Constraining the low energy Pion electromagnetic form factor with space-like and phase of time-like data
Abstract
The Taylor coefficients c and d of the Pion EM form factor are constrained using analyticity, knowledge of the phase of the form factor in the time-like region, 4 mpi2 t 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, that 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 literature and find agreement with the chiral perturbation theory results for c. We obtain d O(10)GeV-6 when c is set to the chiral perturbation theory values.