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.
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Communicated by L. Tolos
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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Most data generated during this study are contained in this published article. Further data, such as computer codes, can be obtained from the authors upon request.]
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Kaiser, N., Passemar, E. Spectral functions of nucleon form factors: Three-pion continua at low energies. Eur. Phys. J. A 55, 16 (2019). https://doi.org/10.1140/epja/i2019-12680-y
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DOI: https://doi.org/10.1140/epja/i2019-12680-y