Abstract
It is well known that cross-sections in perturbative QCD receive large corrections from soft and collinear radiation, which can be resummed to all orders in the coupling. Whether or not the universal properties of this radiation can be extended to next-to-leading power (NLP) in the threshold expansion has been the subject of much recent study. In particular, universal forms for next-to-leading order (NLO) cross-sections have been obtained for general colour-singlet production processes by considering only the emission of gluons. In this paper, we extend such formulae to processes containing final state jets, and show that the dominant NLP terms at NLO can be obtained using a similar prescription to the colour-singlet case. We furthermore consider the emission of soft quarks, which also leads to a class of universal NLP contributions at NLO. We illustrate our results using three different processes at NLO: deep-inelastic scattering, hadroproduction via electron-positron annihilation and prompt photon production.
Highlights
The third set of terms in eq (1.1) make up the next-to-leading power (NLP) contributions to the differential cross-section, as they are suppressed by a single power of the threshold variable
We extend such formulae to processes containing final state jets, and show that the dominant NLP terms at next-to-leading order (NLO) can be obtained using a similar prescription to the colour-singlet case
We find that leading logarithmic effects up to NLP are completely captured by performing a similar kinematic shift to that observed for colour singlet production processes [60], and in addition by the effects of soft quark radiation
Summary
Having reviewed the universal NLO amplitude for the emission of a (next-to-)soft gluon, we turn to the emission of one additional soft quark. While it is certainly possible that a soft quark is emitted from inside the hard scattering process, it will not give rise to an NLP contribution This follows from the fact that the soft quark emission is by itself already a subleading effect in the momentum expansion, and that any internal line is by definition far off-shell. It must change the identity of the parton that enters the hard scattering process In this and the previous section, we have derived a universal next-to-soft amplitude for the emission of a single additional gluon from a general Born process, up to next-to-. (next-to)-soft radiation is fully captured by the above results, so one expects that the leading-logarithmic terms at LP and NLP in the threshold expansion are correctly obtained.4 This may be illustrated by considering specific scattering processes, which we turn to (next-to)-soft radiation is fully captured by the above results, so one expects that the leading-logarithmic terms at LP and NLP in the threshold expansion are correctly obtained. This may be illustrated by considering specific scattering processes, which we turn to
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