Truncated moments of parton distributions

We derive evolution equations satisfied by moments of parton distributions when the integration over the Bjorken variable is restricted to a subset (x0≤x≤1) of the allowed kinematical range 0≤x≤1. The corresponding anomalous dimensions turn out to be given by a triangular matrix which couples the N-th truncated moment with all (N+K)-th truncated moments with integer K≥0. We show that the series of couplings to higher moments is convergent and can be truncated to low orders while retaining excellent accuracy. We give an example of application to the determination of αs from scaling violations.