Spectral functions of isoscalar scalar and isovector electromagnetic form factors of the nucleon at two-loop order

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 $t_0=4m_{\pi }^2$ 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 $t_c=4m_{\pi }^2-m_{\pi }^4/M^2=3.98m_{\pi }^2$. 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.

10 pages, 6 figures, submitted to Physical Review C

References in corpus (16)

• ππscattering
• The ratio of proton's electric to magnetic form factors measured by polarization transfer
• Measurement of GEp/GMp in ep -> ep to Q2 = 5.6 GeV2
• Low energy analysis of the nucleon electromagnetic form factors
• Precise Neutron Magnetic Form Factors
• The Charge Form Factor of the Neutron from the Reaction \pol{2H}(\pol{e},e'n)p
• A Measurement of the Electric Form Factor of the Neutron through $\vec{d}(\vec{e},e^{\prime }n)p$ at $Q^2=0.5$ (GeV/c)${}^2$
• Pion-nucleon scattering inside the Mandelstam triangle
• The Transverse Asymmetry ${\mathbf{A}}_{{\mathbf{T}}^{\prime }}$ from Quasi-elastic ${}^3\overrightarrow{\mathrm{He}}(\vec{e},e^{\prime })$ Process and the Neutron Magnetic Form Factor
• Pion and Kaon Electromagnetic Form Factors
• Pion-nucleon scattering in chiral perturbation theory II: Fourth order calculation
• Low energy analysis of pi N --> pi N
• Extraction of electromagnetic neutron form factors through inclusive and exclusive polarized electron scattering on polarized 3He target
• Polarization transfer in the ${}^4$He$(\vec{e},e^{\prime }{\vec{p}}^3$H reaction
• New empirical fits to the proton electromagnetic form factors
• Determination of the Pion-Nucleon Coupling Constant in the VPI/GW Pion-Nucleon Elastic Scattering Partial Wave and Dispersion Relation Analyis

Cited by in corpus (33)

• Chiral Perturbation Theory and Baryon Properties
• Dispersion analysis of the nucleon form factors including meson continua
• A pure S-wave covariant model for the nucleon
• Electromagnetic form factors of the nucleon in chiral perturbation theory including vector mesons
• Electromagnetic form factors of the nucleon in relativistic baryon chiral perturbation theory
• Isospin violation in the vector form factors of the nucleon
• Chiral extrapolation of nucleon magnetic form factors
• The nucleon and Delta(1232) form factors at low momentum-transfer and small pion masses
• Pion momentum distributions in the nucleon in chiral effective theory
• Octet baryon electromagnetic form factors in a relativistic quark model
• Hadron structure at low Q^2
• On the pion cloud of the nucleon
• Nucleon and gamma N -> Delta lattice form factors in a constituent quark model
• Novel evaluation of the two-pion contribution to the nucleon isovector form factors
• Chiral dynamics and peripheral transverse densities
• Valence quark and meson cloud contributions to the ${\gamma }^{\ast }N\to N^{\ast }(1520)$ form factors
• Quantifying the nucleon's pion cloud with transverse charge densities
• Nucleon form factors in dispersively improved Chiral Effective Field Theory I: Scalar form factor
• Nucleon form factors in dispersively improved Chiral Effective Field Theory II: Electromagnetic form factors
• Peripheral transverse densities of the baryon octet from chiral effective field theory and dispersion analysis
• Realizing vector meson dominance with transverse charge densities
• Systematic study of octet-baryon electromagnetic form factors in covariant chiral perturbation theory
• Light-front representation of chiral dynamics with Delta isobar and large-N_c relations
• Light-front representation of chiral dynamics in peripheral transverse densities
• Spectral functions of nucleon form factors: Three-pion continua at low energies
• Nucleon Form Factors in Dispersion Theory
• Transverse charge and current densities in the nucleon from dispersively improved chiral effective field theory
• Quantum-mechanical picture of peripheral chiral dynamics
• Combined parametrization of the neutron electric form factor and the ${\gamma }^{\ast }N\to \Delta (1232)$ quadrupole form factors
• Nucleons and nuclei in the context of low-energy QCD
• Transverse densities of octet baryons from chiral effective field theory
• Transverse charge and magnetization densities in the nucleon's chiral periphery
• A note on scalar meson dominance