters.
