O(αs2) contributions to the fragmentation function g1(x, Q2) in polarized e+e− annihilation Original Research Article

We present the calculation of the order αs2 contributions to the coefficient functions (singlet and non-singlet) belonging to the longitudinal spin fragmentation function g1(x, Q2) measured in polarized electron-positron annihilation. From this calculation we also obtain the two-loop contribution to the time-like spin splitting functions PqqS and Pgq. These splitting functions are in agreement with recent results in the literature obtained using a different method. We show that in second order the renormalization constant needed for the HVBM prescription of the γ5-matrix is process dependent.