Correspondence between Soft and Rapidity Anomalous Dimensions

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.

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.

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.

t t ¯ H production at NNLO: the flavour off-diagonal channels

We consider QCD radiative corrections to the associated production of a heavy-quark pair ( Q Q ¯ ) with a generic colourless system F at hadron colliders. We discuss the resummation formalism for the production of the Q Q ¯ F system at small values of its total transverse momentum q T . We present the results of the corresponding resummation coefficients at next-to-leading and, partly, next-to-next-to-leading order. The perturbative expansion of the resummation formula leads to the explicit ingredients that can be used to apply the q T subtraction formalism to fixed-order calculations for this class of processes. We use the q T subtraction formalism to perform a fully differential perturbative computation for the production of a top-antitop quark pair and a Higgs boson. At next-to-leading order we compare our results with those obtained with established subtraction methods and we find complete agreement. We present, for the first time, the results for the flavour off-diagonal partonic channels at the next-to-next-to-leading order.

W-boson production in TMD factorization

At hadron colliders, the differential cross section for W production can be factorized and it is sensitive transverse momentum dependent distributions (TMD) for low boson transverse momentum. While, often, the corresponding non-perturbative QCD contributions are extrapolated from Z boson production, here we use an existing extraction (based on the code Artemide) of TMD which includes data coming from Drell-Yan and semi-inclusive deep inelastic scattering, to provide checks and predictions for the W case. Including fiducial cuts with different configurations and kinematical power corrections, we consider transverse momentum dependent cross sections within several intervals of the vector boson transverse mass. We perform the same study for the p T W - / p T W + and p T Z / p T W distributions. We compare our predictions with recent extractions of these quantities at ATLAS and CMS and results from TeVatron. The results encourage a broader experimental and phenomenological work, and a deeper study of TMD for the W case.

Extraction of the Sivers Function from SIDIS, Drell-Yan, and W^{±}/Z Data at Next-to-Next-to-Next-to Leading Order

We perform the global analysis of polarized semi-inclusive deep inelastic scattering (SIDIS), pion-induced polarized Drell-Yan (DY) process, and W^{±}/Z boson production data and extract the Sivers function for u, d, s and for sea quarks. We use the framework of transverse momentum dependent factorization at next-to-next-to-next-to leading order (N^{3}LO) accuracy. The Qiu-Sterman function is determined in a model independent way from the extracted Sivers function. We also evaluate the significance of the predicted sign change of the Sivers function in DY process with respect to SIDIS.

The x-dependence of hadronic parton distributions: A review on the progress of lattice QCD

In this article, we review recent lattice calculations on the x-dependence of parton distributions, with the latter providing information on hadron structure. These calculations are based on matrix elements of boosted hadrons coupled to non-local operators and can be related to the standard, light-cone distribution functions via an appropriate factorization formalism. There is significant progress in several directions, including calculations of flavor-singlet parton distribution functions (PDFs), first calculations of generalized parton distributions (GPDs), as well as the implementation of some of the approaches for the transverse-momentum-dependent PDFs (TMD PDFs). This new direction of lattice calculations is particularly interesting for phenomenological fits on experimental data sets, as the lattice results can help improve the constraints on the distribution functions.

Self-Contained Definition of the Collins-Soper Kernel

The rapidity anomalous dimension (RAD), or Collins-Soper kernel, defines the scaling properties of transverse momentum dependent distributions and can be extracted from the experimental data. I derive a self-contained nonperturbative definition that represents RAD without reference to a particular process. This definition makes possible exploration of the properties of RAD by theoretical methods on one side, and the properties of QCD vacuum with collider measurements on another side. To demonstrate these possibilities, I compute the power correction to RAD, its large-b asymptotic, and compare these estimations with recent phenomenological extractions.

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.

The transverse momentum spectrum of weak gauge bosons at N 3 LL + NNLO

We present accurate QCD predictions for the transverse momentum ( p ⊥ ) spectrum of electroweak gauge bosons at the LHC for 13 TeV collisions, based on a consistent combination of a NNLO calculation at large p ⊥ and N3 LL resummation in the small p ⊥ limit. The inclusion of higher order corrections leads to substantial changes in the shape of the differential distributions, and the residual perturbative uncertainties are reduced to the few percent level across the whole transverse momentum spectrum. We examine the ratio of p ⊥ distributions in charged- and neutral-current Drell-Yan production, and study different prescriptions for the estimate of perturbative uncertainties that rely on different degrees of correlation between these processes. We observe an excellent stability of the ratios with respect to the perturbative order, indicating a strong correlation between the corresponding QCD corrections.

Soft-gluon effective coupling and cusp anomalous dimension

We consider the extension of the CMW soft-gluon effective coupling [1] in the context of soft-gluon resummation for QCD hard-scattering observables beyond the next-to-leading logarithmic accuracy. We present two proposals of a soft-gluon effective coupling that extend the CMW coupling to all perturbative orders in the MS ¯ coupling α S . Although both effective couplings are well-defined in the physical four-dimensional space time, we examine their behaviour in d = 4 - 2 ϵ space time dimensions. We uncover an all-order perturbative relation with the cusp anomalous dimension: the (four dimensional) cusp anomalous dimension is equal to the d-dimensional soft-gluon effective coupling at the conformal point ϵ = β ( α S ) , where the d-dimensional QCD β -function, β ( α S ) - ϵ , vanishes. We present the explicit expressions of the two soft-gluon couplings up to O ( α S 2 ) in d dimensions. In the four-dimensional case we compute the two soft couplings up to O ( α S 3 ) . For one of the two couplings, we confirm the O ( α S 3 ) result previously presented by other authors. For the other coupling, we obtain the explicit relation with the cusp anomalous dimension up to O ( α S 4 ) . We comment on Casimir scaling at O ( α S 4 ) .

Precision QCD Event Shapes at Hadron Colliders: The Transverse Energy-Energy Correlator in the Back-to-Back Limit

We present an operator-based factorization formula for the transverse energy-energy correlator (TEEC) hadron collider event shape in the back-to-back (dijet) limit. This factorization formula exhibits a remarkably symmetric form, being a projection onto a scattering plane of a more standard transverse momentum dependent factorization. Soft radiation is incorporated through a dijet soft function, which can be elegantly obtained to next-to-next-to-leading order (NNLO) due to the symmetries of the problem. We present numerical results for the TEEC resummed to next-to-next-to-leading logarithm (NNLL) matched to fixed order at the LHC. Our results constitute the first NNLL resummation for a dijet event shape observable at a hadron collider, and the first analytic result for a hadron collider dijet soft function at NNLO. We anticipate that the theoretical simplicity of the TEEC observable will make it indispensable for precision studies of QCD at the LHC, and as a playground for theoretical studies of factorization and its violation.

Event-based transverse momentum resummation

We have developed a framework for automated transverse momentum resummation for arbitrary electroweak final states based on reweighting tree-level events. It is fully differential in the kinematics of the electroweak final states, which facilitates a straightforward analysis of arbitrary observables in the small transverse momentum region. We have implemented the resummation at next-to-next-to-leading logarithmic accuracy and match to next-to-leading fixed-order results using the event generator MadGraph5_aMC@NLO. Results for Z and W boson production with leptonic decay as well as WZ production are presented. We compare to experimental measurements for the transverse momentum and the angular observable ϕ ∗ .

Transverse-Momentum-Dependent Distributions with Jets

We investigate the use of jets to measure transverse-momentum-dependent distributions (TMDs). The example we use to present our framework is the dijet momentum decorrelation at lepton colliders. Translating this momentum decorrelation into an angle θ≪1, we analyze the factorization of the cross section for the cases θ≫R, θ∼R, and θ≪R, where R is the jet radius. Critically, for the winner-take-all axis, the jet TMD has the same double-scale renormalization group evolution as TMD fragmentation functions for all radii R. TMD fragmentation functions in factorization theorems may then simply be replaced by the jet TMDs we calculate, and all ingredients to perform the resummation to next-to-next-to-leading logarithmic accuracy are available. Our approach also applies to semi-inclusive deep inelastic scattering, where a jet instead of a hadron is measured in the final state, and we find a clean method to probe the intrinsic transverse momentum of quarks and gluons in the proton that is less sensitive to final-state nonperturbative effects.