Reanalysis of the Das et al. sum rule and application to chiral $O(p^4)$ parameters

Abstract

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.