We calculate soft phase-space and loop master integrals tor the computation of color-singlet cross sections through N$^3$LO in perturbative QCD. Our results are functions of homogeneous transcendental weight and include the first nine terms in the expansion in the dimensional regulator $ε$. We discuss the application of our results to the computation of deeply-inelastic scattering and $e^+e^-$ annihilation processes. We use these results to compute the perturbative coefficient functions for the Drell-Yan and gluon-fusion Higgs boson production cross sections to higher orders in $ε$ through N$^3$LO in QCD in the limit where only soft partons are produced on top of the colorless final state. Furthermore, we extract the anomalous dimension of the inclusive threshold soft function and of the $N$-Jettiness beam and jet functions to N$^4$LO in perturbative QCD.
I present results for soft anomalous dimensions through three loops for many QCD processes. In particular, I give detailed expressions for soft anomalous dimensions in various processes with electroweak and Higgs bosons as well as single top quarks and top-antitop pairs.
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 b…
The soft anomalous dimension governs the infrared divergences of scattering amplitudes in general kinematics to all orders in perturbation theory. By comparing the recent Regge-limit results for $2\to2$ scattering (through Next-to-Next-to-Leading Logarithms) in full colour to a general form for the soft anomalous dimension at four loops we derive powerful constraints on its kinematic dependence, opening the way for a bootstrap-based determination.
We calculate the complete quark and gluon cusp anomalous dimensions in four-loop massless QCD analytically from first principles. In addition, we determine the complete matter dependence of the quark and gluon collinear anomalous dimensions. Our approach is to Laurent expand four-loop quark and gluon form factors in the parameter of dimensional regularization. We employ finite field and syzygy techniques to reduce the relevant Feynman integrals to a basis of finite integrals, and subsequently evaluate the basis integrals directly from their standard parametric representations.
We consider the extension of the CMW soft-gluon effective coupling 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 $\as$. Although both effective couplings are well-defined in the physical four-dimensional space time, we examine their behaviour in $d=4 -2\ep$ space time dimensions. We uncover an all-order perturbative relation with the cusp anomalous dimension: the (four dimensional…
We compute analytically the matter-dependent contributions to the quartic Casimir term of the four-loop light-like cusp anomalous dimension in QCD, with $n_f$ fermion and $n_s$ scalar flavours. The result is extracted from the double pole of a scalar form factor. We adopt a new strategy for the choice of master integrals with simple analytic and infrared properties, which significantly simplifies our calculation. To this end we first identify a set of integrals whose integrands have a dlog form, and are hence expected to have uniform transcendental weight. We then perform a systematic analysis…
We present an analytic derivation of the full four-loop cusp anomalous dimension of $\mathcal{N}=4$ supersymmetric Yang-Mills theory from the Sudakov form factor. To extract the cusp anomalous dimension, we calculate the $ε^{-2}$ pole of the form factor using parametric integrations of finite integrals. We provide uniformly transcendental results for the master integrals through to weight six and confirm a very recent independent analytic result for the full four-loop cusp anomalous dimension of the $\mathcal{N}=4$ model.
I present results for soft anomalous dimensions in single top-quark production processes through three loops. I first discuss the cusp anomalous dimension with one massive and one massless line at three loops. I then calculate the three-loop soft anomalous dimension for $tW$ production and for related processes with new physics such as $tZ$, $tγ$, and $tH^-$ production. This is followed by results at two and three loops for the soft anomalous dimension matrix in $s$-channel single-top production and, finally, in $t$-channel single-top production. These new results are needed for soft-gluon res…
BPS Wilson loops in supersymmetric gauge theories have been the subjects of active research since they are often amenable to exact computation. So far most of the studies have focused on loops that do not intersect. In this paper, we derive exact results for intersecting 1/8 BPS Wilson loops in N=4 supersymmetric Yang-Mills theory, using a combination of supersymmetric localization and the loop equation in 2d gauge theory. The result is given by a novel matrix-model-like representation which couples multiple contour integrals and a Gaussian matrix model. We evaluate the integral at large N, an…
Two-loop soft anomalous dimensions and NNLL resummation for heavy quark production
我目前的结果，双回路软异常尺寸的重夸克的生产控制软胶子的再确认在下一个到下一个到领先的对数（NNLL）的准确性。我推导出一个精确结果的显式表达式，并通过e+ e- -> t tbar对顶夸克产生进行数值研究，我构造了一个令人惊讶的简单但非常精确的近似。我表明，双圈软反常尺寸与大量的夸克显示一个简单的比例关系，单圈的结果，只有在有限的夸克质量消失。本文还讨论了强子对撞机中单top和top对产生计算的推广。
Wilson lines capture important features of scattering amplitudes, for example soft effects relevant for infrared divergences, and the Regge limit. Beyond the leading power approximation, corrections to the eikonal picture have to be taken into account. In this paper, we study such corrections in a model of massive scattering amplitudes in N = 4 super Yang-Mills, in the planar limit, where the mass is generated through a Higgs mechanism. Using known three-loop analytic expressions for the scattering amplitude, we find that the first power suppressed term has a very simple form, equal to a singl…
We present compact integral representations for the calculation of two-loop anomalous dimensions for a generic class of soft functions that are defined in terms of two light-like Wilson lines. Our results are relevant for the resummation of Sudakov logarithms for e+ e- event-shape variables and inclusive hadron-collider observables at next-to-next-to-leading logarithmic accuracy within Soft-Collinear Effective Theory (SCET). Our formalism applies to both SCET-1 and SCET-2 soft functions and we clarify the relation between the respective soft anomalous dimension and the collinear anomaly expone…
I present results through three loops for soft anomalous dimensions that control soft-gluon emission in processes involving the top quark. In particular I present results for channels in single-top production and top-pair production as well as for processes with new physics, including $tZ$, $tZ'$, $t γ$, and $tH^-$ production. These calculations are ingredients to resummations at N$^3$LL accuracy and to derivations of N$^3$LO soft-gluon corrections.
We compute the soft anomalous dimension (SAD) matrices for production of massive quarks $Q$ and $\bar{Q}$ in association with a gluon jet, from massless quarks $q$ and antiquarks $\bar{q}$: $q\bar{q}\rightarrow Q\bar{Q}g$, and in the gluon scattering $gg\rightarrow Q\bar{Q}g$. To analyze the behaviour of the eigenvalues of SAD matrices we perform numerical studies of their eigensystems at two special kinematical configurations.
I present results for soft anomalous dimensions through three loops for several processes involving the production of top quarks. In particular, I discuss single-top and top-pair production. I also present some numerical results for double-differential distributions in $t{\bar t}$ production through approximate N$^3$LO.
Using rapidity evolution equations we study two-to-two gauge-theory scattering amplitudes in the Regge limit. We carry out explicit computations at next-to-next-to-leading logarithmic accuracy through four loops and present new results for both infrared-singular and finite contributions to the amplitude. New techniques are devised in order to derive the colour structure stemming from three-Reggeon exchange diagrams in terms of commutators of channel operators, obtaining results that are valid for any gauge group, and apply to scattered particles in any colour representation. We also elucidate …
We explore how the dilepton production rate is modified near the critical temperature of color superconductivity and QCD critical point by the soft modes inherently associated with the phase transitions of second-order. It is shown that the soft modes affect the photon self-energy significantly through so called the Aslamasov-Larkin, Maki-Thompson and density of states terms, which are known responsible for the paraconductivity in the metalic superconductivity, and cause an anomalous enhancement of the production rate in the low energy/momentum region.
We continue the investigation of the anomalous dimension of subleading-power $N$-jet operators. In this paper, we focus on the operators with fermion number one in each collinear direction, corresponding to quark (antiquark) initiated jets in QCD. We investigate the renormalization effects induced by the soft loop and compute the one-loop mixing of time-ordered products involving power-suppressed SCET Lagrangian insertions into $N$-jet currents through soft loops. We discuss fermion number conservation in collinear directions and provide explicit results for the collinear anomalous dimension m…
We calculate the one-loop corrections to the soft anomalous dimension matrices for the production of a top-antitop quark pair in association with a jet at hadron colliders. This is a step forward towards implementing a procedure for the resummation of soft-gluon emission logarithms for the $t\bar{t}j + X$ hadroproduction process, that will enable the improvement of the accuracy of the $t\bar{t} j + X$ cross sections, beyond the current degree of knowledge. The latter, so far, has reached the next-to-leading order (NLO) level, complemented by the accuracy of the Shower Monte Carlo approaches us…
The soft radiation emitted in jet cross sections can resolve the directions and colors of individual hard partons, leading to a complicated pattern of logarithmically enhanced terms in the perturbative series. Starting from a factorization theorem and solving the renormalization group equations for its ingredients, these large logarithms can be resummed. In this paper, we extract the two-loop anomalous dimension governing the resummation of subleading logarithms in jet cross sections and other non-global observables. This anomalous dimension can be obtained by considering soft limits of hard a…
The rapidity anomalous dimension controls the scaling of transverse momentum dependent observables in the Sudakov region. In a conformal theory it is equivalent to the soft anomalous dimension, but in QCD this relation is broken by anomalous terms proportional to the $β$-function. In this paper we first give a simple proof of this relation using two different representations of the energy-energy correlator observable. We then calculate the anomalous terms to three loops by computing the three-loop fully differential soft function to $\mathcal{O}(ε)$. Combined with recent perturbative data from…
I present higher-order corrections from soft-gluon emission for the associated production of a top quark with a $Z$ boson via anomalous $t$-$q$-$Z$ couplings at LHC energies. Approximate next-to-next-to-leading order (aNNLO) double-differential cross sections are derived from soft-gluon resummation at next-to-leading-logarithm accuracy. The total $tZ$ production cross sections and the top-quark transverse-momentum and rapidity distributions are calculated at aNNLO for various LHC energies. It is shown that the soft-gluon corrections are dominant and large for this process.
We discuss the associated production of a top quark with a photon via anomalous $t$-$q$-$γ$ couplings, and present higher-order corrections from soft-gluon emission for the processes $gq \rightarrow tγ$ at LHC energies. We perform soft-gluon resummation at next-to-leading-logarithm accuracy and derive approximate next-to-next-to-leading order (aNNLO) double-differential cross sections. We calculate at aNNLO the total $tγ$ production cross sections and the top-quark transverse-momentum and rapidity distributions for various LHC energies, and show that the soft-gluon corrections are large and do…
