Abstract
We derive a general expression for the threshold resummation of transverse momentum distributions for processes with a colorless final state, by suitably generalizing the renormalization-group based approach to threshold resummation previously pursued by two of us. The ensuing expression holds to all logarithmic orders, and it can be used to extend available results in the literature, which only hold up to the next-to-leading log (NLL) level. We check agreement of our result with the existing NLL result, as well as against the known fixed next-to-leading order results for the Higgs transverse momentum distribution in gluon fusion, and we provide explicit expressions at the next-to-next-to-leading log level.
Highlights
Be related using the general resummation formalism for multiparton processes of ref. [12]
This approach has the advantage of generality: it provides the form of resummed results to any logarithmic order, though it does not allow for the computation of the coefficients that determine the resummed expressions explicitly, which must be found by matching to fixed-order expressions — the fixed NkLO fully determines the NkLL resummed result
We arrive at a form of the soft resummation which is somewhat more compact than that of ref. [8], with which we prove agreement at next-to-leading log (NLL)
Summary
The transverse momentum distribution is characterized by two scales, which can be constructed out of the invariant mass m and transverse momentum pT, and a scaling variable τ. The scale Q eq (2.4) is the threshold energy, i.e. the minimum energy needed to produce a system with invariant mass m and transverse momentum pT. This ensures factorization in that, with this choice, the kinematic boundary for the scaling variable τ at fixed pT is pT-independent: 0≤τ ≤1. Which shows that any pair of variables among QpT, Q2, m2 can be chosen as independent kinematic variables, along with the dimensionless ratio τ eq (2.5) With any such choice there are two scales and a scaling variable, which can be varied independently without conflicting with factorization, i.e. in such a way that at the factorized level the parton luminosity only depends on τ and a scale
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