Constraining the low-energy pion electromagnetic form factor with space-like and?phase of?time-like data

摘要

The Taylor coefficients c and d of the EM form factor of the pion are constrained using analyticity, knowledge of the phase of the form factor in the time-like region, 4mπ2≤t≤tin and its value at one space-like point, using as input the (g?2) of the muon. This is achieved using the technique of Lagrange multipliers, which gives a transparent expression for the corresponding bounds. We present a detailed study of the sensitivity of the bounds to the choice of time-like phase and errors present in the space-like data, taken from recent experiments. We find that our results constrain c stringently. We compare our results with those in the literature and find agreement with the chiral perturbation-theory results for?c. We obtain ({dsimmathcal{O}(10)~mbox{GeV}^{-6}}) when c is set to the chiral perturbation-theory values.