Hadronic contribution to the muon anomalous magnetic moment and pion electromagnetic form factor

Constraints on the pion electromagnetic form factor F pi(Q(2)) and on its contribution to the hadronic part of the muon anomalous magnetic moment, a(mu)(F), have been derived from the analytic properties of the form factor and from its values measured at 45 spacelike points Q(k)(2) (k = 1,..., 45). It has been demonstrated that, if the actual values of the form factor at the paints Q(k)(2) were equal to the central experimental values, a(mu)(F) would exceed the total hadronic contribution to the muon anomalous magnetic moment a(mu)(h) by a factor of 10(100). This contradiction has been shown to originate from dealing with an ill-posed problem. A means for resolving the contradiction has been indicated, and the constraint a(mu)(F) greater than or equal to 1.06 x 10(-8) has been obtained. A method has been developed that makes it possible to improve the accuracy in measuring the form factor and to evaluate it at those points where it has not yet been measured.