Order In Quantum Chromodynamics Research Articles

Factorisation and Local Subtraction of Infrared Divergences for QCD processes

We review a recently proposed subtraction procedure at next-to- and next-to-next- to-leading order in quantum chromodynamics (QCD), based on the introduction of a set of minimal, local and analytically integrable counterterms. We also provide an operator definition for the counterterms by investigating the factorisation properties of a generic massless virtual amplitude. Our local, analytic scheme is designed for massless final state radiation only, but its main features are extensible to initial state radiation.

Measurement of the cross section for $\text{t}\bar{\text{t}}$ production with additional jets and b jets in pp collisions at $\sqrt{s}=$ 13 TeV

Measurements of the cross section for the production of top quark pairs in association with a pair of jets from bottom quarks $ \left({\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{b}\overline{\mathrm{b}}}\right) $ and in association with a pair of jets from quarks of any flavor or gluons $ \left({\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{jj}}\right) $ and their ratio are presented. The data were collected in proton-proton collisions at a center-of-mass energy of 13 TeV by the CMS experiment at the LHC in 2016 and correspond to an integrated luminosity of 35.9 fb$^{−1}$. The measurements are performed in a fiducial phase space and extrapolated to the full phase space, separately for the dilepton and lepton+jets channels, where lepton corresponds to either an electron or a muon. The results of the measurements in the fiducial phase space for the dilepton and lepton+jets channels, respectively, are $ {\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{jj}} $ = 2.36±0.02 (stat)±0.20 (syst) pb and 31.0±0.2 (stat)±2.9 (syst) pb, and for the cross section ratio 0.017 ± 0.001 (stat) ± 0.001 (syst) and 0.020 ± 0.001 (stat) ± 0.001 (syst). The values of $ {\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{b}\overline{\mathrm{b}}} $ are determined from the product of the $ {\sigma}_{\mathrm{t}\overline{\mathrm{t}}\mathrm{jj}} $ and the cross section ratio, obtaining, respectively, 0.040±0.002 (stat)±0.005 (syst) pb and 0.62±0.03 (stat)±0.07 (syst) pb. These measurements are the most precise to date and are consistent, within the uncertainties, with the standard model expectations obtained using a matrix element calculation at next-to-leading order in quantum chromodynamics matched to a parton shower.[graphic not available: see fulltext]

NLO QCD corrections to inclusive charmonium and Bc meson production in W+ decays

We calculate the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to inclusive processes $W^+\to J/\psi(\eta_c)+c+\bar{s}+X$ and $W^+\to B_c(B_c^{*})+b+\bar{s}+X$ in the framework of nonrelativistic QCD (NRQCD) factorization formalism. Result indicates that the NLO corrections are significant, and the uncertainties in theoretical predictions with NLO corrections are greatly reduced. The charmonium and $B_c$ meson yielding rates at the Large Hadron Collider (LHC) are given.

Measurements of differential Z boson production cross sections in proton-proton collisions at sqrt{s} = 13 TeV

Measurements are presented of the differential cross sections for Z bosons produced in proton-proton collisions at sqrt{s} = 13 TeV and decaying to muons and electrons. The data analyzed were collected in 2016 with the CMS detector at the LHC and correspond to an integrated luminosity of 35.9 fb−1. The measured fiducial inclusive product of cross section and branching fraction agrees with next-to-next-to-leading order quantum chromodynamics calculations. Differential cross sections of the transverse momentum pT, the optimized angular variable {phi}_{eta}^{ast } , and the rapidity of lepton pairs are measured. The data are corrected for detector effects and compared to theoretical predictions using fixed order, resummed, and parton shower calculations. The uncertainties of the measured normalized cross sections are smaller than 0.5% for {phi}_{eta}^{ast } < 0.5 and for {p}_{mathrm{T}}^{mathrm{Z}} < 50 GeV.

Forward-backward asymmetry of Drell–Yan lepton pairs at 14 TeV center-of-mass energy

In this paper, fiducial cross-sections of lepton pairs with opposite charge via Z → l+ l- (l± = μ±, e±) are calculated at a center-of-mass energy of 14 TeV by applying different transverse momentum selections to evaluate their impact on the production cross-section as well as the differential cross-section of Z bosons in terms of lepton pseudorapidity. The predictions are computed by next-to-next-to-leading order quantum chromodynamics including next-to-leading order electroweak corrections. Forward-backward asymmetry prediction for the Drell?Yan production in proton-proton collision is further calculated at 14 TeV using HERAPDF2.0, MMHT2014, NNPDF3.1, and CT14 parton distribution function models. Then 14 TeV QCD predictions of forward-backward asymmetry are presented as a function of dilepton mass for four different Z boson rapidity regions.

Impact of LHCb data on the PDFs from H1 and ZEUS Collaborations

This Next-to-Leading Order (NLO) Quantum Chromo Dynamics (QCD) analysis attempts to investigate the impact of LHCb charm and beauty production data in pp collisions at s=7TeV on the Parton Distribution Functions (PDFs) extracted from H1 and ZEUS collaboration data sets. We show adding the LHCb charm and beauty production data on the H1 and ZEUS combined data sets reduces the uncertainty bands of partonic distributions and improve the relative fit-quality up to 4.0 %.

Detailed k-Factor Studies Using Inclusive Production of W Bosons in pp Collisions

The theoretical k-Factor describes the difference between leading and higher order cross sections and its proper usage has a crucial importance for theoretical predictions. In this paper, three different ways are considered to define the k-Factor of W bosons at $$\sqrt s $$ = 14 TeV in proton-proton collisions. First, we calculate k-Factors using inclusive W± boson leading order (LO), next-toleading order (NLO) and next-to-next-to-leading order (NNLO) quantum chromodynamics (QCD) cross sections with LO, NLO, NNLO parton distribution function (PDF) models, respectively. The second approach used is the calculation of k-Factors based on LO, NLO and NNLO QCD cross sections with the NNLO PDF model. The last method used here is the calculation of k-Factors using the LO QCD cross section with LO, NLO and NNLO PDF models. We further investigated the dependencies of the k-Factor on the renormalization (μR) and the factorization (μF) scales, the strong coupling constant (α s ), the charges of W boson and the collision energy of protons in a range of 7 to 100 TeV.

The Matrix Element Method at next-to-leading order QCD for hadronic collisions: single top-quark production at the LHC as an example application

Recently, a general algorithm to extend the Matrix Element Method (MEM) by taking into account next-to-leading-order (NLO) corrections in quantum chromodynamics (QCD) has been presented. In this article, the algorithm is applied to the most general case that coloured partons are encountered in the initial as well as the final state. This represents a substantial extension compared to previous work. As a concrete example, the production of single top quarks at the LHC is studied. We present in detail the generation of unweighted events following the NLO predictions. By treating these events as the result of a toy experiment, we show the first proof-of-principle application of the Matrix Element Method at NLO QCD for hadronic jet production. As an illustration, we study the determination of the top-quark mass. We find that — apart from elevating the powerful MEM to a sound theoretical foundation at NLO — the inclusion of the NLO corrections can lead to sizeable effects compared to the Matrix Element Method relying on leading-order predictions only. Furthermore, we find that the incorporation of the NLO corrections is mandatory to obtain reliable estimates of the theoretical uncertainties. In addition, this work shows that measuring the top-quark mass using the MEM in single top-quark production offers an interesting alternative to mass measurements in top-quark pair production.

Measurement of the B\xb1 production cross-section in pp collisions at sqrt{s}=7 and 13 TeV

The production of B± mesons is studied in pp collisions at centre-of-mass energies of 7 and 13 TeV, using B± → J/ψ K± decays and data samples corresponding to 1.0 fb−1 and 0.3 fb−1, respectively. The production cross-sections summed over both charges and integrated over the transverse momentum range 0 < pT < 40 GeV/c and the rapidity range 2.0 < y < 4.5 are measured to beσpp→B±X,s=7TeV=43.0±0.2±2.5±1.7μb,σpp→B±X,s=13TeV=86.6±0.5±5.4±3.4μb,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ \\begin{array}{l}\\sigma \\left( pp\\to {B}^{\\pm }X,\\sqrt{s}=7\\kern0.5em \\mathrm{T}\\mathrm{e}\\mathrm{V}\\right)=43.0\\pm 0.2\\pm 2.5\\pm 1.7\\kern0.5em \\upmu \\mathrm{b},\\hfill \\\\ {}\\sigma \\left( pp\\to {B}^{\\pm }X,\\sqrt{s}=13\\kern0.5em \\mathrm{T}\\mathrm{e}\\mathrm{V}\\right)=86.6\\pm 0.5\\pm 5.4\\pm 3.4\\kern0.5em \\upmu \\mathrm{b},\\hfill \\end{array} $$\\end{document}where the first uncertainties are statistical, the second are systematic, and the third are due to the limited knowledge of the B± → J/ψ K± branching fraction. The ratio of the cross-section at 13 TeV to that at 7 TeV is determined to be 2.02 ± 0.02 (stat) ± 0.12 (syst). Differential cross-sections are also reported as functions of pT and y. All results are in agreement with theoretical calculations based on the state-of-art fixed next-to-leading order quantum chromodynamics.

Decoupling the NLO-coupled QED⊗QCD, DGLAP evolution equations, using Laplace transform method

We analytically solved the QED[Formula: see text]QCD-coupled DGLAP evolution equations at leading order (LO) quantum electrodynamics (QED) and next-to-leading order (NLO) quantum chromodynamics (QCD) approximations, using the Laplace transform method and then computed the proton structure function in terms of the unpolarized parton distribution functions. Our analytical solutions for parton densities are in good agreement with those from CT14QED [Formula: see text] (Ref. 6) global parametrizations and APFEL (A PDF Evolution Library) [Formula: see text] (Ref. 4). We also compared the proton structure function, [Formula: see text], with the experimental data released by the ZEUS and H1 collaborations at HERA. There is a nice agreement between them in the range of low and high [Formula: see text] and [Formula: see text].

NLO QCD corrections to ηc+hc(1P)/ψ1,2(1D) production at B-factories**Supported by Ministry of Science and Technology of the People's Republic of China (2015CB856703) and National Natural Science Foundation of China (11175249, 11375200)

We calculate the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to double charmonium production processes e+e− → γ* → ηc+hc(1P)/ψ1,2(1D) within the non-relativistic QCD (NRQCD) factorization framework. We find that the corrections to ηc+hc(1P) production are positive, while those to ηc+ψ1,2(1D) are negative. Unlike the J/ψ+ηc case, all the corrections here are not large. Uncertainties in the renormalization scale, quark mass and running energy of center-of-mass are discussed, and the scale dependence of these processes is found to be greatly reduced with the NLO QCD corrections.

The 3-loop non-singlet heavy flavor contributions to the structure function [formula omitted] at large momentum transfer

We calculate the massive flavor non-singlet Wilson coefficient for the heavy flavor contributions to the polarized structure function g1(x,Q2) in the asymptotic region Q2≫m2 to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable N and the momentum fraction x, and derive heavy flavor corrections to the Bjorken sum-rule. Numerical results are presented for the charm quark contribution. Results on the structure function g2(x,Q2) in the twist-2 approximation are also given.

HZγ production at 14 TeV LHC in next-to-leading order QCD

We investigate the process at the Large Hadron Collider (LHC) up to the quantum chromodynamics (QCD) next-to-leading order (NLO), and discuss the kinematic distributions of the final products after on-shell Higgs and Z-boson decays by adopting the narrow width approximation. The dependence of the leading order (LO) and the QCD NLO corrected integrated cross-sections on the factorization/renormalization scale is studied. Our results show that the LO integrated cross-section and kinematic distributions are significantly enhanced by the NLO QCD corrections, and the NLO QCD K-factor strongly depends on the observables and phase space. We conclude that in precision experimental data analysis for probing the coupling, we should consider the NLO QCD corrections and put proper constraints on the lepton-pair invariant mass to reduce the background.

TMD parton distributions based on three-body decay functions in NLL order of QCD

Three-body decay functions in space-like parton branches are implemented to evaluate transverse-momentum-dependent (TMD) parton distribution functions in the next-to-leading logarithmic (NLL) order of quantum chromodynamics (QCD). Interference contributions due to the next-to-leading order contribution are taken into account for the evaluation of the transverse momenta in initial state parton radiations. Some properties of the decay functions are also examined. As an example, we compare our results with an algorithm proposed in Ref.1), in which a transverse momentum distributions are evaluated at the last step of parton evolutions.

QCD NLO corrections to inclusiveBc*production inZ0decays

We calculate the next-to-leading order(NLO) quantum chromodynamics(QCD) corrections to the inclusive process of $Z_0 \rightarrow B^*_c+\bar{c}+b$ under the non-relativistic QCD(NRQCD) factorization scheme. Technical details about contributions from vector and axial-vector currents in dimensional regularization scheme are discussed. Numerical calculation shows that the NLO correction enhances the leading-order decay width by about 50%, and the dependence on renormalization scale $\mu$ is reduced. The uncertainties induced by quark masses and the renormalization scale $\mu$ are also analyzed.

Measurement of differential cross sections for isolated photon pairs in pp collisions at [formula omitted

The summary of the measurement of differential cross sections for the production of a pair of isolated photons in proton-proton collisions at s=7TeV [CMS Collaboration, CMS-SMP-13-001 (2013), CERN-PH-EP-2014-067 (2014)] is presented. The data sample corresponds to an integrated luminosity of 5.0fb−1 collected with the CMS detector. A data-driven isolation template method is used to extract the prompt diphoton yield. The cross section is measured differentially as a function of different kinematic variables of the diphoton system and compared to theoretical predictions at leading, next-to-leading and next-to-next-to-leading order in quantum chromodynamics (QCD).

Standard Model measurements with the ATLAS detector

Various Standard Model measurements have been performed in proton-proton collisions at a centre-of-mass energy of √ s = 7 and 8 TeV using the ATLAS detector at the Large Hadron Collider. A review of a selection of the latest results of electroweak measurements, W/Z production in association with jets, jet physics and soft QCD is given. Measurements are in general found to be well described by the Standard Model predic- tions. been performed in proton-proton collisions at a centre-of-mass energy of √ s = 7 and 8 TeV using the ATLAS detector (1) at the LHC. These allow for precision tests of the electroweak dynamics of the Standard Model, but also challenge next-to-next-to-leading-order predictions. Differences between measurements and Standard Model predictions could prove evidence for new phenomena. Recent Quantum Chromo Dynamics (QCD) results highlight the importance of precision QCD measurements for improving state-of-the-art theoretical tools and searching for new physics. A selection of the latest results of electroweak measurements, W/Z production in association with jets, jet physics and soft QCD is reported. These consist of the measurement of the WW cross section, first evidence of the electroweak production of W ± W ± jj , and electroweak Zj jproduction. Measurements are in general found to be well described by the Standard Model predictions. Measurements of differential produc- tion cross sections of a Z boson in association with b-jets, the production cross section of the W boson in association with jets as well as the ratio of the production cross sections for W and Z bosons in association with jets are presented. The measurements are compared to next-to-leading-order pertur- bative QCD calculations and to predictions from different Monte Carlo (MC) generators implement- ing leading-order matrix elements supplemented by parton showers. Various inclusive, differential or double differential jet measurements are presented. The dominant experimental uncertainty on these measurements comes from the jet energy scale. Next-to-leading order QCD calculations corrected to account for non-perturbative effects are compared to the measurements. A good agreement between the data and the theoretical predictions based on most of the global parton distribution functions is found over the full kinematic range, covering almost seven orders of magnitude in the measured cross-section values. A measurement of charged-particle distributions sensitive to the properties of

Top quark forward-backward asymmetry in e+ e- annihilation at next-to-next-to-leading order in QCD.

We report on a complete calculation of electroweak production of top-quark pairs in e+ e- annihilation at next-to-next-to-leading order in quantum chromodynamics. Our setup is fully differential in phase space and can be used to calculate any infrared-safe observable. Especially we calculated the next-to-next-to-leading-order corrections to the top-quark forward-backward asymmetry and found sizable effects. Our results show a large reduction of the theoretical uncertainties in predictions of the forward-backward asymmetry, and allow for a precision determination of the top-quark electroweak couplings at future e+ e- colliders.

Electroweak production of top-quark pairs ine+e−annihilation at NNLO in QCD: The vector current contributions

We report on a calculation of the vector current contributions to the electroweak production of top quark pairs in $e^+e^-$ annihilation at next-to-next-to-leading order in Quantum Chromodynamics. Our setup is fully differential and can be used to calculate any infrared-safe observable. The real emission contributions are handled by a next-to-next-to-leading order generalization of the phase-space slicing method. We demonstrate the power of our technique by considering its application to various inclusive and exclusive observables.

Precise QCD predictions for the production of Higgs + jet final states

We compute the cross section and differential distributions for the production of a Standard Model Higgs boson in association with a hadronic jet to next-to-next-to-leading order in quantum chromodynamics (QCD). In Higgs boson studies at the LHC, final states containing one jet are a dominant contribution to the total event rate, and their understanding is crucial for improved determinations of the Higgs boson properties. We observe substantial higher order corrections to transverse momentum spectra and rapidity distributions in Higgs-plus-one-jet final states. Their inclusion stabilises the residual theoretical uncertainty of the predictions around 9%, thereby providing important input to precision studies of the Higgs boson.