2- and 3-Loop Heavy Flavor Corrections to Transversity

We calculate the two- and three-loop massive operator matrix elements (OMEs) contributing to the heavy flavor Wilson coefficients of transversity. We obtain the complete result for the two-loop OMEs and compute the first thirteen Mellin moments at three-loop order. As a by-product of the calculation, the moments N=1 to 13 of the complete two-loop and the $T_F$-part of the three-loop transversity anomalous dimension are obtained.