Pion Electromagnetic Form Factor with Dipion Unitarity

概要

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We construct the pion electromagnetic form factor which is consistent with the dipion unitarity and the analyticity, and it is compatible with the Veneziano-Lovelace-type pion-pion scattering amplitude. Several assumptions are made which restrict the validity of the result in the low and intermediate energy regions. The form factor thus obtained can be fixed uniquely if we give the ρ-meson trajectory α, the P-wave scattering length a_s and the zero point x_0 of the numerator function of the partial wave amplitude. Assuming α=0.5+t/2m_ρ^^-^2, we can obtain an excellent fit to the Novosibirsk data with m_ρ^^-=730 MeV and x_0=∞ for a_s=17m_π^2, the soft-pion prediction of current algebra, or with m_ρ^^-=720 MeV and x_0=x_<04> for the hard-pion value a_s=14.5m_π^2, where x_<04> is the 4-th zero of the Veneziano-Lovelace-type scattering amplitude. The P-wave scattering phase shift is calculated also. In the spacelike region the form factor decreases slower than that of the ρ-dominance prediction with increasing the absolute value of four-momentum transfer squared.
理論物理学刊行会の論文
1970-08-25