Eur. Phys. J. A (2019) 55: 16
https://doi.org/10.1140/epja/i2019-12680-y

Regular Article - Theoretical Physics

Spectral functions of nucleon form factors: Three-pion continua at low energies

¹ Physik-Department T39, Technische Universität München, D-85747, Garching, Germany
² Department of Physics, Indiana University, 47405, Bloomington, IN, USA
³ Center for Exploration of Energy and Matter, Indiana University, 47408, Bloomington, IN, USA
⁴ Theory Center, Thomas Jefferson National Accelerator Facility, 23606, Newport News, VA, USA

^* e-mail: nkaiser@ph.tum.de

Received: 30 October 2018
Accepted: 21 December 2018
Published online: 14 February 2019

Abstract

We study the imaginary parts of the isoscalar electromagnetic and isovector axial form factors of the nucleon close to the -threshold in covariant baryon chiral perturbation theory. At the two-loop level, the contributions arising from leading and next-to-leading order chiral -vertices, as well as pion-induced excitations of virtual -isobars, are calculated. It is found that the heavy baryon treatment overestimates substantially these -continua. From a phenomenological analysis, that includes the narrow -resonance or the broad -resonance, one can recognize small windows near threshold, where chiral -dynamics prevails. However, in the case of the isoscalar electromagnetic form factors , the radiative correction provided by the -intermediate state turns out to be of similar size.