QCD resummation on single hadron transverse momentum distribution with the thrust axis
We derive the transverse momentum dependent (TMD) factorization and resummation formula of the unpolarized transverse momentum distribution ($j_T$) for the single hadron production with the thrust axis in electron-positron collision. Two different kinematic regions are considered, including small transverse momentum limit $j_T \ll Q$, and joint transverse momentum and threshold limit $j_T \ll Q(1-z_h) \ll Q$, where $Q$ and $z_h$ are the hard scattering energy and the observed hadron momentum fraction. Using effective theory methods, we resum logarithms $\ln(Q/j_T)$ and $\ln(1-z_h)$ to all orders. In the end we present the differential cross sections and Gaussian widths calculated for the inclusive charged pion production and find that our results are consistent with the measurements reported by the Belle collaboration.