Two-Loop QED Corrections to the Scattering of Four Massive Leptons.

We study two-loop corrections to the scattering amplitude of four massive leptons in quantum electrodynamics. These amplitudes involve previously unknown elliptic Feynman integrals, which we compute analytically using the differential equation method. In doing so, we uncover the details of the elliptic geometry underlying this scattering amplitude and show how to exploit its properties to obtain compact, easy-to-evaluate series expansions that describe the scattering of four massive leptons in QED in the kinematical regions relevant for Bhabha and Møller scattering processes.

Yangian-Invariant Fishnet Integrals in Two Dimensions as Volumes of Calabi-Yau Varieties.

We argue that ℓ-loop Yangian-invariant fishnet integrals in two dimensions are connected to a family of Calabi-Yau ℓ folds. The value of the integral can be computed from the periods of the Calabi-Yau, while the Yangian generators provide its Picard-Fuchs differential ideal. Using mirror symmetry, we can identify the value of the integral as the quantum volume of the mirror Calabi-Yau. We find that, similar to what happens in string theory, for ℓ=1 and 2 the value of the integral agrees with the classical volume of the mirror, but starting from ℓ=3, the classical volume gets corrected by instanton contributions. We illustrate these claims on several examples, and we use them to provide for the first time results for 2- and 3-loop Yangian-invariant train track integrals in two dimensions for arbitrary external kinematics.

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 and 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%.

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.

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.

Algebraic Structure of Cut Feynman Integrals and the Diagrammatic Coaction.

We study the algebraic and analytic structure of Feynman integrals by proposing an operation that maps an integral into pairs of integrals obtained from a master integrand and a corresponding master contour. This operation is a coaction. It reduces to the known coaction on multiple polylogarithms, but applies more generally, e.g., to hypergeometric functions. The coaction also applies to generic one-loop Feynman integrals with any configuration of internal and external masses, and in dimensional regularization. In this case, we demonstrate that it can be given a diagrammatic representation purely in terms of operations on graphs, namely, contractions and cuts of edges. The coaction gives direct access to (iterated) discontinuities of Feynman integrals and facilitates a straightforward derivation of the differential equations they admit. In particular, the differential equations for any one-loop integral are determined by the diagrammatic coaction using limited information about their maximal, next-to-maximal, and next-to-next-to-maximal cuts.

Three-Loop Corrections to the Soft Anomalous Dimension in Multileg Scattering.

We present the three-loop result for the soft anomalous dimension governing long-distance singularities of multileg gauge-theory scattering amplitudes of massless partons. We compute all contributing webs involving semi-infinite Wilson lines at three loops and obtain the complete three-loop correction to the dipole formula. We find that nondipole corrections appear already for three colored partons, where the correction is a constant without kinematic dependence. Kinematic dependence appears only through conformally invariant cross ratios for four colored partons or more, and the result can be expressed in terms of single-valued harmonic polylogarithms of weight five. While the nondipole three-loop term does not vanish in two-particle collinear limits, its contribution to the splitting amplitude anomalous dimension reduces to a constant, and it depends only on the color charges of the collinear pair, thereby preserving strict collinear factorization properties. Finally, we verify that our result is consistent with expectations from the Regge limit.

Three-Jet Production in Electron-Positron Collisions at Next-to-Next-to-Leading Order Accuracy.

We introduce a completely local subtraction method for fully differential predictions at next-to-next-to-leading order (NNLO) accuracy for jet cross sections and use it to compute event shapes in three-jet production in electron-positron collisions. We validate our method on two event shapes, thrust and C parameter, which are already known in the literature at NNLO accuracy and compute for the first time oblateness and the energy-energy correlation at the same accuracy.

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.