The three-loop splitting functions in QCD: the singlet case

Vogt, A.; Moch, S.; Vermaseren, J. A. M.

doi:10.1016/j.nuclphysb.2004.04.024

Cited by 899 publications

(1,207 citation statements)

References 84 publications

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“…We have suppressed the dependence onâ s and µ 2 in Γ. The factorisation kernel Γ(z j , µ 2 F , ε) satisfies the following renormalisation group equation:where the P(z j , µ 2 F ) are the well-known DGLAP matrix-valued splitting functions which are known upto three-loop level [32,33]:The diagonal terms in the splitting functions P (i) (z j ) have the following structurewhere P (i) reg,II (z j ) are regular when the argument approaches the kinematic limit (here z j → 1). The RG equations can be solved by expanding in powers of the strong coupling constant.…”

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confidence: 99%

QCD threshold corrections to di-lepton and Higgs rapidity distributions beyond N2LO

2007

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We present threshold enhanced QCD corrections to rapidity distributions of di-leptons in the DrellYan process and of Higgs particles in both gluon fusion and bottom quark annihilation processes using Sudakov resummed cross sections. We have used renormalisation group invariance and the mass factorisation theorem that these hard scattering cross sections satisfy as well as Sudakov resummation of QCD amplitudes. We find that these higher order threshold QCD corrections stabilise the theoretical predictions under scale variations.Perturbative Quantum Chromodynamics (pQCD) provides a framework to successfully compute various observables in the collisions of hadrons at high energies. Recent theoretical advances in the computations of higher order QCD radiative corrections have lead to precise results for several important observables. Because of this progress, we can now predict these observables with unprecedented accuracy for physics studies at the Tevatron collider in Fermilab as well as at the upcoming Large Hadron Collider (LHC) in CERN [1].The Drell-Yan (DY) production of di-leptons [2] has been one of the most important probes of the structure of hadrons. It is also one of the dominant production processes at hadron colliders. At the LHC, it will serve as a luminosity monitor which is very important to precisely calibrate the machine for searches for physics beyond the Standard Model (SM). In DY production, a pair of leptons is produced through the decay of virtual photons, Z and W bosons that result from the collisions of incoming partons (quarks and gluons) in the hadrons. At hadron colliders, the DY process provides precise measurements of various standard model parameters. Rapidity distributions of Z bosons [3] and charge asymmetries of leptons coming from W boson decays [4] can probe the structure of the hadrons and possible excess events in di-lepton invariant mass distributions can point to physics beyond the standard model such as R-parity violating supersymmetric models and models with Z ′ , or with contact interactions [5]. Both D0 and CDF collaborations [6] at the Fermilab Tevatron made precise measurements of Z and W production cross sections and asymmetries which not only allowed for stringent tests of the standard model but also play an important role in the Higgs search at future colliders. These measurements are also possible at the LHC due to the large cross sections for the DY process.The other process which is equally important is Higgs boson production at these colliders because it will establish the Standard Model as well as look for beyond the SM Higgs [7,8]. The Higgs boson, which is responsible for the electroweak symmetry breaking in the Standard Model, is yet to be discovered. The search for this particle has been going on at the Fermilab Tevatron and is one of the most important tasks for the CERN LHC. The LEP experiments in the past provided vital information on the possible mass range of this particle [9]. The lower bound on the mass is 114.4 GeV/c 2 and an upper bound is ...

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confidence: 99%

QCD threshold corrections to di-lepton and Higgs rapidity distributions beyond N2LO

2007

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“…The anomalous dimension of Konishi is known up to threeloop [4,17,18,19]. As we have done the explicit computation (2.31), we dare to predict Table 1: Particle spectrum in su(2) subsector the four-loop value under the assumption of a valid PWMT-SYM-relationship…”

Section: Degenerate Spectrum and Higher Chargesmentioning

confidence: 99%

“…This, however, appears to be beyond present capability in the perturbative quantum field theory, where the state of the art is at three-loop order [17,18,19].…”

Section: Introductionmentioning

confidence: 96%

Planar plane-wave matrix theory at the four loop order: Integrability without BMN scaling

Fischbacher

Klose

Plefka

2005

J. High Energy Phys.

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We study SU(N ) plane-wave matrix theory up to fourth perturbative order in its large N planar limit. The effective Hamiltonian in the closed su(2) subsector of the model is explicitly computed through a specially tailored computer program to perform large scale distributed symbolic algebra and generation of planar graphs. The number of graphs here was in the deep billions. The outcome of our computation establishes the four-loop integrability of the planar plane-wave matrix model. To elucidate the integrable structure we apply the recent technology of the perturbative asymptotic Bethe ansatz to our model. The resulting S-matrix turns out to be structurally similar but nevertheless distinct to the so far considered long-range spin-chain S-matrices of Inozemtsev, Beisert-Dippel-Staudacher and Arutyunov-Frolov-Staudacher in the AdS/CFT context. In particular our result displays a breakdown of BMN scaling at the four-loop order. That is, while there exists an appropriate identification of the matrix theory mass parameter with the coupling constant of the N = 4 superconformal Yang-Mills theory which yields an eighth order lattice derivative for well separated impurities (naively implying BMN scaling) the detailed impurity contact interactions ruin this scaling property at the four-loop order. Moreover we study the issue of "wrapping" interactions, which show up for the first time at this loop-order through a Konishi descendant length four operator.

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“…where the splitting functions P i j are known to NNLO [31,26]. These describe the different possible parton splittings in the collinear limit, i.e.…”

Section: Non-perturbative Parametersmentioning

confidence: 99%

Status of perturbative QCD calculations for deep-inelastic scattering and related processes

Moch¹

2012

Nuclear Physics B - Proceedings Supplements

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We give a brief overview of the status of perturbative QCD calculations for deep-inelastic scattering. The radiative corrections to the Wilson coefficients are generally available to next-to-next-to-leading order in QCD and we address the accuracy of the strong coupling constant, the parton distributions of the nucleon and the heavy quark masses which is required for precision predictions. We also discuss related processes at hadron colliders such as Higgs production via weak boson fusion which can be described through structure functions of deep-inelastic scattering, building upon an approximate, although very accurate, factorization of the perturbative QCD corrections. Keywords: Deep-inelastic scatteringDeep-inelastic scattering (DIS) and the observed scaling violations have been central to the formulation of Quantum Chromodynamics (QCD) as the gauge theory of the strong interactions [1,2]. Over the decades the available high precision experimental data from lepton-and neutrino scattering off fixed targets at CERN, FNAL and SLAC as well as from electronproton collisions at the HERA collider at DESY have successfully probed QCD in a wide kinematical range. The key observables are inclusive structure functions or differential cross sections which provide the theoretical description of the hard hadronic interactions in the QCD improved parton model. Precision predictions in perturbative QCD rest on the fact that we can separate the sensitivity to dynamics from different scales, i.e., the physics at scale of the nucleon mass from hard highenergy scattering at a large scale Q 2 . In Fig. 1 this is depicted for lepton-proton DIS in the one-boson exchange approximation, see e.g., Ref. [3] for the definitions of the kinematic variables.The factorization at a scale µ allows to express for instance the unpolarized inclusive structure functions

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The three-loop splitting functions in QCD: the singlet case

Cited by 899 publications

References 84 publications

QCD threshold corrections to di-lepton and Higgs rapidity distributions beyond N2LO

QCD threshold corrections to di-lepton and Higgs rapidity distributions beyond N2LO

Planar plane-wave matrix theory at the four loop order: Integrability without BMN scaling

Status of perturbative QCD calculations for deep-inelastic scattering and related processes

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