Quark and Gluon Form Factors in Four-Loop QCD

We compute the photon-quark and Higgs-gluon form factors to four-loop order within massless perturbative quantum chromodynamics. Our results constitute ready-to-use building blocks for N^{4}LO cross sections for Drell-Yan processes and gluon-fusion Higgs boson production at the LHC. We present complete analytic expressions for both form factors and show several of the most complicated master integrals.

Next-to-Next-to-Leading Order Mixed QCD-Electroweak Corrections to On-Shell Z Production

We present the first analytical results for the O(αα_{s}) corrections to the total cross section for the inclusive production of an on-shell Z boson at hadron colliders. We include the complete set of contributions, with photonic and massive weak gauge boson effects, which have been computed in analytical form and expressed in terms of polylogarithmic and elliptic integrals. We present numerical results, relevant for the precision studies at the LHC. These corrections increase the accuracy of the predictions and contribute to the reduction of the QCD component of the theoretical uncertainty.

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 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.

Higgs Boson 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-flavor scheme, treating the bottom quark as a massless parton while retaining a nonvanishing Yukawa coupling to the Higgs boson. We find that the dependence of the hadronic cross section on the renormalization and factorization scales is substantially reduced. For judicious choices of the scales the perturbative expansion of the cross section shows a convergent behavior. 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-flavor schemes, we predict a slightly higher cross section, though the two predictions are consistent within theoretical uncertainties.

Quark Transverse Parton Distribution at the Next-to-Next-to-Next-to-Leading Order

We report a calculation of the perturbative matching coefficients for the transverse-momentum-dependent parton distribution functions for quark at the next-to-next-to-next-to-leading order in QCD, which involves calculation of nonstandard Feynman integrals with rapidity divergence. We introduce a set of generalized integration-by-parts equations, which allows an algorithmic evaluation of such integrals using the machinery of modern Feynman integral calculation.

Full-Color Two-Loop Four-Gluon Amplitude in N=2 Supersymmetric QCD

We present the fully integrated form of the two-loop four-gluon amplitude in N=2 supersymmetric quantum chromodynamics with gauge group SU(N_{c}) and with N_{f} massless supersymmetric quarks (hypermultiplets) in the fundamental representation. Our result maintains full dependence on N_{c} and N_{f}, and relies on the existence of a compact integrand representation that exhibits the duality between color and kinematics. Specializing to the N=2 superconformal theory, where N_{f}=2N_{c}, we obtain remarkably simple amplitudes that have an analytic structure close to that of N=4 super-Yang-Mills theory, except that now certain lower-weight terms appear. We comment on the corresponding results for other gauge groups.

Double Resummation for Higgs Production

We present the first double-resummed prediction of the inclusive cross section for the main Higgs production channel in proton-proton collisions, namely, gluon fusion. Our calculation incorporates to all orders in perturbation theory two distinct towers of logarithmic corrections which are enhanced, respectively, at threshold, i.e., large x, and in the high-energy limit, i.e., small x. Large-x logarithms are resummed to next-to-next-to-next-to-leading logarithmic accuracy, while small-x ones to leading logarithmic accuracy. The double-resummed cross section is furthermore matched to the state-of-the-art fixed-order prediction at next-to-next-to-next-to-leading accuracy. We find that double resummation corrects the Higgs production rate by 2% at the currently explored center-of-mass energy of 13 TeV and its impact reaches 10% at future circular colliders at 100 TeV.

Bootstrapping Rapidity Anomalous Dimensions for Transverse-Momentum Resummation

A soft function relevant for transverse-momentum resummation for Drell-Yan or Higgs production at hadron colliders is computed through to three loops in the expansion of strong coupling, with the help of the bootstrap technique and supersymmetric decomposition. The corresponding rapidity anomalous dimension is extracted. An intriguing relation between anomalous dimensions for transverse-momentum resummation and threshold resummation is found.

Prospects for Higgs physics at energies up to 100 TeV

We summarize the prospects for Higgs boson physics at future proton-proton colliders with centre of mass (c.m.) energies up to 100 TeV. We first provide the production cross sections for the Higgs boson of the Standard Model from 13 TeV to 100 TeV, in the main production mechanisms and in subleading but important ones such as double Higgs production, triple production and associated production with two gauge bosons or with a single top quark. We then discuss the production of Higgs particles in beyond the Standard Model scenarios, starting with the one in the continuum of a pair of scalar, fermionic and vector dark matter particles in Higgs-portal models in various channels with virtual Higgs exchange. The cross sections for the production of the heavier CP-even and CP-odd neutral Higgs states and the charged Higgs states in two-Higgs doublet models, with a specific study of the case of the Minimal Supersymmetric Standard Model, are then given. The sensitivity of a 100 TeV proton machine to probe the new Higgs states is discussed and compared to that of the LHC with a c.m. energy of 14 TeV and at high luminosity.

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 (N^{3}LO) 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 N^{3}LO in the large top-mass limit. For renormalization and factorization scales equal to half the Higgs boson mass, the N^{3}LO corrections are of the order of +2.2%. The total scale variation at N^{3}LO is 3%, reducing the uncertainty due to missing higher order QCD corrections by a factor of 3.

Rapidity distributions in Drell-Yan and Higgs productions at threshold to third order in QCD

We present the threshold N(3)LO perturbative QCD corrections to the rapidity distributions of dileptons in the Drell-Yan process and Higgs boson in gluon fusion. Sudakov resummation of QCD amplitudes, renormalization group invariance, and the mass factorization theorem provide useful guidelines to obtain them in an elegant manner. We use various state of the art three loop results that have been recently available to obtain these distributions. For the Higgs boson, we demonstrate numerically the importance of these corrections at the LHC.