Timelike single-logarithm-resummed splitting functions Original Research Article

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 (image) 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 image 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 image 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.