Abstract
We concentrate on the mathematical aspects connected with the derivation of the model independent information one can get on the pion electromagnetic form factorF(t) inside the analyticity region (the cutt-plane) from the knowledge of upper and lower bounds of its modulus on the cutt≧4m 2 using analyticity, reality, and the normalizationF(0)=1. It turns out that (in a certain sense) this information depends only on the upper bound, whereas the lower one is irrelevant.
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References
Raszillier, I.: Lettere al Nuovo Cimento2, 349 (1971).
— Maximal information on the pion electromagnetic form factor att <4m 2 and its derivative att=0 frome + e −→π+π− data. Institute of Physics Bucharest Preprint, September 1971.
Privalov, I. I.: Boundary properties of analytic functions (in Russian), Second Edition, p. 107. Moscow-Leningrad: GITTL 1950.
Carathéodory, C.: Funktionentheorie, Vol. 2, p. 14. Basel: Birkhäuser 1950.
—— Funktionentheorie, Vol. 2, p. 21. Basel: Birkhäuser 1950.
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Work performed under contract with the Romanian Nuclear Energy Committee.
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Raszillier, I. The information on the pion electromagnetic form factor inside its analyticity region provided by bounds on its modulus on the cut (t≧4m 2). Commun.Math. Phys. 26, 121–129 (1972). https://doi.org/10.1007/BF01645699
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DOI: https://doi.org/10.1007/BF01645699