dorsal/arxiv
View SchemaSpectral functions of isoscalar scalar and isovector electromagnetic form factors of the nucleon at two-loop order
| Authors | N. Kaiser |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/0302072 |
| URL | https://arxiv.org/abs/nucl-th/0302072 |
| DOI | 10.1103/PhysRevC.68.025202 |
| Journal | Phys.Rev. C68 (2003) 025202 |
Abstract
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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"abstract": "We calculate the imaginary parts of the isoscalar scalar and isovector\nelectromagnetic form factors of the nucleon up to two-loop order in chiral\nperturbation theory. Particular attention is paid on the correct behavior of Im\n$\\sigma_N(t)$ and Im $G_{E,M}^V(t)$ at the two-pion threshold $t_0=4 m_\\pi^2$\nin connection with the non-relativistic 1/M-expansion. We recover the\nwell-known strong enhancement near threshold originating from the nearby\nanomalous singularity at $t_c = 4m_\\pi^2-m_\\pi^4/M^2 = 3.98 m_\\pi^2$. In the\ncase of the scalar spectral function Im $\\sigma_N(t)$ one finds a significant\nimprovement in comparison to the lowest order one-loop result. Higher order\n$\\pi\\pi$-rescattering effects are however still necessary to close a remaining\n20%-gap to the empirical scalar spectral function. The isovector electric and\nmagnetic spectral functions Im $G_{E,M}^V(t)$ get additionally enhanced near\nthreshold by the two-pion-loop contributions. After supplementing their\ntwo-loop results by a phenomenological $\\rho$-meson exchange term one can\nreproduce the empirical isovector electric and magnetic spectral functions\nfairly well.",
"arxiv_id": "nucl-th/0302072",
"authors": [
"N. Kaiser"
],
"categories": [
"nucl-th"
],
"doi": "10.1103/PhysRevC.68.025202",
"journal_ref": "Phys.Rev. C68 (2003) 025202",
"title": "Spectral functions of isoscalar scalar and isovector electromagnetic form factors of the nucleon at two-loop order",
"url": "https://arxiv.org/abs/nucl-th/0302072"
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