Space-like (vs. time-like) collinear limits in QCD: is factorization violated?

Abstract

We consider the singular behaviour of QCD scattering amplitudes in kinematical configurations where two or more momenta of the external partons become collinear. At the tree level, this behaviour is known to be controlled by factorization formulae in which the singular collinear factor is universal (process independent). We show that this strict (process-independent) factorization is not valid at one-loop and higher-loop orders in the case of the collinear limit in space-like regions (e.g., collinear radiation from initial-state partons). We introduce a generalized version of all-order collinear factorization, in which the space-like singular factors retain some dependence on the momentum and colour charge of the non-collinear partons. We present explicit results on one-loop and two-loop amplitudes for both the two-parton and multiparton collinear limits. At the level of squared amplitudes and, more generally, cross sections in hadron-hadron collisions, the violation of strict collinear factorization has implications on the non-abelian structure of logarithmically-enhanced terms in perturbative calculations (starting from the next-to-next-to-leading order) and on various factorization issues of mass singularities (starting from the next-tonext-to-next-to-leading order).

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“…Furthermore, recent studies have shown that strict collinear factorization is violated if the observable considered is not sufficiently inclusive [32,33]. As a consequence, coherenceviolating (or super-leading) logarithms appear, which further complicate the resummation of certain observables.…”

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“…The required momentum mapping is motivated by general factorization properties in QCD [114,118] and the topological identification in Fig. 12.…”

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“…(3.6). We note that for space-like splitting involving more than two hard partons, collinear factorisation is expected to be violated [47]. At two loops, we write…”