Abstract
We study the large-x behaviour of the physical evolution kernels for flavour non-singlet observables in deep-inelastic scattering, where x is the Bjorken variable, semi-inclusive e+e− annihilation and Drell-Yan lepton-pair production. Unlike the corresponding -scheme coefficient functions, all these kernels show a single-logarithmic large-x enhancement at all orders in 1−x. We conjecture that this universal behaviour, established by Feynman-diagram calculations up to the fourth order, holds at all orders in the strong coupling constant αs. The resulting predictions are presented for the highest lnn(1−x) contributions to the higher-order coefficient functions. In Mellin-N space these predictions take the form of an exponentiation which, however, appears to be less powerful than the well-known soft-gluon exponentiation of the leading (1−x)−1ln n(1−x) terms. In particular in deep-inelastic scattering the 1/N corrections are non-negligible for all practically relevant N.
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