Physics – Nuclear Physics – Nuclear Theory
Scientific paper
2003-02-24
Phys.Rev. C68 (2003) 025202
Physics
Nuclear Physics
Nuclear Theory
10 pages, 6 figures, submitted to Physical Review C
Scientific paper
10.1103/PhysRevC.68.025202
We calculate the imaginary parts of the isoscalar scalar and isovector electromagnetic form factors of the nucleon up to two-loop order in chiral perturbation theory. Particular attention is paid on the correct behavior of Im $\sigma_N(t)$ and Im $G_{E,M}^V(t)$ at the two-pion threshold $t_0=4 m_\pi^2$ in connection with the non-relativistic 1/M-expansion. We recover the well-known strong enhancement near threshold originating from the nearby anomalous singularity at $t_c = 4m_\pi^2-m_\pi^4/M^2 = 3.98 m_\pi^2$. In the case of the scalar spectral function Im $\sigma_N(t)$ one finds a significant improvement in comparison to the lowest order one-loop result. Higher order $\pi\pi$-rescattering effects are however still necessary to close a remaining 20%-gap to the empirical scalar spectral function. The isovector electric and magnetic spectral functions Im $G_{E,M}^V(t)$ get additionally enhanced near threshold by the two-pion-loop contributions. After supplementing their two-loop results by a phenomenological $\rho$-meson exchange term one can reproduce the empirical isovector electric and magnetic spectral functions fairly well.
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