Dispersive Analysis of Low Energy $\gamma N\to \pi N$ Process and Studies on the $N^{\ast }(890)$ Resonance

Abstract

We present a dispersive representation of the $\gamma N\to \pi N$ partial-wave amplitude based on unitarity and analyticity. In this representation, the right-hand-cut contribution responsible for $\pi N$ final-state-interaction effect are taken into account via an Omnés formalism with elastic $\pi N$ phase shifts as inputs, while the left-hand-cut contribution is estimated by invoking chiral perturbation theory. Numerical fits are performed in order to pin down the involved subtraction constants. It is found that good fit quality can be achieved with only one free parameter and the experimental data of the multipole amplitude $E_0^{+}$ in the energy region below the $\Delta (1232)$ are well described. Furthermore, we extend the $\gamma N\to \pi N$ partial-wave amplitude to the second Riemann sheet so as to extract the couplings of the $N^{\ast }(890)$. The modulus of the residue of the multipole amplitude $E_0^{+}$ ($S_{11pE}$) is $2.41\mathrm{mfm}\cdot \mathrm{Ge}{\mathrm{V}}^2$ and the partial width of $N^{\ast }(890)\to \gamma N$ at the pole is about $0.369\mathrm{MeV}$, which is almost the same as the one of $N^{\ast }(1535)$, indicating that $N^{\ast }(890)$ strongly couples to $\pi N$ system.

References in corpus (24)

• Unitary Isobar Model - MAID2007
• Extended Partial-Wave Analysis of piN Scattering Data
• Improved description of the $\pi N$-scattering phenomenology in covariant baryon chiral perturbation theory
• Unified Chew-Mandelstam SAID analysis of pion photoproduction data
• Photon- and pion-nucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian
• Analyses of pion-nucleon elastic scattering amplitudes up to $O(p^4)$ in extended-on-mass-shell subtraction scheme
• The $\kappa$ resonance in s wave $\pi K$ scatterings
• Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances
• The pole structure of the unitary, crossing symmetric low energy $\pi \pi$ scattering amplitudes
• Left Hand Singularities, Hadron Form Factors and the Properties of the Sigma Meson
• An improved study of the kappa resonance and the non-exotic $s$ wave $\pi K$ scatterings up to $\sqrt{s}=2.1$GeV of LASS data
• Aspects of near threshold neutral pion photoproduction off protons
• Pole positions and residues from pion photoproduction using the Laurent+Pietarinen expansion method
• Threshold ${\pi }^0$ photoproduction in relativistic chiral perturbation theory
• A Dispersive Analysis on the $f_0(600)$ and $f_0(980)$ Resonances in $\gamma \gamma \to {\pi }^{+}{\pi }^{-},{\pi }^0{\pi }^0$ Processes
• Baryon photo-decay amplitudes at the pole
• Elastic and inelastic pion-nucleon scattering to fourth order in chiral perturbation theory
• New Insights on Low Energy $\pi N$ Scattering Amplitudes
• Pion photoproduction off nucleons in covariant chiral perturbation theory
• $\Delta (1232)$ resonance in the $\vec{\gamma }p\to p{\pi }^0$ reaction at threshold
• Pion Polarizabilities from $\gamma \gamma \to \pi \pi$ Analysis
• New Insights on Low Energy $\pi N$ Scattering Amplitudes: Comprehensive Analyses at $\mathcal{O}(p^3)$ Level
• How does the $S_{11}$ $N^{\ast }(890)$ state emerge from a naive $K$ matrix fit?
• The properties of the $\sigma$ and $\kappa$ resonances in a new unitarization approach

Cited by in corpus (5)

• Pion Photoproduction off Nucleon with Hamiltonian Effective Field Theory
• Radiative Correction to Lepton Proton Scatterings in Manifestly Lorentz-Invariant Chiral Perturbation Theory
• Dispersive analysis of low energy ${\gamma }^{\ast }N\to \pi N$ process
• On the pole trajectory of the subthreshold negative parity nucleon with varying pion masses
• Review on recent progress in the study of the $N^{\ast }(920)$ subthreshold singularity and the $\sigma /f_0(500)$ meson