학술논문
Spectral functions of nucleon form factors: Three-pion continua at low energies
Document Type
Working Paper
Author
Source
Subject
Language
Abstract
We study the imaginary parts of the isoscalar electromagnetic and isovector axial form factors of the nucleon close to the $3\pi$-threshold in covariant baryon chiral perturbation theory. At the two-loop level, the contributions arising from leading and next-to-leading order chiral $\pi N$-vertices, as well as pion-induced excitations of virtual $\Delta(1232)$-isobars, are calculated. It is found that the heavy baryon treatment overestimates substantially these $3\pi$-continua. From a phenomenological analysis, that includes the narrow $\omega(783)$-resonance or the broad $a_1$-resonance, one can recognize small windows near threshold, where chiral $3\pi$-dynamics prevails. However, in the case of the isoscalar electromagnetic form factors $G_{E,M}^s(t)$, the radiative correction provided by the $\pi^0\gamma$-intermediate state turns out to be of similar size.
Comment: 12 pages, 9 figures, accepted for publication in Eur. Phys. J. A
Comment: 12 pages, 9 figures, accepted for publication in Eur. Phys. J. A