Evaluation of multipoles for photo- and electroproduction of pions

Abstract

With this paper we start a systematic study of the multipole amplitudes for electroand photoproduction of pions in the low energy region. It is based on the integral equations following from fixed t dispersion relations and the Watson theorem. We start with a discussion of general mathematical problems one encounters when solving the singular integral equations. Especially the non-uniqueness of their solutions poses difficult problems which cannot be solved within the framework of the dispersion theory. As boundary conditions "from outside" we use at threshold the predictions of the static theory. But thereby only the magnetic dipole excitation of the first isobar is determined. For the electric quadrupole amplitude one needs additional conditions.

Electromagnetic excitation of the Δ(1232)-resonance

“…This is the standard method to apply fixed-t dispersion relations to pion photoproduction at threshold and in the (1232) resonance region, which was successfully used by many authors [165][166][167][168]. The reliability of this method at low energies (W < 1400 MeV) is mainly based on the finding that Eq.…”

“…If one further makes an assumption about the high-energy behavior of the multipole phases, we obtain a system of coupled integral equations for ReM α (W ). This is the standard method to apply fixed-t dispersion relations to pion photoproduction at threshold and in the ∆(1232) resonance region, which was successfully used by many authors [165][166][167][168]. The reliability of this method at low energies (W < 1400 MeV) is mainly based on the finding that Eq.…”

“…(i) dispersion theory, first proposed by Chew et al [163] for photoproduction, and by Fubini et al [164] for electroproduction, has been successfully applied in the first multipole analyses [165,166] as well as in the modern ones [167][168][169]. The dispersion approach is based on general principles, such unitarity, analyticity, crossing symmetry, as well as relies on a phenomenological input from the πN scattering.…”

P33(1232)resonance contribution to the amplitudesM1+Aznauryan1, Stepanyan2 1999Phys. Rev. D14090View full textAdd to dashboardCite

“…[26] using the fixed-t dispersion relations within the approach of Refs. [27,28]. This approach is very usefull for the extraction of an information on the γ * N → P 33 (1232) transition, because it in a natural way reproduces the resonance and noresonance contributions into the multipole amplitudes, and the obtained solutions satisfy unitarity condition (1.1).…”

“…Thus, the dispersion relation (1.2) transforms into the singular integral equation which has a solution in the following analytical form (see Ref. [27] and the references therein):…”