Exact solution of a meiman problem with an application to the pionic contribution to the muon magnetic moment

An exact solution is obtained tp the follpwing problem: given a form factor F(t) analytic in the cut t plane, to find a lower bpund to a weighted ontegral over |F(t)|² over the cut in the presence of space-like data and also time-like data on both the modulus and the phase of F(t). The solution is used to obtain a lower bound on the pionic contribution to the muon magnetic moment (a_μ(ππ)). We obtain a_μ(ππ) ≥ 41.8 × 10^?9.