Deeply virtual pion production through two-loop order

Deeply virtual meson production (DVMP) is among the most prominent channels to extract the nucleon's generalized parton distributions (GPDs) at $ep$ scattering facilities such as {\tt JLab} and the upcoming {\tt EIC/EicC} experiments, which plays a vital role in unravelling the three-dimensional internal structure of nucleon. In this work we calculate for the first time the next-to-next-to-leading order (NNLO) QCD radiative corrections to the DV$\pi$P processes $\gamma_L^* p\to \pi^+ n$ and $\gamma_L^* p\to \pi^0 p$ in the generalized Bjorken limit $Q^2\gg \vert t\vert, \Lambda_{\text{QCD}}^2$, accurate at the leading twist within collinear factorization framework. The impact of the two-loop QCD corrections appears to be positive and substantial, including which considerably improves the agreement between the perturbative QCD prediction and the available {\tt JLab} data. In addition to the differential longitudinal DV$\pi$P cross section, we also study the impact of the two-loop QCD corrections on the transverse single-spin asymmetries (TSSA) in some benchmark kinematics at {\tt JLab}, {\tt EIC} and {\tt EicC}.