Dispersive analysis of low energyγN→πNprocess and studies on theN*(890) resonance

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 is 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 to pin down the involved subtraction constants. Good fit quality can be achieved with only one free parameter, and the experimental data regarding 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 to extract the couplings of the $ N^\ast(890) $ . The modulus of the residue of the multipole amplitude $ E_{0}^+ $ ( 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 approximately $ 0.369\ {\rm MeV} $ , which is almost the same as that of the $ N^*(1535) $ resonance, indicating that $ N^\ast(890) $ strongly couples to the $ \pi N $ system.