Measurement of the space-like transition form factor and study of direct production of ${\chi }_{c1}$ at BESIII

The transition form factors (TFF) of mesons are important experimental inputs to the calculation of the hadronic light-by-light (HLbL) contribution of muon anomaly, a${}_{\mu }$. The HLbL contribution is one of the two limitations of the accuracy of the theoretical calculation. The TFFs can be measured in space-like regime through two-photon process at e${}^{+}$e${}^{-}$ collision machine, such as BESIII. The advantage of the measurement at BESIII is that the working center-of-mass (CM) energy allows measurement of the TFF in relative low Q${}^2$ region, which is the relevant kinematic region for the calculation. The measurements of the TFF of ${\pi }^0$ as a function of Q${}^2$ from 0.3 to 3.0 GeV${}^2$ and the amplitude of ${\pi }^{+}{\pi }^{-}$ with Q${}^2$ from 0.1 to 4.0 GeV${}^2$ will be presented. In gamma-gamma interactions, a direct production of non-vector resonances becomes possible at e${}^{+}$e${}^{-}$ accelerators. Currently, only the direct production of vector meson with J${}^{PC}$=1${}^{-}$ has been observed, mesons with other quantum numbers are produced through the decays of the vector mesons. With a dedicated set of four data samples collected at CM energies around the ${\chi }_{c1}$ mass, the direct production of ${\chi }_{c1}$ in e${}^{+}$e${}^{-}$ machine has been studied. The status of the analysis will be presented.