Abstract
We present a formalism and detailed analytical results for soft-gluon resummation for $2\rightarrow n$ processes in single-particle-inclusive (1PI) kinematics. This generalizes previous work on resummation for $2 \rightarrow 2$ processes in 1PI kinematics. We also present soft anomalous dimensions at one and two loops for certain $2 \rightarrow 3$ processes involving top quarks and Higgs or $Z$ bosons, and we provide some brief numerical results.
Highlights
In theoretical calculations of hard-scattering cross sections of relevance to hadron colliders, the state of the art has been moving steadily towards higher orders, more loops, and resummations at higher logarithmic accuracy; it has been gradually expanded to processes with larger numbers of final-state particles
Soft-gluon resummation follows from factorization properties of the cross section [1,2,3,4,5,6] and it has been applied to a large number of processes in hadron collisions
III, we provide some kinematical details about the cross section calculation at the partonic and hadronic levels
Summary
In theoretical calculations of hard-scattering cross sections of relevance to hadron colliders, the state of the art has been moving steadily towards higher orders, more loops, and resummations at higher logarithmic accuracy; it has been gradually expanded to processes with larger numbers of final-state particles. We define a threshold variable sth which measures the extra energy in soft radiation and which vanishes at partonic threshold Logarithms of this threshold variable appear in the perturbative expansion as plus distributions of the general form 1⁄2lnmðsth=sÞ=sthþ, with m ≤ 2n − 1 at nth order. We can define the threshold variable as sth 1⁄4 ðp þ p3 þ pgÞ2 − ðp þ p3Þ2 This clearly gives the same physical meaning as extra energy from gluon emission and clearly vanishes as pg → 0. We see that our results here are a natural extension of the relations for 2 → 2 kinematics These relations can be extended to an arbitrary number of particles: we consider processes that are 2 → n at lowest order, pa þ pb → p1 þ p2 þÁÁÁþ pn. We note that one can appropriately redefine the above relations if, instead of particle 1, the observed particle is n or any of the other particles
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