The two-pseudoscalar-meson decay of ${\chi }_{cJ}$ with twist-3 corrections

The decays of ${\chi }_{cJ}\to {\pi }^{+}{\pi }^{-},K^{+}{K}^{-}$ $(J=0,2)$ are discussed within the standard and modified hard scattering approach when including the contributions from twist-3 distribution amplitudes and wave functions of the light pseudoscalar meson. A model for twist-2 and twist-3 distribution amplitudes and wave functions of the pion and kaon with BHL prescription are proposed as the solution to the end-point singularities. The results show that the contributions from twist-3 parts are actually not power suppressed comparing with the leading-twist contribution. After including the effects from the transverse momentum of light meson valence-quark state and Sudakov factors, the decay widths of the ${\chi }_{cJ}$ into pions or kaons are comparable with the their experimental data.