QCD Analysis Research Articles

QCD analysis and effective temperature of direct photons in lead-lead collisions at the LHC

We present a systematic theoretical analysis of the ALICE measurement of low-pT direct-photon production in central lead-lead collisions at the LHC with a centre-of-mass energy of sNN=2.76 TeV. Using next-to-leading order of perturbative QCD, we compute the relative contributions to prompt-photon production from different initial and final states and the theoretical uncertainties coming from independent variations of the renormalisation and factorisation scales, the nuclear parton densities and the fragmentation functions. Based on different fits to the unsubtracted and prompt-photon subtracted ALICE data, we consistently find an exponential, possibly thermal, photon spectrum from the quark-gluon plasma (or hot medium) with slope T=304±58 MeV and 309±64 MeV at pT∈[0.8;2.2] GeV and pT∈[1.5;3.5] GeV as well as a power-law (pT−4) behavior for pT>4 GeV as predicted by QCD hard scattering.

Measurement of the muon charge asymmetry in inclusive pp → W + X production at [formula omitted] at CMS and an improved determination of light parton distribution functions

Measurements of the muon charge asymmetry in inclusive pp→WX production at s=7 TeV are presented. The data sample corresponds to an integrated luminosity of 4.7 fb-1 recorded with the CMS detector at the LHC. With a sample of more than twenty million W→μν events, the statistical precision is greatly improved in comparison to previous measurements. These new results provide additional constraints on the parton distribution functions of the proton in the range of the Bjorken scaling variable x from 10-3 to 10-1. These measurements are used together with the cross sections for inclusive deep inelastic ep scattering at HERA in a next-to-leading-order QCD analysis.

Differential cross sections for top pair production at the LHC

We present results of phenomenological studies for top-quark pair production at the LHC at the center of mass energy S=7 TeV. The transverse momentum and rapidity distributions for final-state top quarks are calculated in perturbative QCD at approximate next-to-next-to-leading order O(αs4) by using methods of threshold resummation beyond the leading logarithmic accuracy. The theoretical predictions are obtained by using the computer code Difftop and are compared to recent measurements by the ATLAS and CMS collaborations. Difftop can be employed in the general case of heavy-quark pair production at hadron-hadron colliders and provides a basis for applications in QCD analyses for parton distribution functions determination.

Measurement of Jet Production Properties in pp Collisions with the ATLAS Detector

Several aspects of the jet production in pp collisions have been measured by the ATLAS collaboration using data collected at the LHC. The measurements of the production cross sections of inclusive, di- and three-jet events probe the dynamics of QCD and can constrain the parton proton structure. The cross sections are measured using jets clustered with the anti-kt algorithm with different distance parameters and compared to expectations based on next-to-leading order QCD calculations, corrected for non-perturbative and electroweak effects, as well as to next-to-leading order Monte Carlo simulations. Ratios of inclusive cross sections measured at different centre-of-mass energies allow for reduced experimental and/or theoretical uncertainties. Double-differential dijet and three-jet cross sections have been measured in proton-proton collisions at 7 TeV as a function of di- and three-jet masses and the jet rapidity separation. An NLO QCD analysis of the data indicates constraining power for parton distribution functions of the proton.

Parton Distributions based on a Maximally Consistent Dataset

The choice of data that enters a global QCD analysis can have a substantial impact on the resulting parton distributions and their predictions for collider observables. One of the main reasons for this has to do with the possible presence of inconsistencies, either internal within an experiment or external between different experiments. In order to assess the robustness of the global fit, different definitions of a conservative PDF set, that is, a PDF set based on a maximally consistent dataset, have been introduced. However, these approaches are typically affected by theory biases in the selection of the dataset. In this contribution, after a brief overview of recent NNPDF developments, we propose a new, fully objective, definition of a conservative PDF set, based on the Bayesian reweighting approach. Using the new NNPDF3.0 framework, we produce various conservative sets, which turn out to be mutually in agreement within the respective PDF uncertainties, as well as with the global fit. We explore some of their implications for LHC phenomenology, finding also good consistency with the global fit result. These results provide a non-trivial validation test of the new NNPDF3.0 fitting methodology, and indicate that possible inconsistencies in the fitted dataset do not affect substantially the global fit PDFs.

Proton structure and parton distribution functions from HERA

The H1 and ZEUS collaborations at the electron-proton collider HERA collected e ± p scattering data corresponding to an integrated luminosity of about 1 fb −1 . The data were taken at proton beam energies of 920, 820, 575 and 460 GeV and an electron beam energy of 27.5 GeV, with different electric charges and longitudinal polarisation of the electron beam. Using these data inclusive neutral and charged current deep inelastic cross sections were measured over six orders of magnitude in negative four-momentum-transfer squared, Q 2 , and Bjorken x . A combination of all inclusive cross sections, published by the H1 and ZEUS collaborations at HERA, was performed. Using these combined HERA data and the individual H1 and ZEUS data taken using the polarised electron beams, the proton structure functions F 2 , F γZ 2 , x F γZ 3 and F L were obtained, and scaling violations, electroweak unification, and polarisation effects in the charged current process were demonstrated. The combined cross sections were used as a sole input to QCD analyses at leading, next-to-leading and next-to-next-to-leading orders, providing a new set of parton distribution functions, denoted as HERAPDF2.0. An extension of the analysis by including HERA data on charm and jet production allowed a simultaneous determination of parton distributions and the strong coupling.

A determination of the flavor asymmetric sea quarks in the proton

Using the DGLAP evolution equation with the corrections of parton recombinations, the flavor asymmetric sea quark distributions in the proton are first extracted from the available experimental data with the global QCD analysis method. Comparisons of our predictions with the CTEQ, MRS, and GRV parton distribution functions for sea quarks are presented. Based on the separation of the flavor symmetric and asymmetric sea, the possible relations between strange quark distribution and symmetric light quark distribution are discussed. The results are used to explain the recent HERMES result of the strange quark distribution.

New advances in the statistical parton distributions approach*

The quantum statistical parton distributions approach proposed more than one decade ago is revisited by considering a larger set of recent and accurate Deep Inelastic Scattering experimental results. It enables us to improve the description of the data by means of a new determination of the parton distributions. This global next-to-leading order QCD analysis leads to a good description of several structure functions, involving unpolarized parton distributions and helicity distributions, in terms of a rather small number of free parameters. There are many serious challenging issues. The predictions of this theoretical approach will be tested for single-jet production and charge asymmetry in W ± production in p p and pp collisions up to LHC energies, using recent data and also for forthcoming experimental results.

Final Combined Deep Inelastic Scattering Cross Sections at HERA

The combination is presented of all inclusive deep inelastic scattering cross sections previously published by the H1 and ZEUS collaborations at HERA for neutral and charged current $ep$ scattering for zero beam polarisation. The data were taken at proton beam energies of 920, 820, 575 and 460 GeV and an electron beam energy of 27.5 GeV. The data correspond to an integrated luminosity of about 1 fb$^{-1}$ and span six orders of magnitude in negative four-momentum-transfer squared, $Q^2$, and Bjorken $x$. The correlations of the systematic uncertainties were evaluated and taken into account for the combination. The combined cross sections were input to QCD analyses at leading order, next-to-leading order and at next-to-next-to-leading order, providing a new set of parton distribution functions, called HERAPDF2.0. Additionally, the inclusion of jet-production cross sections made a simultaneous and precise determination of parton distributions and the strong coupling constant possible. Brief highlights of the results are presented.

Non-singlet Q2-evolution by inverse Mellin transform in the analytic perturbation theory

We discuss the application of the analytic approach called the fractional Analytic Perturbation Theory (APT) to the QCD analysis of the non-singlet structure function xF3(x,Q2). The inverse Mellin transform method applyed for the fit of experimental data and for estimation of the Jacobi polynomial method accuracy in extraction of values of the scale parameter ΛQCD and the form of the xF3 structure function. Our estimates give the accuracy of the Jacobi polynomials method for the x-shape of the structure function about 10%, and accuracy for the scale parameter ΛQCD 4%.

Importance of proper renormalization scale-setting for QCD testing at colliders

A primary problem for perturbative QCD analyses is how to set the renormalization scale of the QCD running coupling in order to achieve maximally precise fixed-order predictions for physical observables. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, giving predictions which are independent of the choice of renormalization scheme. The scales of the QCD couplings and the effective number of quark flavors are set order by order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance and all of the the self-consistency conditions derived from the renormalization group......In this brief report, we summarize the results of our recent PMC applications for a number of collider processes, emphasizing their generality and applicability....... These results demonstrate that the application of the PMC systematically eliminates a major theoretical uncertainty for pQCD predictions, thus increasing the sensitivity of the colliders to possible new physics beyond the Standard Model.

Combination of measurements of inclusive deep inelastic $${e^{\pm }p}$$ e ± p scattering cross sections and QCD analysis of HERA data

A combination is presented of all inclusive deep inelastic cross sections previously published by the H1 and ZEUS collaborations at HERA for neutral and charged current $e^{\pm}p$ scattering for zero beam polarisation. The data were taken at proton beam energies of 920, 820, 575 and 460 GeV and an electron beam energy of 27.5 GeV. The data correspond to an integrated luminosity of about 1 fb$^{-1}$ and span six orders of magnitude in negative four-momentum-transfer squared, $Q^2$, and Bjorken $x$. The correlations of the systematic uncertainties were evaluated and taken into account for the combination. The combined cross sections were input to QCD analyses at leading order, next-to-leading order and at next-to-next-to-leading order, providing a new set of parton distribution functions, called HERAPDF2.0. In addition to the experimental uncertainties, model and parameterisation uncertainties were assessed for these parton distribution functions. Variants of HERAPDF2.0 with an alternative gluon parameterisation, HERAPDF2.0AG, and using fixed-flavour-number schemes, HERAPDF2.0FF, are presented. The analysis was extended by including HERA data on charm and jet production, resulting in the variant HERAPDF2.0Jets. The inclusion of jet-production cross sections made a simultaneous determination of these parton distributions and the strong coupling constant possible, resulting in $\alpha_s(M_Z)=0.1183 \pm 0.0009 {\rm(exp)} \pm 0.0005{\rm (model/parameterisation)} \pm 0.0012{\rm (hadronisation)} ^{+0.0037}_{-0.0030}{\rm (scale)}$. An extraction of $xF_3^{\gamma Z}$ and results on electroweak unification and scaling violations are also presented.

Unveiling the proton spin decomposition at a future electron-ion collider

We present a detailed assessment of how well a future Electron-Ion Collider could constrain helicity parton distributions in the nucleon and, therefore, unveil the role of the intrinsic spin of quarks and gluons in the proton's spin budget. Any remaining deficit in this decomposition will provide the best indirect constraint on the contribution due to the total orbital angular momenta of quarks and gluons. Specifically, all our studies are performed in the context of global QCD analyses based on realistic pseudo-data and in the light of the most recent data obtained from polarized proton-proton collisions at BNL-RHIC that have provided evidence for a significant gluon polarization in the accessible, albeit limited range of momentum fractions. We also present projections on what can be achieved on the gluon's helicity distribution by the end of BNL-RHIC operations. All estimates of current and projected uncertainties are performed with the robust Lagrange multiplier technique.

AnQCD: Fortran programs for couplings at complex momenta in various analytic QCD models

We provide three Fortran programs which evaluate the QCD analytic (holomorphic) couplings Aν(Q2) for complex or real squared momenta Q2. These couplings are holomorphic analogs of the powers a(Q2)ν of the underlying perturbative QCD (pQCD) coupling a(Q2)≡αs(Q2)/π, in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2δanQCD), and Massive Perturbation Theory (MPT). The index ν can be noninteger. The provided programs do basically the same job as the Mathematica package anQCD.m published by us previously (Ayala and Cvetič, 2015), but are now written in Fortran. Program summaryProgram title: AanQCDextCatalogue identifier: AEYK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEYK_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 12105No. of bytes in distributed program, including test data, etc.: 98822Distribution format: tar.gzProgramming language: Fortran.Computer: Any work-station or PC where Fortran 95/2003/2008 (gfortran) is running.Operating system: Operating system Linux (Ubuntu and Scientific Linux), Windows (in all cases using gfortran).Classification: 11.1, 11.5.Nature of problem: Calculation of values of the running analytic couplings Aν(Q2;Nf) for general complex squared momenta Q2≡−q2, in three analytic QCD models, where Aν(Q2;Nf) is the analytic (holomorphic) analog of the power (αs(Q2;Nf)/π)ν. Here, Aν(Q2;Nf) is a holomorphic function in the Q2 complex plane, with the exception of the negative semiaxis (−∞,−Mthr2], reflecting the analyticity properties of the spacelike renormalization invariant quantities D(Q2) in QCD. In contrast, the perturbative QCD power (αs(Q2;Nf)/π)ν has singularities even outside the negative semiaxis (Landau ghosts). The three considered models are: Analytic Perturbation theory (APT); Two-delta analytic QCD (2δanQCD); Massive Perturbation Theory (MPT). We refer to Ref. [1] for more details and literature.Solution method: The Fortran programs for FAPT and 2δanQCD models contain routines and functions needed to perform two-dimensional numerical integrations involving the spectral function, in order to evaluate Aν(Q2) couplings. In MPT model, one-dimensional numerical integration involving A1(Q2) is sufficient to evaluate any Aν(Q2) coupling.Restrictions: For unphysical choices of the input parameters the results are meaningless. When Q2 is close to the cut region of the couplings (Q2 real negative), the calculations can take more time and can have less precision.Running time: For evaluation of a set of about 10 related couplings, the times vary in the range t∼101–102 s. MPT requires less time, t∼1–101 s.

Extended Goldberger-Treiman relation in a three-flavor parity doublet model

We study masses and decay widths of positive and negative parity nucleons using a three-flavor parity doublet model, in which we introduce three representations, $\left[({\bf 3} , \bar{{\bf 3}})\oplus (\bar{{\bf 3}} , {\bf 3})\right]$, $\left[({\bf 3} , {\bf 6}) \oplus ({\bf 6}, {\bf 3})\right]$, and $\left[({\bf 8} , {\bf 1}) \oplus ({\bf 1} , {\bf 8})\right]$ of the chiral U$(3)_{\rm L}\times$U$(3)_{\rm R}$ symmetry. We find an extended version of the Goldberger-Treiman relation among the mass differences and the coupling constants for pionic transitions. This relation leads to an upper bound for the decay width of $N(1440) \rightarrow N(939) + \pi$ independently of the model parameters. We perform the numerical fitting of the model parameters and derive several predictions, which can be tested in future experiments or lattice QCD analysis. Furthermore, when we use the axial coupling of the excited nucleons obtained from lattice QCD analyses as inputs, we find that the ground state nucleon $N(939)$ consists of about 80% of $\left[({\bf 3} , {\bf 6}) \oplus ({\bf 6}, {\bf 3})\right]$ component, and that the chiral invariant mass of $N(939)$ is roughly $500$ -- $800$MeV.

QCD analysis of W- and Z-boson production at Tevatron

Recent measurements of the $W$-boson charge asymmetry and of the $Z$-boson production cross sections, performed at the Tevatron collider in Run II by the D0 and CDF collaborations, are studied using the HERAFitter framework to assess their impact on the proton parton distribution functions (PDFs). The Tevatron measurements, together with deep-inelastic scattering data from HERA, are included in a QCD analysis performed at next-to-leading order, and compared to the predictions obtained using other PDF sets from different groups. Good agreement between measurements and theoretical predictions is observed. The Tevatron data provide significant constraints on the $d$-valence quark distribution.

Improved nonsinglet QCD analysis of fixed-target DIS data

Deep inelastic scattering data on F2 structure function obtained by BCDMS, SLAC and NMC collaborations in fixed-target experiments are analyzed in the non-singlet approximation with next-to-next-to-leading-order accuracy. The strong coupling constant is found to be , which is seen to be well compatible with the average world value. The results, obtained in the present paper by carrying out fits similar to what were performed in (B G Shaikhatdenov et al 2010 Phys. Rev. D 81 034008), with the exception for systematic errors in BCDMS data taken into account in a different way, confirm our previous ones derived in that same paper. This study is also meant to at least partially explain differences in the latest predictions for LHC observables, caused by usage of different sets of parton distribution functions obtained by different groups.

Impact of heavy-flavour production cross sections measured by the LHCb experiment on parton distribution functions at low x

The impact of recent measurements of heavy-flavour production in deep inelastic $ep$ scattering and in $pp$ collisions on parton distribution functions is studied in a QCD analysis in the fixed-flavour number scheme at next-to-leading order. Differential cross sections of charm- and beauty-hadron production measured by LHCb are used together with inclusive and heavy-flavour production cross sections in deep inelastic scattering at HERA. The heavy-flavour data of the LHCb experiment impose additional constraints on the gluon and the sea-quark distributions at low partonic fractions $x$ of the proton momentum, down to $x \sim 5 \times 10^{-6}$. This kinematic range is currently not covered by other experimental data in perturbative QCD fits.

How to perform a QCD analysis of DIS in analytic perturbation theory

We apply (Fractional) Analytic Perturbation Theory (FAPT) to the QCD analysis of the nonsinglet nucleon structure function $F_2(x,Q^2)$ in deep inelastic scattering up to the next leading order and compare the results with ones obtained within the standard perturbation QCD. Based on a popular parameterization of the corresponding parton distribution we perform the analysis within the Jacobi Polynomial formalism and under the control of the numerical inverse Mellin transform. To reveal the main features of the FAPT two-loop approach, we consider a wide range of momentum transfer from high $Q^2\sim 100 {\rm GeV}^2$ to low $Q^2\sim 0.3 {\rm GeV}^2$ where the approach still works.

New developments in the statistical approach of parton distributions: Tests and predictions up to LHC energies

The quantum statistical parton distributions approach proposed more than one decade ago is revisited by considering a larger set of recent and accurate Deep Inelastic Scattering experimental results. It enables us to improve the description of the data by means of a new determination of the parton distributions. This global next-to-leading order QCD analysis leads to a good description of several structure functions, involving unpolarized parton distributions and helicity distributions, in a broad range of x and Q2 and in terms of a rather small number of free parameters. There are several challenging issues and in particular the confirmation of a large positive gluon helicity distribution. The predictions of this theoretical approach will be tested for single-jet production and charge asymmetry in W± production in p¯p and pp collisions up to LHC energies, using recent data and also for forthcoming experimental results.