Higgs production in bottom-quark fusion to third order in the strong coupling

We present the inclusive cross section at next-to-next-to-next-to-leading order (N$^3$LO) in perturbative QCD for the production of a Higgs boson via bottom-quark fusion. We employ the five-flavour scheme, treating the bottom quark as a massless parton while retaining a non-vanishing Yukawa coupling to the Higgs boson. We find that the dependence of the hadronic cross section on the renormalisation and factorisation scales is substantially reduced. For judicious choices of the scales the perturbative expansion of the cross section shows a convergent behaviour. We present results for the N$^3$LO cross section at various collider energies. In comparison to the cross section obtained from the Santander-matching of the four and five-flavour schemes we predict a slightly higher cross section, though the two predictions are consistent within theoretical uncertainties.Comment: 3 pretty plots with pretty colours. Published versio

Charged Current Drell-Yan Production at N3LO

We present the production cross section for a lepton-neutrino pair at the Large Hadron Collider computed at next-to-next-to-next-to leading order (N3LO) in QCD perturbation theory. We compute the partonic coefficient functions of a virtual $W^{\pm}$ boson at this order. We then use these analytic functions to study the progression of the perturbative series in different observables. In particular, we investigate the impact of the newly obtained corrections on the inclusive production cross section of $W^{\pm}$ bosons, as well as on the ratios of the production cross sections for $W^+$, $W^-$ and/or a virtual photon. Finally, we present N3LO predictions for the charge asymmetry at the LHC.Comment: 22 pages, 11 figures. v2: Fixed mistake in figure

The Drell-Yan cross section to third order in the strong coupling constant

We present phenomenological results for the inclusive cross section for the production of a lepton-pair via virtual photon exchange at next-to-next-to-next-to-leading order (N$^3$LO) in perturbative QCD. In line with the case of Higgs production, we find that the hadronic cross section receives corrections at the percent level, and the residual dependence on the perturbative scales is reduced. However, unlike in the Higgs case, we observe that the uncertainty band derived from scale variation is no longer contained in the band of the previous order.Comment: Published versio

The Four-Loop Rapidity Anomalous Dimension and Event Shapes to Fourth Logarithmic Order

We obtain the quark and gluon rapidity anomalous dimension to fourth order in QCD. We calculate the N$^3$LO rapidity anomalous dimensions to higher order in the dimensional regulator and make use of the soft/rapidity anomalous dimension correspondence in conjunction with the recent determination of the N$^4$LO threshold anomalous dimensions to achieve our result. We show that the results for the quark and gluon rapidity anomalous dimensions at four loops are related by generalized Casimir scaling. Using the N$^4$LO rapidity anomalous dimension, we perform the resummation of the Energy-Energy Correlation in the back-to-back limit at N$^4$LL, achieving for the first time the resummation of an event shape at this logarithmic order. We present numerical results and observe a reduction of perturbative uncertainties on the resummed cross section to below 1%.Comment: 5 pages, 3 figures, 2 ancillary files. v2: corrected typo in tabled values from ref [28] in eq. 10 and 11. Analytic formulae, EEC section and ancillary files unchange

Soft Expansion of Double-Real-Virtual Corrections to Higgs Production at N3^3LO

We present methods to compute higher orders in the threshold expansion for the one-loop production of a Higgs boson in association with two partons at hadron colliders. This process contributes to the N$^3$LO Higgs production cross section beyond the soft-virtual approximation. We use reverse unitarity to expand the phase-space integrals in the small kinematic parameters and to reduce the coefficients of the expansion to a small set of master integrals. We describe two methods for the calculation of the master integrals. The first was introduced for the calculation of the soft triple-real radiation relevant to N$^3$LO Higgs production. The second uses a particular factorization of the three body phase-space measure and the knowledge of the scaling properties of the integral itself. Our result is presented as a Laurent expansion in the dimensional regulator, although some of the master integrals are computed to all orders in this parameter.Comment: 30 page

Inclusive Production Cross Sections at N3LO

We present for the first time the inclusive cross section for associated Higgs boson production with a massive gauge boson at next-to-next-to-next-to-leading order in QCD. Furthermore, we introduce n3loxs, a public, numerical program for the evaluation of inclusive cross sections at the third order in the strong coupling constant. Our tool allows to derive predictions for charged- and neutral-current Drell-Yan production, gluon- and bottom-quark-fusion Higgs boson production and Higgs boson associated production with a heavy gauge boson. We discuss perturbative and parton distribution function (PDF) uncertainties of the aforementioned processes. We perform a comparison of global PDF sets for a variety of process including associated Higgs boson production and observe $1\sigma$ deviations among predictions for several processes.Comment: 53 pages, 20 figures, 12 tables. Associated public computer program to be found at https://github.com/jubaglio/n3lox

Higgs boson gluon-fusion production in QCD at Three Loops

We present the cross-section for the production of a Higgs boson at hadron-colliders at next-to- next-to-next-to-leading order (N3LO) in perturbative QCD. The calculation is based on a method to perform a series expansion of the partonic cross-section around the threshold limit to an arbitrary order. We perform this expansion to sufficiently high order to obtain the value of the hadronic cross at N3LO in the large top-mass limit. For renormalisation and factorisation scales equal to half the Higgs mass, the N3LO corrections are of the order of +2.2%. The total scale variation at N3LO is 3%, reducing the uncertainty due to missing higher order QCD corrections by a factor of three.Comment: 5 pages, 3 figure

Higgs boson gluon-fusion production beyond threshold in N3LO QCD

In this article, we compute the gluon fusion Higgs boson cross-section at N3LO through the second term in the threshold expansion. This calculation constitutes a major milestone towards the full N3LO cross section. Our result has the best formal accuracy in the threshold expansion currently available, and includes contributions from collinear regions besides subleading corrections from soft and hard regions, as well as certain logarithmically enhanced contributions for general kinematics. We use our results to perform a critical appraisal of the validity of the threshold approximation at N3LO in perturbative QCD