Constraining the low-energy pion electromagnetic form factor with spacelike data

Abstract

The pionic contribution to the g−2 of the muon involves a certain integral over the modulus squared of $F_\pi(t)$, the electromagnetic form factor of the pion. We extend techniques that use cut-plane analyticity properties of $F_\pi(t)$ in order to account for present day estimates of the pionic contribution and experimental information at a finite number of points in the spacelike region. Using data from several experiments over a large kinematic range for $|t|$, we find bounds on the expansion coefficients of $F_\pi(t)$, sub-leading to the charge radius. The value of one of these coefficients in chiral perturbation theory respects these bounds. Furthermore, we present a sensitivity analysis to the inputs. A brief comparison with results in the literature that use observables other than the g−2 and timelike data is presented.