# Dispersive Analysis of Low Energy γN→πN Process and Studies on the N*(890) Resonance

• We present a dispersive representation of the $\gamma N\rightarrow \pi N$ partial-wave amplitude based on unitarity and analyticity. In this representation, the right-hand-cut contribution responsible for $\pi N$ final-state-interaction effects 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 $\gamma N\rightarrow \pi N$ 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 $E_{0}^+$ (${\rm S_{11}pE}$) is $2.41\rm{mfm\cdot GeV^2}$ and the partial width of $N^*(890)\to\gamma N$ at the pole is about $0.369\ {\rm MeV}$, which is almost the same as the one of the $N^*(1535)$ resonance, indicating that $N^\ast(890)$ strongly couples to $\pi N$ system.
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Yao Ma, Wen-Qi Niu, De-Liang Yao and Han-Qing Zheng. Dispersive Analysis of Low Energy γN→πN Process and Studies on the N*(890) Resonance[J]. Chinese Physics C.
Yao Ma, Wen-Qi Niu, De-Liang Yao and Han-Qing Zheng. Dispersive Analysis of Low Energy γN→πN Process and Studies on the N*(890) Resonance[J]. Chinese Physics C.
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沈阳化工大学材料科学与工程学院 沈阳 110142

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## Dispersive Analysis of Low Energy γN→πN Process and Studies on the N*(890) Resonance

###### Corresponding author: De-Liang Yao, yaodeliang@hnu.edu.cn
• 1. Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, P. R. China
• 2. School of Physics and Electronics, Hunan University, Changsha 410082, P. R. China
• 3. Collaborative Innovation Center of Quantum Matter, Beijing, Peoples Republic of China

Abstract: We present a dispersive representation of the $\gamma N\rightarrow \pi N$ partial-wave amplitude based on unitarity and analyticity. In this representation, the right-hand-cut contribution responsible for $\pi N$ final-state-interaction effects 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 $\gamma N\rightarrow \pi N$ 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 $E_{0}^+$ (${\rm S_{11}pE}$) is $2.41\rm{mfm\cdot GeV^2}$ and the partial width of $N^*(890)\to\gamma N$ at the pole is about $0.369\ {\rm MeV}$, which is almost the same as the one of the $N^*(1535)$ resonance, indicating that $N^\ast(890)$ strongly couples to $\pi N$ system.

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