Bochum 1998 – scientific programme
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HK: Hadronen und Kerne
HK 36: Electromagnetic Probes V, CERN, HERA Results
HK 36.1: Group Report
Tuesday, March 17, 1998, 17:00–17:30, B
Spectral functions of Nucleon Form Factors near Threshold — •Norbert Kaiser2, Véronique Bernard1, and Ulf-G. Meißner3 — 1Univ. Louis Pasteur, Strasbourg, France — 2Technische Universität München, Physik Department T39 — 3FZ Jülich, IKP (Th)
We investigate the spectral functions of the electromagnetic and axial nucleon form factors near threshold in chiral perturbation theory. From dispersion theory it is known that the spectral functions of the isovector electromagnetic form factors are strongly enhanced near threshold t=4mπ2. This effect originates from a logarithmic singularity at the anomalous threshold tc=4mπ2−mπ4/M2=3.98 mπ2 on the second Riemann sheet. We are able to reproduce in one-loop approximation the near threshold part of the isovector electromagnetic spectral functions (after subtracting the ρ(770)-contribution). Then we clarify the up to now open question whether a similar strong enhancement occurs in the isoscalar electromagnetic form factors near t=9mπ2. We calculate the imaginary parts of the corresponding two loop diagrams and find no visible enhancement. The three-body phase space masks the singularity at a nearby anomalous threshold at t=8.9 mπ2. Similarly small is the contribution of the three-pion continuum to the isovector axial form factor.
[1] V. Bernard, N. Kaiser and Ulf-G. Meißner, Nucl. Phys. A611 (1996) 429.