https://doi.org/10.1140/epjc/s10052-013-2520-9
Regular Article - Theoretical Physics
Parametrisation-free determination of the shape parameters for the pion electromagnetic form factor
1
Centre for High Energy Physics, Indian Institute of Science, Bangalore, 560 012, India
2
Horia Hulubei National Institute for Physics and Nuclear Engineering, P.O.B. MG-6, 077125, Bucharest-Magurele, Romania
3
Institute of Mathematical Sciences, Taramani, Chennai, 600113, India
4
Theoretische Physik 1, Naturwissenschaftlich-Technische Fakultät, Universität Siegen, 57068, Siegen, Germany
* e-mail: anant@cts.iisc.ernet.in
Received:
26
February
2013
Revised:
7
July
2013
Published online:
9
August
2013
Recent data from high-statistics experiments that have measured the modulus of the pion electromagnetic form factor from threshold to relatively high energies are used as input in a suitable mathematical framework of analytic continuation to find stringent constraints on the shape parameters of the form factor at t=0. The method uses also as input a precise description of the phase of the form factor in the elastic region based on Fermi–Watson theorem and the analysis of the ππ scattering amplitude with dispersive Roy equations, and some information on the spacelike region coming from recent high precision experiments. Our analysis confirms the inconsistencies of several data on the modulus, especially from low energies, with analyticity and the input phase, noted in our earlier work. Using the data on the modulus from energies above 0.65 GeV, we obtain, with no specific parametrisation, the prediction 
for the charge radius. The same formalism leads also to very narrow allowed ranges for the higher-order shape parameters at t=0, with a strong correlation among them.
© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica, 2013
