QCD evolution of naive-time-reversal-odd fragmentation functions

We study QCD evolution equations of the first transverse-momentum moment of the naive-time-reversal-odd fragmentation functions--the Collins function and the polarizing fragmentation function. We find for the Collins function case that the evolution kernel has a diagonal piece the same as that for the transversity fragmentation function, while for the polarizing fragmentation function case this piece is the same as that for the unpolarized fragmentation function. Our results might have important implications in the current global analysis of spin asymmetries.