Charm hadroproduction within k T -factorization approach

In the problem of describing heavy-quark production in high-energy hadron collisions, a comparison is made between the theoretical status and numerical predictions of two approaches, the traditional parton model in the leading order (LO) and the k _T-factorization approach. Basic assumptions underlying relevant calculations are discussed. A very simple gluon structure function and a fixed coupling constant are chosen for the calculations in order to highlight distinctions associated with the use of nonidentical matrix elements in these two approaches. It is shown that, in the k _T-factorization approach, formal LO calculations performed with allowance for the Sudakov form factor include many terms usually treated as next-to-leading-order (NLO) contributions of the traditional parton model (or even contributions next to NLO ones, NNLO).     

Study of scalar meson f 0(980) from B→f 0(980)K * decays

We show how parton distributions unintegrated over the parton transverse momentum, k _t , may be generated, at NLO accuracy, from the known integrated (DGLAP-evolved) parton densities determined from global data analyses. A few numerical examples are given, which demonstrate that sufficient accuracy is obtained by keeping only the LO splitting functions together with the NLO integrated parton densities. However, it is important to keep the precise kinematics of the process, by taking the scale to be the virtuality rather than the transverse momentum, in order to be consistent with the calculation of the NLO splitting functions.     

Estimating the effect of NNLO contributions on global parton analyses

We use the recent estimates of NNLO splitting functions, made by van Neerven and Vogt, to perform exploratory fits to deep inelastic and related hard scattering data. We investigate the hierarchy of parton distributions obtained at LO, NLO and NNLO, and, more important, the stability of the resulting predictions for physical observables. We use the longitudinal structure function and the cross sections for W and Z hadroproduction as examples. For we find relatively poor convergence, with increasing order, at small x; whereas are much more reliably predicted. Received: 7 September 2000 / Published online: 13 November 2000     

Markovian MC simulation of QCD evolution at NLO level with minimum <Emphasis Type="Italic">k</Emphasis><Subscript><Emphasis Type="Italic">T</Emphasis></Subscript>

We present two Monte Carlo algorithms of the Markovian type which solve the modified QCD evolution equations at NLO level. The modifications with respect to the standard DGLAP evolution concern the argument of the strong coupling constant, α _S. We first analyze the z-dependent argument and then the k _T -dependent one. The evolution time variable is identified with the rapidity. The two algorithms are tested to 0.05% precision level. We find that the NLO corrections in the evolution of the parton momentum distributions with k _T -dependent coupling constant are of the order of 10 to 20%, and in the small-x region even up to 30%, with respect to the LO contributions. The project is partly supported by the EU grant MTKD-CT-2004-510126, realized in a partnership with the CERN Physics Department and by the Polish Ministry of Science and Information Society Technologies grant No. 620/E-77/6.PR UE/DIE 188/2005-2008.     

Longitudinal Proton Structure Function at LO and NLO Approximations

The purpose of this paper is to calculate the longitudinal structure function of proton through the well-known equation F _L =F ₂?2xF ₁. To determine this structure function, we need to identify parton distribution functions to find F ₂. In this case, the valon model and DGLAP equations are utilized to obtain the parton distributions. Our calculations are carried out in two approximations LO and NLO. The results at the NLO approximation are in better agreement with the experimental data.     

Factorization scheme and parton distributions in the polarized virtual photon target

We investigate spin-dependent parton distributions in the polarized virtual photon target in perturbative QCD up to the next-to-leading order (NLO). In the case , where is the mass squared of the probe (target) photon, the parton distributions can be predicted completely up to NLO, but they are factorization-scheme dependent. We analyze the parton distributions in six different factorization schemes and discuss their scheme dependence. We study, in particular, the QCD and QED axial anomaly effects on the first moments of the parton distributions to see the interplay between the axial anomalies and factorization schemes. We also show that the factorization-scheme dependence is characterized by the large-x behaviors of the quark distributions in the virtual photon. The gluon distribution is predicted to be the same up to NLO among the six factorization schemes examined. In particular, the first moment of the gluon distribution is found to be factorization-scheme independent up to NLO. Received: 24 January 2001 / Published online: 18 May 2001     

Parton distribution functions at LO,NLO and NNLO with correlated uncertainties between orders

Sets of parton distribution functions (PDFs) of the proton are reported for the leading (LO), next-to-leading (NLO) and next-to-next-to-leading-order (NNLO) QCD calculations. The parton distribution functions are determined with the HERAFitter program using the data from the HERA experiments and preserving correlations between uncertainties for the LO, NLO and NNLO PDF sets. The sets are used to study cross-section ratios and their uncertainties when calculated at different orders in QCD. A reduction of the overall theoretical uncertainty is observed if correlations between the PDF sets are taken into account for the ratio of \(WW\) di-boson to \(Z\) boson production cross sections at the LHC.     

Automation of NLO QCD and EW corrections with <Emphasis Type="BoldSmallCaps">Sherpa</Emphasis> and <Emphasis Type="BoldSmallCaps">Recola</Emphasis>

This publication presents the combination of the one-loop matrix-element generator Recola with the multipurpose Monte Carlo program Sherpa. Since both programs are highly automated, the resulting Sherpa +Recola framework allows for the computation of – in principle – any Standard Model process at both NLO QCD and EW accuracy. To illustrate this, three representative LHC processes have been computed at NLO QCD and EW: vector-boson production in association with jets, off-shell \(\mathrm{Z}\)-boson pair production, and the production of a top-quark pair in association with a Higgs boson. In addition to fixed-order computations, when considering QCD corrections, all functionalities of Sherpa, i.e. particle decays, QCD parton showers, hadronisation, underlying events, etc. can be used in combination with Recola. This is demonstrated by the merging and matching of one-loop QCD matrix elements for Drell–Yan production in association with jets to the parton shower. The implementation is fully automatised, thus making it a perfect tool for both experimentalists and theorists who want to use state-of-the-art predictions at NLO accuracy.     

Dynamical parton distributions of the proton and small-x physics

The perturbative properties of parton distributions generated radiatively from a valence-like input at some low resolution scale are discussed with the aim of explaining the physical aspects underlying the reliability of the predicted distributions in the small-x region. Aspects of higher-twist (shadowing) effects as well as small-x resummations are discussed. Utilizing recent improved data atx?10^?2 and a factorization scheme in which the heavy quarksc, b, ..., arenot entailed among the intrinsic (massless) parton distributions, we readjust our valencelike input and provide parametrizations of the slightly modified dynamical LO and NLO $(\overline {MS} ,DIS)$ predictions for parton distributions.     

The improved nuclear parton distributions

In this paper we propose an improvement of the EKS nuclear parton distributions for the small x region of high energy processes, where the perturbative high parton density effects cannot be disregarded. We analyze the behavior of the ratios and and verify that at small x they are strongly modified when compared to the EKS predictions. The implications of our results for heavy ion collisions in RHIC and LHC are discussed. Received: 18 January 2001 / Revised version: 6 March 2001 / Published online: 3 May 2001     

Multiple parton scattering in nuclei: twist-four nuclear matrix elements and off-forward parton distributions

Multiple parton scatterings inside a large nucleus generally involve higher-twist nuclear parton matrix elements. The gluon bremsstrahlung induced by multiple scattering depends not only on direct parton matrix elements but also on momentum-crossed ones, due to the Landau–Pomeranchuk–Migdal interference effect. We show that both types of twist-four nuclear parton matrix elements can be factorized approximately into the product of twist-two nucleon matrix elements in the limit of extremely large nuclei, A→∞, as assumed in previous studies. Due to the correlative nature of the twist-four matrix elements under consideration, it is actually the off-forward parton distributions that appear naturally in this decomposition, rather than the ordinary diagonal distributions probed in deeply-inelastic scattering. However, we argue that the difference between these two distribution classes is small in certain kinematic regimes. In these regions, the twist-four nuclear parton matrix elements are evaluated numerically and compared to the factorized form for different nuclear sizes within a schematic model of the two-nucleon correlation function. The nuclear size dependence is found to be A^4/3 in the limit of large A, as expected. We find that the factorization is reasonably good when the momentum fraction carried by the gluon field is moderate. The deviation can be more than a factor of 2, however, for small gluon momentum fractions, where the gluon distribution is very large.     

Four jet event shapes in electron-positron annihilation

We report next-to-leading order perturbative QCD predictions of 4 jet event shape variables for the process obtained using the general purpose Monte Carlo EERAD2. This program is based on the known `squared' one loop matrix elements for the virtual parton contribution and squared matrix elements for 5 parton production. To combine the two distinct final states numerically we present a hybrid of the commonly used subtraction and slicing schemes based on the colour antenna structure of the final state which can be readily applied to other processes. We have checked that the numerical results obtained with EERAD2 are consistent with next-to-leading order estimates of the distributions of previously determined four jet-like event variables. We also report the next-to-leading order scale independent coefficients for some previously uncalculated observables; the light hemisphere mass, narrow jet broadening and the 4 jet transition variables with respect to the JADE and Geneva jet finding algorithms. For each of these observables, the next-to-leading order corrections calculated at the physical scale significantly increase the rate compared to leading order (the K factor is approximately 1.5–2). With the exception of the 4 jet transition variables, the published DELPHI data lies well above the predictions. The renormalisation scale uncertainty is still large and in most cases the data prefers a scale significantly smaller than the physical scale. This situation is reminiscent of that for three jet shape variables, and should be improved by the inclusion of power corrections and resummation of large infrared logarithms. Received: 17 November 1998 / Revised version: 26 January 1999 / Published online: 7 April 1999     

Connection formulas between the different QCD orders in application to the valence parton distribution functions

Formulas directly connecting parton distribution functions (PDFs) at the leading (LO) and next to leading (NLO) QCD orders are applied with respect to both unpolarized and polarized valence PDFs. It is shown that the connection formulas allow without any restriction on the allowed Q ² range for the analyzed data to produce improved LO results on valence PDFs, which strongly differ from the standard parametrizations on these quantities, and which could be obtained within the standard approach only by using the data produced at very high Q ² values (that is hardly possible in reality).     

Precision Calculations for the T-Odd Quark Pair Production at the CLIC e+e- Linear Collider

We perform the precision calculations for the e⁺e^-→q_q_(q_q_=u_u_, c_c_, d_d_,s_s_) processes up to the QCD next-to-leading order (NLO) including full weak decays for the final T-odd mirror quarks in the littlest Higgs model with T-parity (LHT) at the Compact Linear Collider (CLIC). We show the dependence of the leading order (LO) and NLO QCD corrected cross sections on the colliding energy √s, and provide the LO and QCD NLO kinematic distributions of final particles. The results show that the LO cross section can be enhanced by the NLO QCD correction and the K-factor increases obviously when the threshold of the on-shell q_q_-pair production approaches the colliding energy √s. The K-factor value varies in the range of 1.04 ～ 1.41 in our chosen parameter space. We find that a simple approximation of multiplying the LO kinematic distribution with the integrated K-factor is not appropriate for precision study of the e⁺e^-→q_q_(q_q_=u_u_, c_c_, d_d_,s_s_) processes, since the NLO QCD corrections are phase space dependent. It is necessary to calculate the differential cross sections including full NLO QCD corrections to get reliable results.     

PDF and scale uncertainties of various DY distributions in ADD and RS models at hadron colliders

In the extra dimension models of ADD and RS we study the dependence of the various parton distribution functions on observables of Drell–Yan processes to NLO in QCD at LHC and Tevatron energies. Uncertainties at LHC due to factorisation scales in going from leading to next-to-leading order in QCD for the various distributions get reduced by about 2.75 times for a μ_F range 0.5Q<μ_F<1.5Q. Further uncertainties arising from the error on the experimental data are estimated using the MRST parton distribution functions.     

Dynamical parton distributions of the nucleon and very small-x physics

Utilizing recent DIS measurements (F_2,L) and data on dilepton and high-E_T jet production we determine the dynamical parton distributions of the nucleon generated radiatively from valence-like positive input distributions at optimally chosen low resolution scales. These are compared with ‘standard’ distributions generated from positive input distributions at some fixed and higher resolution scale. It is shown that up to the next-to-leading order NLO(, DIS) of perturbative QCD considered in this paper, the uncertainties of the dynamical distributions are, as expected, smaller than those of their standard counterparts. This holds true in particular in the presently unexplored extremely small-x region relevant for evaluating ultrahigh energy cross sections in astrophysical applications. It is noted that our new dynamical distributions are compatible, within the presently determined uncertainties, with previously determined dynamical parton distributions.     

The scale dependent nuclear effects in parton distributions for practical applications

The scale dependence of the ratios of parton distributions in a proton of a nucleus A and in the free proton, , is studied within the framework of the lowest order leading-twist DGLAP evolution. By evolving the initial nuclear distributions obtained with the GRV-LO and CTEQ4L sets at a scale , we show that the ratios are only moderately sensitive to the choice of a specific modern set of free parton distributions. We propose that to a good first approximation, this parton distribution set-dependence of the nuclear ratios can be neglected in practical applications. With this result, we offer a numerical parametrization of for all parton flavours i in any , and at any and any for computing cross sections of hard processes in nuclear collisions. Received: 10 August 1998 / Published online: 27 April 1999     

Precise predictions for same-sign W-boson scattering at the LHC

Vector-boson scattering processes are of great importance for the current run-II and future runs of the Large Hadron Collider. The presence of triple and quartic gauge couplings in the process gives access to the gauge sector of the Standard Model (SM) and possible new-physics contributions there. To test any new-physics hypothesis, sound knowledge of the SM contributions is necessary, with a precision which at least matches the experimental uncertainties of existing and forthcoming measurements. In this article we present a detailed study of the vector-boson scattering process with two positively-charged leptons and missing transverse momentum in the final state. In particular, we first carry out a systematic comparison of the various approximations that are usually performed for this kind of process against the complete calculation, at LO and NLO QCD accuracy. Such a study is performed both in the usual fiducial region used by experimental collaborations and in a more inclusive phase space, where the differences among the various approximations lead to more sizeable effects. Afterwards, we turn to predictions matched to parton showers, at LO and NLO: we show that on the one hand, the inclusion of NLO QCD corrections leads to more stable predictions, but on the other hand the details of the matching and of the parton-shower programs cause differences which are considerably larger than those observed at fixed order, even in the experimental fiducial region. We conclude with recommendations for experimental studies of vector-boson scattering processes.     

Parton distributions,small-x physics and the spin structure of the nucleon

Several theoretical aspects in leading (1-loop) and higher (2-loop) order as well as various approaches of extracting leading twist-2 parton distributions from structure function measurements are discussed and summarized. Their implications for the small-x region (x⩽10⁻²) are analyzed and compared with alternative approaches where higher twist contributions (‘fans’) are added to the twist-2 LO terms in the evolution equations. The second part of these lectures deals with longitudinally polarized parton distributions related to the structure functiong ₁, in particular with various scenarios to explain the total spin structure of nucleons, including the gluon anomaly as well. Specific (realistic) tests for discriminating between these alternatives are discussed as well asx-dependent expectations, in particular for neutron targets in connection with the Bjorken sum rule. Furthermore, various theoretical expectations and sum rules for the transverse (chiral-even) structure functiong ₂ are presented and very recent developments of transverse chiral-odd (‘transversity’) distributions are briefly discussed.