Timelike single-logarithm-resummed splitting functions

We calculate the single logarithmic contributions to the quark singlet and gluon matrix of timelike splitting functions at all orders in the modified minimal-subtraction (MS¯) scheme. We fix two of the degrees of freedom of this matrix from the analogous results in the massive-gluon regularization scheme by using the relation between that scheme and the MS¯ scheme. We determine this scheme transformation from the double logarithmic contributions to the timelike splitting functions and the coefficient functions of inclusive particle production in e+e− annihilation now available in both schemes. This approach fixes two of the four degrees of freedom, and a third degree of freedom is fixed by reasonable physical assumptions. The results agree with the fixed-order results at next-to-next-to-leading order in the literature.