Cusp and Collinear Anomalous Dimensions in Four-Loop QCD from Form Factors

Determination of the Collins-Soper Kernel from Lattice QCD

This Letter presents a determination of the quark Collins-Soper kernel, which relates transverse-momentum-dependent parton distributions (TMDs) at different rapidity scales, using lattice quantum chromodynamics (QCD). This is the first such determination with systematic control of quark mass, operator mixing, and discretization effects. Next-to-next-to-leading logarithmic matching is used to match lattice-calculable distributions to the corresponding TMDs. The continuum-extrapolated lattice QCD results are consistent with several recent phenomenological parametrizations of the Collins-Soper kernel and are precise enough to disfavor other parametrizations.

Infrared Singularities of Multileg QCD Amplitudes with a Massive Parton at Three Loops

We derive the structure of three-loop anomalous dimensions governing infrared singularities of QCD amplitudes with one massive and an arbitrary number of massless external partons. The contributions of tripole and quadrupole correlations involving a massive parton are studied in detail. The analytical expression of tripole correlations between one massive and two massless partons is obtained at three loops for the first time. We regularize the infrared divergences in the soft matrix element in a novel approach, where no extra scale dependence is involved, and the calculation can be performed in momentum space. Our results are essential to improve the theoretical predictions of single top and top quark pair productions at hadron colliders.

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%.

Third-Order Fiducial Predictions for Drell-Yan Production at the LHC

The Drell-Yan process at hadron colliders is a fundamental benchmark for the study of strong interactions and the extraction of electroweak parameters. The outstanding precision of the LHC demands very accurate theoretical predictions with a full account of fiducial experimental cuts. In this Letter we present a state-of-the-art calculation of the fiducial cross section and of differential distributions for this process at third order in the strict fixed-order expansion in the strong coupling, as well as including the all-order resummation of logarithmic corrections. Together with these results, we present a detailed study of the subtraction technique used to carry out the calculation for different sets of experimental cuts, as well as of the sensitivity of the fiducial cross section to infrared physics. We find that residual theory uncertainties are reduced to the percent level and that the robustness of the predictions can be improved by a suitable adjustment of fiducial cuts.

Three-Loop Gluon Scattering in QCD and the Gluon Regge Trajectory

We compute the three-loop helicity amplitudes for the scattering of four gluons in QCD. We employ projectors in the 't Hooft-Veltman scheme and construct the amplitudes from a minimal set of physical building blocks, which allows us to keep the computational complexity under control. We obtain relatively compact results that can be expressed in terms of harmonic polylogarithms. In addition, we consider the Regge limit of our amplitude and extract the gluon Regge trajectory in full three-loop QCD. This is the last missing ingredient required for studying single-Reggeon exchanges at next-to-next-to-leading logarithmic accuracy.

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.

Disentangling the Regge Cut and Regge Pole in Perturbative QCD

The high-energy limit of gauge-theory amplitudes features both a Regge pole and Regge cuts. We show how to disentangle these, and hence how to determine the Regge trajectory beyond two loops. While the nonplanar part of multiple Reggeon t-channel exchange forms a Regge cut, the planar part contributes to the pole along with the single Reggeon. With this, we find that the infrared singularities of the trajectory are given by the cusp anomalous dimension. By matching to recent QCD results, we determine the quark and gluon impact factors to two loops and the Regge trajectory to three loops.

Rapidity distribution at soft-virtual and beyond for n-colorless particles to N 4 LO in QCD

We present a systematic framework to study the threshold contributions of the differential rapidity distribution for the production of any number of colorless particles in the hadronic colliders. This has been achieved based on the universality structure of the soft enhancements associated with the real emissions, along with the factorization property of the differential cross section and the renormalization group invariance. In this formalism, we present a universal soft-collinear operator to compute the soft virtual differential cross section for a generic 2 → n scattering process up to next-to-next-to-next-to-next-to-leading order ( N 4 LO) in perturbative QCD. We also provide a universal operator to perform the threshold resummation to next-to-next-to-next-to-leading logarithmic ( N 3 LL) accuracy. We explicitly present the approximate analytical results of the rapidity distributions at N 4 LO and N 3 LL for the Higgs boson production through gluon fusion and bottom quark annihilation, and also for the Drell-Yan production at the hadronic collider. We extend our framework to include the next to threshold contributions for the diagonal partonic channels.

Higgs p_{T} Spectrum and Total Cross Section with Fiducial Cuts at Third Resummed and Fixed Order in QCD

We present predictions for the gluon-fusion Higgs p_{T} spectrum at third resummed and fixed order (N^{3}LL^{'}+N^{3}LO) including fiducial cuts as required by experimental measurements at the Large Hadron Collider. Integrating the spectrum, we predict for the first time the total fiducial cross section to third order (N^{3}LO) and improved by resummation. The N^{3}LO correction is enhanced by cut-induced logarithmic effects and is not reproduced by the inclusive N^{3}LO correction times a lower-order acceptance. These are the highest-order predictions of their kind achieved so far at a hadron collider.

Nonplanar Cusp and Transcendental Anomalous Dimension at Four Loops in N=4 Supersymmetric Yang-Mills Theory

We compute the nonplanar contribution to the universal anomalous dimension of the SU(4)-singlet twist-two operators in N=4 supersymmetric Yang-Mills theory at four loops through Lorentz spin 18. From this, we numerically evaluate the nonplanar contribution to the four-loop lightlike cusp anomalous dimension and derive the transcendental ζ_{3} and ζ_{5} parts of the universal anomalous dimension for arbitrary Lorentz spin in analytic form. As for the lightlike cusp anomalous dimension and the ζ_{5} part of the universal anomalous dimension, we confirm previous results.

Full Angle Dependence of the Four-Loop Cusp Anomalous Dimension in QED

The angle-dependent cusp anomalous dimension governs divergences coming from soft gluon exchanges between heavy particles, such as top quarks. We focus on the matter-dependent contributions and compute the first truly nonplanar terms. They appear at four loops and are proportional to a quartic Casimir operator in color space. Specializing our general gauge theory result to U(1), we obtain the full QED four-loop angle-dependent cusp anomalous dimension. While more complicated functions appear at intermediate steps, the analytic answer depends only on multiple polylogarithms with singularities at fourth roots of unity. It can be written in terms of four rational structures and contains functions of up to maximal transcendental weight seven. Despite this complexity, we find that numerically the answer is tantalizingly close to the appropriately rescaled one-loop formula, over most of the kinematic range. We take several limits of our analytic result, which serves as a check and allows us to obtain new, power-suppressed terms. In the antiparallel lines limit, which corresponds to production of two massive particles at threshold, we find that the subleading power correction vanishes. Finally, we compute the quartic Casimir contribution for scalars in the loop. Taking into account a supersymmetric decomposition, we derive the first nonplanar corrections to the quark antiquark potential in maximally supersymmetric gauge theory.

Soft Anomalous Dimensions and Resummation in QCD

I discuss and review soft anomalous dimensions in QCD that describe soft-gluon threshold resummation for a wide range of hard-scattering processes. The factorization properties of the cross section in moment space and renormalization-group evolution are implemented to derive a general form for differential resummed cross sections. Detailed expressions are given for the soft anomalous dimensions at one, two, and three loops, including some new results, for a large number of partonic processes involving top quarks, electroweak bosons, Higgs bosons, and other particles in the standard model and beyond.