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• W4233058327 abstract "The dependence of the electromagnetic $Nensuremath{rightarrow}ensuremath{Delta}(1232)$ transition form factor ${G}_{M}^{*}({q}^{2})$ on ${q}^{2}$, the four-momentum transfer squared, has been calculated with the use of relativistic dispersion relations supplemented with some dynamical assumptions. In the first place, they regard the phase of the magnetic dipole amplitude of electroproduction of pions on nucleons in the ${p}_{33}$ final state beyond the region of elastic unitarity. Namely, over the range from the lowest inelastic threshold up to 1780 MeV pion-nucleon c.m. energy, the phase in question has been identified with the real part of the respective phase shift of pion-nucleon scattering. Secondly, contributions to the dispersion integral from the higher energy region have been neglected. Finally, the polynomial ambiguity which appears in the problem has been fixed by requiring that the foregoing amplitude of electroproduction vanishes, independently of ${q}^{2}$, at the upper end of the integration interval as defined above. These assumptions which preserve unitarity were shown previously to lead to very good results when applied to the calculation of the multipole amplitudes ${M}_{1+}^{(frac{3}{2})}$ and ${E}_{1+}^{(frac{3}{2})}$ of photopion production on nucleons in the $ensuremath{Delta}(1232)$ region. Now it is also shown that ${G}_{M}^{*}({q}^{2})$ calculated in that fashion follows remarkably well the data over the whole range $0ensuremath{le}{q}^{2}ensuremath{le}2.5$ ${(mathrm{G}mathrm{e}mathrm{V}/mathit{c})}^{2}$ currently covered by quantitative experimental studies. Some speculation concerning a possible dynamical rooting of the foregoing assumptions is presented." @default.
• W4233058327 created "2022-05-12" @default.
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• W4233058327 date "1980-02-01" @default.
• W4233058327 modified "2023-10-08" @default.
• W4233058327 title "<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>N</mml:mi><mml:mo>→</mml:mo><mml:mi>Δ</mml:mi><mml:mn /><mml:mo>(</mml:mo><mml:mn>1232</mml:mn><mml:mo>)</mml:mo><mml:mn /></mml:math>electromagnetic transition form factor and pion-nucleon dynamics at moderate energies" @default.
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• W4233058327 doi "https://doi.org/10.1103/physrevd.21.695" @default.
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