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 m_pi^2 \le t \le \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, 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 \sim O(10)GeV^{-6} when c is set to the chiral perturbation theory values.

8 pages, latex using EPJ style file, 10 figures; replaced with version accepted by European Physical Journal; expanded version of v1, with improvements in text, corrections of nomenclature, and a substantial computation using Roy equation fits for phase shifts and 3 additional figures and several additional references

References in corpus (13)

• ππscattering
• Roy equation analysis of pi pi scattering
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• Pion and Kaon Electromagnetic Form Factors
• Tau Decays and Chiral Perturbation Theory
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• Electromagnetic form factor of the pion
• pi pi scattering
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• Constraining the low energy pion electromagnetic form factor with space-like data

Cited by in corpus (8)

• Model-independent approach to eta -> pi+ pi- gamma and eta' -> pi+ pi- gamma
• Pion form factors from two-flavor lattice QCD with exact chiral symmetry
• Quark mass dependence of the pion vector form factor
• Implications of the recent high statistics determination of the pion electromagnetic form factor in the timelike region
• Theory of unitarity bounds and low energy form factors
• Implications of unitarity and analyticity for the Dπform factors
• New constraints on the Pion EM form factor using Pi'(-Q^2)
• Constraining Form Factors with the Method of Unitarity Bounds