A posteriori inclusion of parton density functions in NLO QCD final-state calculations at hadron colliders: The APPLGRID Project

A method to facilitate the consistent inclusion of cross-section measurements based on complex final-states from HERA, TEVATRON and the LHC in proton parton density function (PDF) fits has been developed. This can be used to increase the sensitivity of LHC data to deviations from Standard Model predictions. The method stores perturbative coefficients of NLO QCD calculations of final-state observables measured in hadron colliders in look-up tables. This allows the posteriori inclusion of parton density functions (PDFs), and of the strong coupling, as well as the a posteriori variation of the renormalisation and factorisation scales in cross-section calculations. The main novelties in comparison to original work on the subject are the use of higher-order interpolation, which substantially improves the trade-off between accuracy and memory use, and a CPU and computer memory optimised way to construct and store the look-up table using modern software tools. It is demonstrated that a sufficient accuracy on the cross-section calculation can be achieved with reasonably small look-up table size by using the examples of jet production and electro-weak boson (Z, W) production in proton-proton collisions at a center-of-mass energy of 14 TeV at the LHC. The use of this technique in PDF fitting is demonstrated in a PDF-fit to HERA data and simulated LHC jet cross-sections as well as in a study of the jet cross-section uncertainties at various centre-of-mass energies

What did HERA teach us about the structure of the proton?

Starting in 2008 the H1 and ZEUS experiments have been combining their data in order to provide the most complete and accurate set of deep-inelastic data as the legacy of HERA. The present review presents these combinations, both published and preliminary, and explores how they have been used to give information on the structure of the proton. The HERAPDF parton distribution functions (PDFs) are presented and compared with other current PDFs and with data from the Tevatron and LHC colliders.Comment: 49 pages, 49 figures, to be published in J.Phys.

The high energy neutrino cross-section in the Standard Model and its uncertainty

Updated predictions are presented for high energy neutrino and antineutrino charged and neutral current cross-sections within the conventional DGLAP formalism of NLO QCD using modern PDF fits. PDF uncertainties from model assumptions and parametrization bias are considered in addition to the experimental uncertainties. Particular attention is paid to assumptions and biases which could signal the need for extension of the conventional formalism to include effects such as ln(1/x) resummation or non-linear effects of high gluon density.Comment: 15 pages, 13 figures, 2 tables (REVTeX4); clarifying comments and link to tabulated cross sections at http://www-pnp.physics.ox.ac.uk/~cooper/neutrino/ added; to appear in JHE

The PDF4LHC21 combination of global PDF fits for the LHC Run III

A precise knowledge of the quark and gluon structure of the proton, encoded by the parton distribution functions (PDFs), is of paramount importance for the interpretation of high-energy processes at present and future lepton-hadron and hadron-hadron colliders. Motivated by recent progress in the PDF determinations carried out by the CT, MSHT, and NNPDF groups, we present an updated combination of global PDF fits: PDF4LHC21. It is based on the Monte Carlo combination of the CT18, MSHT20, and NNPDF3.1 sets followed by either its Hessian reduction or its replica compression. Extensive benchmark studies are carried out in order to disentangle the origin of the differences between the three global PDF sets. In particular, dedicated fits based on almost identical theory settings and input datasets are performed by the three groups, highlighting the role played by the respective fitting methodologies. We compare the new PDF4LHC21 combination with its predecessor, PDF4LHC15, demonstrating their good overall consistency and a modest reduction of PDF uncertainties for key LHC processes such as electroweak gauge boson production and Higgs boson production in gluon fusion. We study the phenomenological implications of PDF4LHC21 for a representative selection of inclusive, fiducial, and differential cross sections at the LHC. The PDF4LHC21 combination is made available via the LHAPDF library and provides a robust, user-friendly, and efficient method to estimate the PDF uncertainties associated to theoretical calculations for the upcoming Run III of the LHC and beyond.Comment: 87 pages, 44 figures, 11 table

Measurement of inclusive D*+- and associated dijet cross sections in photoproduction at HERA

Inclusive photoproduction of D*+- mesons has been measured for photon-proton centre-of-mass energies in the range 130 < W < 280 GeV and a photon virtuality Q^2 < 1 GeV^2. The data sample used corresponds to an integrated luminosity of 37 pb^-1. Total and differential cross sections as functions of the D* transverse momentum and pseudorapidity are presented in restricted kinematical regions and the data are compared with next-to-leading order (NLO) perturbative QCD calculations using the "massive charm" and "massless charm" schemes. The measured cross sections are generally above the NLO calculations, in particular in the forward (proton) direction. The large data sample also allows the study of dijet production associated with charm. A significant resolved as well as a direct photon component contribute to the cross section. Leading order QCD Monte Carlo calculations indicate that the resolved contribution arises from a significant charm component in the photon. A massive charm NLO parton level calculation yields lower cross sections compared to the measured results in a kinematic region where the resolved photon contribution is significant.Comment: 32 pages including 6 figure

Measurement of Jet Shapes in Photoproduction at HERA

The shape of jets produced in quasi-real photon-proton collisions at centre-of-mass energies in the range $134-277$ GeV has been measured using the hadronic energy flow. The measurement was done with the ZEUS detector at HERA. Jets are identified using a cone algorithm in the $\eta - \phi$ plane with a cone radius of one unit. Measured jet shapes both in inclusive jet and dijet production with transverse energies $E^{jet}_T>14$ GeV are presented. The jet shape broadens as the jet pseudorapidity ($\eta^{jet}$) increases and narrows as $E^{jet}_T$ increases. In dijet photoproduction, the jet shapes have been measured separately for samples dominated by resolved and by direct processes. Leading-logarithm parton-shower Monte Carlo calculations of resolved and direct processes describe well the measured jet shapes except for the inclusive production of jets with high $\eta^{jet}$ and low $E^{jet}_T$. The observed broadening of the jet shape as $\eta^{jet}$ increases is consistent with the predicted increase in the fraction of final state gluon jets.Comment: 29 pages including 9 figure

Measurement of the F2 structure function in deep inelastic e+^{+}p scattering using 1994 data from the ZEUS detector at HERA

We present measurements of the structure function \Ft\ in e^+p scattering at HERA in the range 3.5\;\Gevsq < \qsd < 5000\;\Gevsq. A new reconstruction method has allowed a significant improvement in the resolution of the kinematic variables and an extension of the kinematic region covered by the experiment. At \qsd < 35 \;\Gevsq the range in x now spans 6.3\cdot 10^{-5} < x < 0.08 providing overlap with measurements from fixed target experiments. At values of Q^2 above 1000 GeV^2 the x range extends to 0.5. Systematic errors below 5\perc\ have been achieved for most of the kinematic urray, W

Measurement of the Diffractive Cross Section in Deep Inelastic Scattering using ZEUS 1994 Data

The DIS diffractive cross section, $d\sigma^{diff}_{\gamma^* p \to XN}/dM_X$, has been measured in the mass range $M_X < 15$ GeV for $\gamma^*p$ c.m. energies $60 < W < 200$ GeV and photon virtualities $Q^2 = 7$ to 140 GeV$^2$. For fixed $Q^2$ and $M_X$, the diffractive cross section rises rapidly with $W$, $d\sigma^{diff}_{\gamma^*p \to XN}(M_X,W,Q^2)/dM_X \propto W^{a^{diff}}$ with $a^{diff} = 0.507 \pm 0.034 (stat)^{+0.155}_{-0.046}(syst)$ corresponding to a $t$-averaged pomeron trajectory of \bar{\alphapom} = 1.127 \pm 0.009 (stat)^{+0.039}_{-0.012} (syst) which is larger than \bar{\alphapom} observed in hadron-hadron scattering. The $W$ dependence of the diffractive cross section is found to be the same as that of the total cross section for scattering of virtual photons on protons. The data are consistent with the assumption that the diffractive structure function $F^{D(3)}_2$ factorizes according to \xpom F^{D(3)}_2 (\xpom,\beta,Q^2) = (x_0/ \xpom)^n F^{D(2)}_2(\beta,Q^2). They are also consistent with QCD based models which incorporate factorization breaking. The rise of \xpom F^{D(3)}_2 with decreasing \xpom and the weak dependence of $F^{D(2)}_2$ on $Q^2$ suggest a substantial contribution from partonic interactions

Measurement of Elastic ϕ\phi Photoproduction at HERA

The production of $\phi$ mesons in the reaction $e^{+}p \rightarrow e^{+} \phi p$ ($\phi \rightarrow K^{+}K^{-}$) at a median $Q^{2}$ of $10^{-4} \ \rm{GeV^2}$has been studied with the ZEUS detector at HERA. The differential$\phi$photoproduction cross section$d\sigma/dt$has an exponential shape and has been determined in the kinematic range$0.1<|t|<0.5 \ \rm{GeV^2}$and$60 < W < 80 \ \rm{GeV}$. An integrated cross section of$\sigma_{\gamma p \rightarrow \phi p} = 0.96 \pm 0.19^{+0.21}_{-0.18}$$\rm{\mu b}$has been obtained by extrapolating to {\it t} = 0. When compared to lower energy data, the results show a weak energy dependence of both$\sigma_{\gamma p \rightarrow \phi p}$and the slope of the$t$distribution. The$\phi$decay angular distributions are consistent with$s$-channel helicity conservation. From lower energies to HERA energies, the features of$\phi$ photoproduction are compatible with those of a soft diffractive process.Comment: 23 pages, including 6 post script figure