The $K^{-}p\to {\mathrm{\Sigma }}^0{\pi }^0$ reaction at low energies in a chiral quark model

A chiral quark-model approach is extended to the study of the $\bar{K}N$ scattering at low energies. The process of $K^{-}p\to {\mathrm{\Sigma }}^0{\pi }^0$ at $P_K\lesssim 800$ MeV/c (i.e. the center mass energy $W\lesssim 1.7$ GeV) is investigated. This approach is successful in describing the differential cross sections and total cross section with the roles of the low-lying $\mathrm{\Lambda }$ resonances in $n=1$ shells clarified. The $\mathrm{\Lambda }(1405)S_{01}$ dominates the reactions over the energy region considered here. Around $P_K\simeq 400$ MeV/c, the $\mathrm{\Lambda }(1520)D_{03}$ is responsible for a strong resonant peak in the cross section. The $\mathrm{\Lambda }(1670)S_{01}$ has obvious contributions around $P_K=750$ MeV/c, while the contribution of $\mathrm{\Lambda }(1690)D_{03}$ is less important in this energy region. The non-resonant background contributions, i.e. $u$-channel and $t$-channel, also play important roles in the explanation of the angular distributions due to amplitude interferences.