Perturbative cross-sections in QCD are beset by logarithms of kinematic invariants, whose arguments vanish when heavy particles are produced near threshold. Contributions of this type often need to be summed to all orders in the coupling, in order to improve the behaviour of the perturbative expansion, and it has long been known how to do this at leading power in the threshold variable, using a variety of approaches. Recently, the problem of extending this resummation to logarithms suppressed by a single power of the threshold variable has received considerable attention. In this paper, we show that such next-to-leading power (NLP) contributions can indeed be resummed, to leading logarithmic (LL) accuracy, for any QCD process with a coloursinglet final state, using a direct generalisation of the diagrammatic methods available at leading power. We compare our results with other approaches, and comment on the implications for further generalisations beyond leading-logarithmic accuracy. arXiv:1905.13710v1 [hep-ph] 31 May 2019 those appearing at LP level, but including extra contributions that describe, for example, the emission of wide-angle soft gluons from within jets. A more complete analysis for scalar theories coupled to electromagnetism was undertaken in Refs. [54][55][56], which again stress the importance of new quantities (both universal and non-universal) that appear beyond LP order in emitted gluon momentum. Related analyses have been carried out in SCET [57-62] (see Ref.[63] for earlier work in the context of flavour physics), and results using either diagrammatic or effective theory methods have been shown to be potentially useful for improving the accuracy of fixed-order calculations [59,[64][65][66][67][68][69][70][71][72][73]. Recently, the SCET framework has been used to demonstrate that the leading-logarithmic (LL) NLP contributions can be resummed, first for event shapes [74], and then for Drell-Yan production [75], where the results agree with the predictions of the physical evolution kernel approach of Refs. [30][31][32][33][34]. Our aim in this paper is to show how a similar resummation of LL NLP effects can be achieved using the diagrammatic approach developed in Refs. [28,29], and itself analogous to the original LP resummations of Refs. [6,7,[9][10][11]. As in the SCET approach of Ref.[75] (and as observed in Refs. [52][53][54][55][56]), we will see that, while it is true that a number of new functions appear at NLP level in the threshold expansion, many of them are irrelevant for discussing the highest power of the NLP logarithm at any given order in perturbation theory. Thus, the resummation of LL NLP contributions is remarkably straightforward. Importantly, this method is sufficiently simple and universal that it can be directly applied to any hadronic cross section with colour-singlet final states: indeed, we explicitly discuss applications to Higgs boson production in the gluon fusion channel, and the formalism can readily be generalised to multi-boson final states. There are a number ...

The cross-section for Drell-Yan production of a vector boson has been previously calculated at next-to-next-to-leading order, supplemented by enhanced logarithmic terms associated with the threshold region. In this paper, we calculate a large set of enhanced terms associated with the colour structure C 3 F at N 3 LO, for the double real emission contribution in the quark-antiquark channel, as an expansion around the threshold region up to and including the first subleading power. We perform our calculation using the method of regions, which systematically characterises all contributions according to whether the virtual gluon is (next-to) soft, collinear or hard in nature. Our results will prove useful for developing general formalisms for classifying next-to-leading power (NLP) threshold effects. They are also interesting in their own right, given that they constitute a previously unknown contribution to the Drell-Yan cross-section at O(α 3 s ).

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