Abstract:We consider the inclusive production of a Higgs boson in gluon-fusion and we study the impact of threshold resummation at next-to-next-to-next-to-leading logarithmic accuracy (N 3 LL) on the recently computed fixed-order prediction at next-to-next-to-nextto-leading order (N 3 LO). We propose a conservative, yet robust way of estimating the perturbative uncertainty from missing higher (fixed-or logarithmic-) orders. We compare our results with two other different methods of estimating the uncertainty from missing higher orders: the Cacciari-Houdeau Bayesian approach to theory errors, and the use of algorithms to accelerate the convergence of the perturbative series, as suggested by David and Passarino. We confirm that the best convergence happens at µ R = µ F = m H /2, and we conclude that a reliable estimate of the uncertainty from missing higher orders on the Higgs cross section at 13 TeV is approximately ±4%.

In global fits of parton distribution functions (PDFs) a large fraction of data points, mostly from the HERA collider, lies in a region of x and Q 2 that is sensitive to small-x logarithmic enhancements. Thus, the proper theoretical description of these data requires the inclusion of small-x resummation. In this work we provide all the necessary ingredients to perform a PDF fit to deep-inelastic scattering (DIS) data which includes small-x resummation in the evolution of PDFs and in the computation of DIS structure functions. To this purpose, not only we include the resummation of DIS massless structure functions, but we also consider the production of a massive final state (e.g. a charm quark), and the consistent resummation of mass collinear logarithms through the implementation of a variable flavour number scheme at small x. As a result, we perform the small-x resummation of the matching conditions in PDF evolution at heavy flavour thresholds. The resummed results are accurate at next-to-leading logarithmic (NLL) accuracy and matched, for the first time, to next-to-next-to-leading order (NNLO). Furthermore, we improve on our previous work by considering a novel all-order treatment of running coupling contributions. These results, which are implemented in a new release of HELL, version 2.0, will allow to fit PDFs from DIS data at the highest possible theoretical accuracy, NNLO+NLL, thus providing an important step forward towards precision determination of PDFs and consequently precision phenomenology at the LHC and beyond.

We derive a general resummation formula for transverse-momentum distributions of hard processes at the leading logarithmic level in the high-energy limit, to all orders in the strong coupling. Our result is based on a suitable generalization of high-energy factorization theorems, whereby all-order resummation is reduced to the determination of the Born-level process but with incoming off-shell gluons. We validate our formula by applying it to Higgs production in gluon fusion in the infinite top mass limit. We check our result up to next-to-leading order by comparison to the high energy limit of the exact expression and to next-to-next-to leading order by comparison to NNLL transverse momentum (Sudakov) resummation, and we predict the high-energy behaviour at next 3 -to-leading order. We also show that the structure of the result in the small transverse momentum limit agrees to all orders with general constraints from Sudakov resummation.

Abstract:We construct an approximate expression for the total cross section for the production of a heavy quark-antiquark pair in hadronic collisions at next-to-next-to-nextto-leading order (N 3 LO) in α s . We use a technique which exploits the analyticity of the Mellin space cross section, and the information on its singularity structure coming from large N (soft gluon, Sudakov) and small N (high energy, BFKL) all order resummations, previously introduced and used in the case of Higgs production. We validate our method by comparing to available exact results up to NNLO. We find that N 3 LO corrections increase the predicted top pair cross section at the LHC by about 4% over the NNLO.

We present a combined resummation for the transverse momentum distribution of a colorless final state in perturbative QCD, expressed as a function of transverse momentum p T and the scaling variable x. Its expression satisfies three requirements: it reduces to standard transverse momentum resummation to any desired logarithmic order in the limit p T → 0 for fixed x, up to power suppressed corrections in p T ; it reduces to threshold resummation to any desired logarithmic order in the limit x → 1 for fixed p T , up to power suppressed correction in 1 − x; upon integration over transverse momentum it reproduces the resummation of the total cross cross at any given logarithmic order in the threshold x → 1 limit, up to power suppressed correction in 1 − x. Its main ingredient, and our main new result, is a modified form of transverse momentum resummation, which leads to threshold resummation upon integration over p T , and for which we provide a simple closed-form analytic expression in Fourier-Mellin (b, N ) space. We give explicit coefficients up to NNLL order for the specific case of Higgs production in gluon fusion in the effective field theory limit. Our result allows for a systematic improvement of the transverse momentum distribution through threshold resummation which holds for all p T , and elucidates the relation between transverse momentum resummation and threshold resummation at the inclusive level, specifically by providing within perturbative QCD a simple derivation of the main consequence of the so-called collinear anomaly of SCET. 1 M 2 defined in analogy to ξ p , Eq. (2.2), and performing the angular integrationswhere J − is implicitly defined by Eq. (3.20) and it reduces to the Bessel function J 0 when → 0. We get dΦ n+1 (p 1 , p 2 ; q, k 1 , . . . , k n ) = x π 3−2 Γ (1 − ) dξ p db 2 (bp T ) − b n J − (bp T ) J − (bk T 1 ) M − (ξ 1 ) − 2 dz 1 dξ 1 4 (2π) 2− (1 − z 1 ) 2 − 4xξ 1 . . .