On correlation between the pion charge radius and the pionic contribution to the muon magnetic moment

The possible values of the pion charge radius rsub(π) are correlated with those of the pionic contribution asub(μ)(π+π-) to the muon magnetic moment in terms of the normalization of the pion form factor, its modulus on part of the unitarity cut, and the quality of the chisup(2)-fit to values measured for it in a number of spacelike points. The correlation is expressed as a 3-dimensional set (D) of values (h'(0),||h||sup(2),chi) allowed for the functions h(z) analytic in the unit disk and belonging to a set Ω in the Hilbert space Hsup(2). The set D, which depends through Ω and chi on the information used, has simple convexity properties. Its computation is reduced to a problem of finite-dimensional convex optimization. (author)