Inclusive D production in $\gamma \gamma$ collisions: including the single-resolved contribution with massive quarks

We have calculated the next-to-leading order cross section for the inclusive production of charm quarks as a function of the transverse momentum p_T and the rapidity in two approaches using massive or massless charm quarks. For the single-resolved cross section we have derived the massless limit from the massive theory. We find that this limit differs from the genuine massless version with factorization by finite corrections. By adjusting subtraction terms we establish a massive theory with subtraction which approaches the massless theory very fast with increasing transverse momentum. With these results and including the equivalent results for the direct cross section obtained previously as well as double-resolved contributions, we calculate the inclusive cross section in collisions using realistic evolved non-perturbative fragmentation functions and compare with recent data from the LEP collaborations ALEPH, L3 and OPAL. We find good agreement. Received: 14 February 2003 / Published online: 5 May 2003     

Measuring the photon fragmentation function at HERA

The production of final state photons in deep inelastic scattering originates from photon radiation off leptons or quarks involved in the scattering process. Photon radiation off quarks involves a contribution from the quark-to-photon fragmentation function, corresponding to the non-perturbative transition of a hadronic jet into a single, highly energetic photon accompanied by some limited hadronic activity. Up to now, this fragmentation function was measured only in electron–positron annihilation at LEP. We demonstrate by a dedicated parton-level calculation that a competitive measurement of the quark-to-photon fragmentation function can be obtained in deep inelastic scattering at HERA. Such a measurement can be obtained by studying the photon energy spectra in γ+(0+1)-jet events, where γ denotes a hadronic jet containing a highly energetic photon (the photon jet). Isolated photons are then defined from the photon jet by imposing a minimal photon energy fraction. For this so-called democratic clustering approach, we study the cross sections for isolated γ+(0+1)-jet and γ+(1+1)-jet production as well as for the inclusive isolated photon production in deep inelastic scattering.     

Inclusive photoproduction of neutral pions in the photon hemisphere at HERA

The inclusive cross section for the photoproduction of neutral pions has been measured as a function of the transverse momentum, rapidity, and Feynman x of the mesons at an average photon–proton centre-of-mass energy of 208 GeV and for photon virtualities below GeV. The measurement extends the range covered by previous charged particle measurements at HERA by two units of rapidity in the photon direction down to a value of in the centre-of-mass frame. The transverse momentum distribution is well described over the whole measured range by a power law ansatz, while an exponential fit falls below the data at transverse momentum values above 1.5 GeV/c. Good agreement with the predictions of the Monte Carlo models PYTHIA and PHOJET is found. In the context of the PYTHIA model the data are inconsistent with large intrinsic transverse momentum values in the photon. Received: 14 June 2000 / Published online: 27 November 2000     

Di-Jet production in photon-photon collisions at \sqrt{s}_{\rm ee}=161 and 172 GeV

Di-jet production is studied in collisions of quasi-real photons radiated by the LEP beams at ee centre-of-mass energies and 172 GeV. The jets are reconstructed using a cone jet finding algorithm. The angular distributions of direct and double-resolved processes are measured and compared to the predictions of leading order and next-to-leading order perturbative QCD. The jet energy profiles are also studied. The inclusive di-jet cross-section is measured as a function of and and compared to next-to-leading order perturbative QCD calculations. The inclusive di-jet cross-section as a function of is compared to the prediction of the leading order Monte Carlo generators PYTHIA and PHOJET. The Monte Carlo predictions are calculated with different parametrisations of the parton distributions of the photon. The influence of the ‘underlying event’ has been studied to reduce the model dependence of the predicted jet cross-sections from the Monte Carlo generators. Received: 15 July 1999 / Published online: 12 August 1999     

Predictions for high-energy real and virtual photon–photon scattering from color dipole BFKL–Regge factorization

High-energy virtual photon–virtual photon scattering can be viewed as an interaction of small size color dipoles from the beam and target photons, which makes scattering at high energies (LEP, LEP200 and NLC) an indispensable probe of the short distance properties of the QCD pomeron exchange. Based on the color dipole representation, we investigate the consequences for the scattering of the incorporation of asymptotic freedom into the BFKL equation which makes the QCD pomeron a series of isolated poles in the angular momentum plane. The emerging color dipole BFKL–Regge factorization allows us to relate in a model-independent way the contributions of each BFKL pole to scattering and DIS off protons. Numerical predictions based on our early works on the color dipole BFKL phenomenology of DIS on protons are in good agreement with the experimental data on the photon structure function and the most recent data on the cross section from the OPAL and L3 experiments at LEP200. We discuss the role of non-perturbative dynamics and predict a pronounced effect of the Regge-factorization breaking due to large unfactorizable non-perturbative corrections to the perturbative vacuum exchange. We comment on the salient features of the BFKL–Regge expansion for scattering including the issue of the decoupling of subleading BFKL poles and the soft plus rightmost hard BFKL pole dominance. Received: 9 January 2001 / Revised version: 25 September 2001 / Published online: 7 December 2001     

Measurement of the bremsstrahlung spectra generated from thick targets with <Emphasis Type="Italic">Z</Emphasis>=2–78 under the impact of 10 keV electrons

We present new experimental data on thick target bremsstrahlung spectra generated from the interaction of energetic electrons with bulk matter. The ‘photon yields’ in terms of double differential cross-sections (DDCS) are measured for pure elements of thick targets: Ti (Z = 22), Ag (Z = 47), W (Z = 74) and Pt (Z = 78) under the impact of 10 keV electrons. Comparison of DDCS obtained from the experimental data is made with those predicted by Monte-Carlo (MC) calculations using PENELOPE code. A close agreement between the experimental data and the MC calculations is found for all the four targets within the experimental error of 16%. Furthermore, the ratios of DDCS of bremsstrahlung photons emitted from Ag, W and Pt with those from Ti as a function of photon energy are examined with a relatively lower uncertainty of about 10% and they are compared with MC calculations. A satisfactory agreement is found between the experiment and the calculations within some normalizing factors. The variations of DDCS as a function of Z and of photon energy are also studied which show that the DDCS vary closely with Z; however, some deviations are observed for ‘tip’ photons emitted from high Z targets.     

LEP Higgs boson searches beyond the standard model and minimum supersymmetric standard model

Ever since the center-of-mass energy was increased in 1995 above the Zℴ resonance, the four LEP experiments (ALEPH, DELPHI, OPAL and L3) have renewed their effort to search for the Higgs boson. Data taking ended in the year 2000 with about 130 pb⁻¹ of data collected per experiment above 206 GeV ine ⁺ e ⁻¹ collisions but the data analysis is still very active. Most recently, the wealth of theoretical models and predictions has stimulated new analyses and model interpretations which go beyond the standard model and minimal supersymmetric standard model. These include the searches for charged Higgs bosons, models with two Higgs field doublets, searches for ‘fermiophobic’ Higgs decay, invisible Higgs boson decays, decay-mode independent searches, and limits on Yukawa and anomalous Higgs couplings. I review the searches done by the four LEP experiments and present the LEP combined results when they exist.     

Off-diagonal helicity density matrix elements for vector mesons produced at LEP

Final state interactions may give origin to non-zero values of the off-diagonal element of the helicity density matrix of vector mesons produced in annihilations, as confirmed by recent OPAL data on and 's. Predictions are given for of several mesons produced at large and small , i.e. collinear with the parent jet; the values obtained for and are in agreement with data. The fragmentation functions of quarks and gluons into photons are studied beyond the Leading Logarithm approximation. We address the nature of the initial conditions of the evolution equation solutions and study problems related to factorization scheme invariance. The possibility of measuring these distributions in LEP experiments is discussed, and a comparison with existing data is made. Received: 15 May 1997 / Published online: 20 February 1998     

High-energy strong interactions: from ‘hard’ to ‘soft’

We discuss the qualitative features of the recent data on multiparticle production observed at the LHC. The tolerable agreement with Monte Carlos based on LO DGLAP evolution indicates that there is no qualitative difference between ‘hard’ and ‘soft’ interactions; and that a perturbative QCD approach may be extended into the soft domain. However, in order to describe the data, these Monte Carlos need an additional infrared cutoff k _min with a value k _min∼2–3 GeV which is not small, and which increases with collider energy. Here we explain the physical origin of the large k _min. Using an alternative model which matches the ‘soft’ high-energy hadron interactions smoothly on to perturbative QCD at small x, we demonstrate that this effective cutoff k _min is actually due to the strong absorption of low k _t partons. The model embodies the main features of the BFKL approach, including the diffusion in transverse momenta, ln k _t , and an intercept consistent with resummed next-to-leading log corrections. Moreover, the model uses a two-channel eikonal framework, and includes the contributions from the multi-Pomeron exchange diagrams, both non-enhanced and enhanced. The values of a small number of physically-motivated parameters are chosen to reproduce the available total, elastic and proton dissociation cross section (pre-LHC) data. Predictions are made for the LHC, and the relevance to ultra-high-energy cosmic rays is briefly discussed. The low x inclusive integrated gluon PDF, and the diffractive gluon PDF, are calculated in this framework, using the parameters which describe the high-energy pp and p[`(p)]p\bar{p} ‘soft’ data. Comparison with the PDFs obtained from the global parton analyses of deep inelastic and related hard scattering data and from diffractive deep inelastic data looks encouraging.     

A NLO calculation of the hadron-jet cross section in photoproduction reactions

We study the photoproduction of large charged hadrons in e p collisions, both for the inclusive case and for the case where a jet in the final state is also measured. Our results are obtained by a NLO generator of partonic events. We discuss the sensitivity of the cross section to the renormalisation and factorisation scales, and to various fragmentation function parametrisations. The possibility to constrain the parton densities in the proton and in the photon is assessed. Comparisons are made with H1 data for inclusive charged hadron production. Received: 25 June 2002 / Published online: 18 October 2002     

Quantum chromodynamics studies at LEP2

Several studies have been made to the hadronic final states in e ⁺ e ⁻ collisions at LEP. Studies of the annihilation process at LEP2 have given rise to results on jet rate, event shape, heavy flavour production, inclusive momentum spectra, Bose-Einstein correlation and colour reconnection effects. Event shape studies have given rise to accurate determination of the strong coupling constant α _s using O (α _s ² ) with resummed leading and next-to-leading log calculation and also with power law corrections. Studies of 2-photon processes have yielded results on γγ cross-section, heavy flavour production, photon structure function and γ*γ* scattering.     

Heavy quark and quarkonium production at CERN LEP2: <Emphasis Type="Italic">k</Emphasis><Subscript>T</Subscript>-factorization versus data

We present calculations of heavy quark and quarkonium production at CERN LEP2 in the k _T-factorization QCD approach. Both direct and resolved photon contributions are taken into account. A conservative error analysis is performed. The unintegrated gluon distribution in the photon is obtained from the full CCFM evolution equation. The traditional color-singlet mechanism to describe the non-perturbative transition of a -pair into a final quarkonium is used. Our analysis covers the polarization properties of heavy quarkonia at moderate and large transverse momenta. We find that the total and differential open charm production cross sections are consistent with the recent experimental data taken by the L3, OPAL and ALEPH collaborations. At the same time the DELPHI data for the inclusive production exceed our predictions, but experimental uncertainties are too large to claim a significant inconsistency. The bottom production in photon-photon collisions at CERN LEP2 is hard to explain within the k _T-factorization formalism.Received: 22 December 2004, Revised: 15 February 2005, Published online: 12 April 2005     

Wigner function and Bell’s inequalities for even and odd coherent states

The Wigner function and the symplectic tomogram of an entangled quantum state, which is a superposition of the photon’s coherent states (even and odd coherent states), is studied. Photon statistics and violation of Bell’s inequality for the photon state are discussed.     

Inclusive photoproduction of <Emphasis Type="Italic">D</Emphasis><Superscript>*±</Superscript>-mesons at next-to-leading order in the general-mass variable-flavor-number scheme

We discuss the inclusive production of D ^*±-mesons in γ p collisions at DESY HERA, based on a calculation at next-to-leading order in the general-mass variable-flavor-number scheme. In this approach, subtraction is applied in such a way that large logarithmic corrections are resummed in universal parton distribution and fragmentation functions and finite-mass terms are taken into account. We present detailed numerical results for a comparison with data obtained at HERA and discuss various sources of theoretical uncertainties.     

Measurement of the quark to photon fragmentation function through the inclusive production of prompt photons in hadronic {\rm Z^0} decays

The inclusive production of prompt photons with energy above 10 GeV is measured using the OPAL detector in hadronic decays at LEP. Minimal isolation cuts were imposed upon the prompt photons. The production rate and energy spectrum of prompt photons are found to be in agreement with QCD predictions for the quark-to-photon fragmentation function. Received: 17 July 1997     

Color confining parton model for heavy quarkonium decay

We present a gluon jet model for the heavy quarkonium decay incorporating the color neutralization mechanism. Postulating that final hadrons are produced from the color singlet quark-antiquark pair originated each from different gluons, we formulate the production mechanism of hadrons from gluons explicitly. The fragmentation function thus obtained can describe the hadron production not only in the fragmentation region but also in the central one owing to the usage of the Sudakov variables. The result of the average charged multiplicity from Υ(9.46) is in reasonable agreement with the data, in contrast to the naive estimates. Furthermore, the inclusive momentum and multiplicity distributions are discussed.     

Constraints on the Z-Z′ mixing angle from data measured for the process e+e? → W+W? at the LEP2 collider

An analysis of effects induced by new neutral gauge Z′ bosons was performed on the basis of data from the OPAL, DELPHI, ALEPH, and L3 experiments devoted to measuring differential cross sections for the process of the annihilation production of pairs of charged gauge W ^± bosons at the LEP2 collider. By using these experimental data, constraints on the Z′-boson mass and on the angle of Z-Z′ mixing were obtained for a number of extended gauge models.     

Azimuthal correlations with high-pT multi-hadron cluster triggers in Au+Au collisions at ?{sNN } \sqrt {s_{NN} } = 200 GeV from STAR

Di-hadron correlation measurements have been used to probe di-jet production in heavy ion collisions at RHIC. A strong suppression of the away-side high-p _T yield in these measurements is direct evidence that high-p _T partons lose energy as they traverse the strongly interacting medium. However, since the momentum of the trigger particle is not a good measure of the jet energy, azimuthal di-hadron correlations have limited sensitivity to the shape of the fragmentation function. We explore the possibility to better constrain the initial parton energy by using clusters of multiple high-p _T hadrons in a narrow cone as the ‘trigger particle’ in the azimuthal correlation analysis. We present first results from this analysis of multi-hadron triggered correlated yields in Au+Au collisions at $ \sqrt {s_{NN} } $ \sqrt {s_{NN} } = 200 GeV from STAR. The results are compared with measurements in d + Au collisions and Pythia calculations, and the implications for energy loss and jet fragmentation are discussed.     

The components of the \gamma^* \gamma^* cross section

We extend our previous treatment of the p cross section based on Gribov's hypothesis to the case of photon–photon scattering. With the aid of two parameters, determined from the experimental data, we separate the interactions into two categories corresponding to short (“soft”) and long (“hard”) distance processes. The photon–photon cross section thus receives contributions from three sectors, soft–soft, hard–hard and hard–soft. The additive quark model is used to describe the soft–soft sector, pQCD the hard–hard sector, while the hard–soft sector is determined by relating it to the system. We calculate and display the behaviour of the total photon–photon cross section and its various components and polarizations for different values of energy and virtuality of the two photons, and discuss the significance of our results. Received: 12 January 2000 / Published online: 6 April 2000     

Measurement of the low-x behaviour of the photon structure function F_2^\gamma

The photon structure function has been measured using data taken by the OPAL detector at centre-of-mass energies of 91 GeV, 183 GeVand 189 \GeV, in ranges of 1.5–30.0 GeV (LEP1), and 7.0–30.0 GeV (LEP2), probing lower values of x than ever before. Since previous OPAL analyses, new Monte Carlo models and new methods, such as multi-variable unfolding, have been introduced, reducing significantly the model dependent systematic errors in the measurement. The results do not conclusively prove, but are completely consistent with, the presence of a rise in at low-x as expected from QCD. Received: 9 June 2000 / Published online: 13 November 2000