The Electromagnetic Pion Form Factor and Instantons

We calculate the electromagnetic pion form factor at intermediate spacelike momentum transfer from the QCD sum rule for the correlation function of two pseudoscalar interpolating fields and the electromagnetic current. This correlator receives essential contributions from direct (i.e. small-scale) instantons, which we evaluate under the assumption of an instanton size distribution consistent with instanton liquid and lattice simulations. The resulting form factor is in good agreement both with the sum rule based on the axial-current correlator and with experiment. Address after Nov. 1, 1994: European Centre for Theoretical Studies in Nuclear Physics and Related Areas, Villa Tambosi, Strada delle Tabarelle 286, I-38050 Villazzano, Italy Permanent address: Instituto de F́ısica, Universidade de São Paulo, 01498 SPBrazil. 1 A central goal of strong-interaction physics is the understanding of hadrons on the basis of quantum chromodynamics (QCD). It is very unlikely that this goal can be reached without a thorough understanding of the QCD vacuum. At present, however, direct links between observed hadron properties and the vacuum structure are still rare and rely mostly on extensive numerical simulations. The aim of this letter is to study one such link – between direct instantons, i.e. small-scale topological vacuum fields, and electromagnetic pion properties – analytically in the framework of a QCD sum rule [1,2]. Due to the Goldstone nature of the pion, sum rule calculations of pionic properties can be based on two in principle (but not in practice!) equally suitable sets of correlation functions, corresponding to the use of pseudoscalar or axial vector interpolating fields. The pion couples strongly to both of these source currents and thus contributes to the correlators in both channels. The pseudoscalar channel has some principal advantages for sum rule calculations. The accuracy of the standard pole-continuum parametrization for the corresponding spectral functions profits from the almost complete dominance of the pion in the low-mass region [3,4]. Furthermore, correlators involving the pseudoscalar interpolators have a simpler tensor structure. This simplifies in particular the calculation of three-point functions. All existing sum rule applications in the pion channel (with the exception of ref. [5], see below), however, are based on axial vector current correlators [1,2,6,7]. The use of the pseudoscalar interpolating field has been avoided, since it is known to receive essential contributions from direct instantons [3]. Like instanton contributions in general, they could initially not be estimated reliably, due to insufficient knowledge of the instanton size distribution in the vacuum. The attempt of an ab initio description in the dilute gas approximation [8], in particular, failed for all but the smallest instanton sizes due to infrared problems with large instantons. The same problems were encountered in the attempt to supplement the conventional operator product expansion (OPE) in QCD sum rules with direct instanton contributions and led to the preference for the axial vector correlators.