Measurements of inclusive and exclusive particle production at ZEUS

Charged particle production, scaled momentum distributions of identified particles, K _s ⁰ and Λ, and charged particles for dijet events have been measured in ep scattering with the ZEUS detector. The evolution of these distributions with the photon virtuality, Q ², are studied in the kinematic region 10 < Q ² < 40000 GeV². The calculations reproduce the measured distributions reasonably well.     

Measurement of dijet production at low <Emphasis Type="Italic">Q</Emphasis><Superscript>2</Superscript> at HERA

Triple differential dijet cross sections in interactions are presented in the region of photon virtualities 2 < Q ² < 80 GeV², inelasticities 0.1 < y < 0.85, jet transverse energies E ^* _{T 1} > 7 GeV, E ^* _{T 2} > 5 GeV, and pseudorapidities . The measurements are made in the centre-of-mass frame, using an integrated luminosity of 57 pb^-1. The data are compared with NLO QCD calculations and LO Monte Carlo programs with and without a resolved virtual photon contribution. NLO QCD calculations fail to describe the region of low Q ² and low jet transverse energies, in contrast to a LO Monte Carlo generator which includes direct and resolved photon interactions with both transversely and longitudinally polarised photons. Initial and final state parton showers are tested as a mechanism for including higher order QCD effects in low E _T jet production.Received: 13 January 2004, Revised: 21 July 2004, Published online: 18 August 2004     

Gluon distributions in real and virtual photon and the photon structure function

Gluon distributions in real and virtual photons are calculated using evolution equations in the NLO approximation. The quark distributions in the photon determined on the basis of the QCD sum rule approach in [1] are taken as an input. It is shown that gluon distribution in the photon can be reliably determined up tox=0.03÷0.05, much lower than the corresponding values in the case of quark distributions. Two variants of the calculations are considered: (1) it is assumed that there are no intrinsic gluons in the photon at some low normalization pointQ ²=Q ₀ ² ∼1GeV²; (2) it is assumed that gluonic content of the photon at lowQ ₀ ² is described by gluonic content of vector mesonsρ, ω, ϕ. The gluon distributions in these two variants appear to be different. This fact permits one to clarify the origin of nonperturbative gluonic content of the photon by comparing the results with experiment. Structure functionsF ₂(x) for real and virtual photon are calculated and it is shown that in the regionx≥0.2 where QCD approach is valid, there is a good agreement with experiment.     

Studies of the neutron spin structure at Jefferson Lab

The polarized ³He program of Hall A at Jefferson Lab will be described. Results on the generalized Gerasimov-Drell-Hearn integral for the neutron in a Q² range between 0.02 GeV²/c² < Q² < 0.9 GeV²/c² will be presented. Preliminary results of the virtual photon asymmetry A₁ⁿ(x, Q²) and the spin structure function g₂ⁿ(x, Q²) at large values of Bjorken x and low Q², respectively, will be discussed.Received: 1 November 2002, Published online: 15 July 2003PACS: 11.55.Hx Sum rules - 13.40.Gp Electromagnetic form factors - 13.88.+e Polarization in interactions and scattering - 29.25.Pj Polarized and other targets     

Probing the photon at γe-colliders

We investigate the feasibility of studying the photon structure function at a e-collider. We show that the deep inelastic probe of the real photon by a highly virtual photon in such a collider will extend significantly thex andQ ² range presently accessible ate ⁺ e ^– colliders. In addition, we study the production of large transverse momentum dijet final states to determine the sensitivity of these cross sections to different parametrisations of the quark and gluon distributions in the photon.     

Tests of QCD factorisation in the diffractive production of dijets in deep-inelastic scattering and photoproduction at HERA

Measurements are presented of differential dijet cross sections in diffractive photoproduction (Q²<0.01 GeV²) and deep-inelastic scattering processes (DIS, 4<Q²<80 GeV²). The event topology is given by ep→eXY, in which the system X, containing at least two jets, is separated from a leading low-mass baryonic system Y by a large rapidity gap. The dijet cross sections are compared with NLO QCD predictions based on diffractive parton densities previously obtained from a QCD analysis of inclusive diffractive DIS cross sections by H1. In DIS, the dijet data are well described, supporting the validity of QCD factorisation. The diffractive DIS dijet data are more sensitive to the diffractive gluon density at high fractional parton momentum than the measurements of inclusive diffractive DIS. In photoproduction, the predicted dijet cross section has to be multiplied by a factor of approximately 0.5 for both direct and resolved photon interactions to describe the measurements. The ratio of measured dijet cross section to NLO prediction in photoproduction is a factor 0.5±0.1 smaller than the same ratio in DIS. This suppression is the first clear observation of QCD hard scattering factorisation breaking at HERA. The measurements are also compared to the two soft colour neutralisation models SCI and GAL. The SCI model describes diffractive dijet production in DIS but not in photoproduction. The GAL model fails in both kinematic regions.     

MREI‐model calculations of Raman‐active modes in layered mixed crystals TiS2−xSex(0≤x≤2)

A modified random‐element isodisplacement model has been developed and used to calculate the concentration dependence of the wavenumbers of Raman‐active modes in mixed crystal system, TiS_2−xSe_x(0≤x≤2). Earlier theoretical work, based on the Jaswal model, predicted a phase transition in this system on cooling up to 125 K temperature for the composition x ≥ 1.2. But recently reported resistivity measurements did not find the existence of any phase transition for a composition x < 1.4 on cooling. Our calculations show these findings and give remarkably better fitting to Raman data. The estimated values of the force constants are found to lie generally in the range 10⁵–10⁶ amu cm⁻². Copyright © 2007 John Wiley & Sons, Ltd.     

Diffractive photoproduction of dijets in ep collisions at HERA

Diffractive photoproduction of dijets was measured with the ZEUS detector at the ep collider HERA using an integrated luminosity of 77.2 pb^-1. The measurements were made in the kinematic range Q² < 1 GeV², 0.20<y<0.85 and x_IP<0.025, where Q² is the photon virtuality, y is the inelasticity and x_IP is the fraction of the proton momentum taken by the diffractive exchange. The two jets with the highest transverse energy, E_T ^jet, were required to satisfy E_T ^jet>7.5 and 6.5 GeV, respectively, and to lie in the pseudorapidity range -1.5<η^jet<1.5. Differential cross sections were compared to perturbative QCD calculations using available parameterisations of diffractive parton distributions of the proton.     

Spin structure function of deuteron g<Subscript>1</Subscript><Superscript>d</Superscript> from COMPASS

New results on the longitudinal inclusive spin asymmetry A ₁ ^d in the range 1 < Q ² < 100(GeV/c)^2 and 0.004 < x < 0.7 are presented. From these results we derive the spin-dependent structure function g ₁ ^d which we use to evaluate the scale-invariant flavor-singlet axial charge . The contribution of the measured region is evaluated by a QCD fit of the world data. The data were obtained by the COMPASS experiment at CERN using a 160GeV polarized muon beam scattered off a large double-cell polarized ⁶LiD target. The results are in agreement with those from previous experiments and improve considerably the statistical accuracy in the region x < 0.03.     

Dijet production in diffractive deep inelastic scattering at HERA

The production of dijets in diffractive deep inelastic scattering has been measured with the ZEUS detector at HERA using an integrated luminosity of 61 pb^-1. The dijet cross section has been measured for virtualities of the exchanged virtual photon, 5 < Q² < 100 GeV², and γ^*p centre-of-mass energies, 100 < W < 250 GeV. The jets, identified using the inclusive k_T algorithm in the γ^*p frame, were required to have a transverse energy E^* _T,jet > 4 GeV and the jet with the highest transverse energy was required to have E^* _T,jet > 5 GeV. All jets were required to be in the pseudorapidity range -3.5<η^* _jet<0. The differential cross sections are compared to leading-order predictions and next-to-leading-order QCD calculations based on recent diffractive parton densities extracted from inclusive diffractive deep inelastic scattering data.     

On the rise of the proton structure function F2 towards low x

A measurement of the derivative (∂ lnF₂/∂ lnx)_Q²≡−λ(x,Q²) of the proton structure function F₂ is presented in the low x domain of deeply inelastic positron–proton scattering. For 5×10⁻⁵x0.01 and Q²1.5 GeV², λ(x,Q²) is found to be independent of x and to increase linearly with lnQ².     

Diffractive deep-inelastic scattering with a leading proton at HERA

The cross section for the diffractive deep-inelastic scattering process ep→eXp is measured, with the leading final state proton detected in the H1 Forward Proton Spectrometer. The data analysed cover the range x_IP<0.1 in fractional proton longitudinal momentum loss, 0.08<|t|<0.5 GeV^-2 in squared four-momentum transfer at the proton vertex, 2<Q²<50 GeV² in photon virtuality and 0.004<β=x/x_IP<1, where x is the Bjorken scaling variable. For , the differential cross section has a dependence of approximately dσ/dt∝e^6t, independently of x_IP, β and Q² within uncertainties. The cross section is also measured triple differentially in x_IP, β and Q². The x_IP dependence is interpreted in terms of an effective pomeron trajectory with intercept α_IP(0)=1.114±0.018(stat.)±0.012(syst.)^+0.040 _-0.020(model) and a sub-leading exchange. The data are in good agreement with an H1 measurement for which the event selection is based on a large gap in the rapidity distribution of the final state hadrons, after accounting for proton dissociation contributions in the latter. Within uncertainties, the dependence of the cross section on x and Q² can thus be factorised from the dependences on all studied variables which characterise the proton vertex, for both the pomeron and the sub-leading exchange.     

A phenomenological analysis of the longitudinal structure function at small <Emphasis Type="Italic">x</Emphasis> and low <Emphasis Type="Italic">Q</Emphasis><Superscript>2</Superscript>

The longitudinal structure function in deep-inelastic scattering is one of the observables from which the gluon distribution can be unfolded. Consequently, this observable can be used to constrain the QCD dynamics at small x. In this work we compare the predictions of distinct QCD models with the recent experimental results for F _L(x,Q ²) at small x and low Q ² obtained by the H1 Collaboration. We focus mainly on the color dipole approach, selecting those models which include saturation effects. Such models are suitable at this kinematical region and also resum a wide class of higher-twist contributions to the observables. Therefore, we investigate the influence of these corrections to F _L in the present region of interest.Received: 23 June 2004, Revised: 13 July 2004, Published online: 14 September 2004     

On the perturbative stability of the QCD predictions for the ratio R=FL/FT in heavy-quark leptoproduction

We analyze the perturbative and parametric stability of the QCD predictions for the Callan–Gross ratio, R(x,Q ²)=F _L /F _T , in heavy-quark leptoproduction. We consider the radiative corrections to the dominant photon–gluon fusion mechanism. In various kinematic regions, the following contributions are investigated: exact NLO results at low and moderate Q ²≲m ², asymptotic NLO predictions at high Q ²≫m ², and both NLO and NNLO soft-gluon (or threshold) corrections at large Bjorken variable x. Our analysis shows that large radiative corrections to the structure functions F _T (x,Q ²) and F _L (x,Q ²) cancel each other in their ratio R(x,Q ²) with good accuracy. As a result, the NLO contributions to the Callan–Gross ratio are less than 10% in a wide region of the variables x and Q ². We provide compact LO predictions for R(x,Q ²) in the case of low x ≪1. A simple formula connecting the high-energy behavior of the Callan–Gross ratio and low-x asymptotics of the gluon density is derived. It is shown that the obtained hadron-level predictions for R(x→0,Q ²) are stable under the DGLAP evolution of the gluon distribution function. Our analytic results simplify the extraction of the structure functions F ₂ ^c (x,Q ²) and F ₂ ^b (x,Q ²) from measurements of the corresponding reduced cross sections, in particular at DESY HERA.     

Parton distributions in the virtual photon target up to NNLO in QCD

Parton distributions in the virtual photon target are investigated in perturbative QCD up to the next-to-next-to-leading order (NNLO). In the case Λ ²≪P ²≪Q ², where −Q ² (−P ²) is the mass squared of the probe (target) photon, parton distributions can be predicted completely up to the NNLO, but they are factorisation-scheme dependent. We analyse parton distributions in two different factorisation schemes, namely the and DIS _γ schemes, and we discuss their scheme dependence. We show that the factorisation-scheme dependence is characterised by the large-x behaviours of the quark distributions. The gluon distribution is predicted to be very small in absolute value except in the small-x region.     

Measurement and QCD analysis of the diffractive deep-inelastic scattering cross section at HERA

A detailed analysis is presented of the diffractive deep-inelastic scattering process ep→eXY, where Y is a proton or a low mass proton excitation carrying a fraction 1-x_IP>0.95 of the incident proton longitudinal momentum and the squared four-momentum transfer at the proton vertex satisfies |t|<1 GeV². Using data taken by the H1 experiment, the cross section is measured for photon virtualities in the range 3.5≤Q²≤1600 GeV², triple differentially in x_IP, Q² and β=x/x_IP, where x is the Bjorken scaling variable. At low x_IP, the data are consistent with a factorisable x_IP dependence, which can be described by the exchange of an effective pomeron trajectory with intercept α_IP(0)=1.118±0.008(exp.)^+0.029 _-0.010(model). Diffractive parton distribution functions and their uncertainties are determined from a next-to-leading order DGLAP QCD analysis of the Q² and β dependences of the cross section. The resulting gluon distribution carries an integrated fraction of around 70% of the exchanged momentum in the Q² range studied. Total and differential cross sections are also measured for the diffractive charged current process e⁺p→ν̄_eXY and are found to be well described by predictions based on the diffractive parton distributions. The ratio of the diffractive to the inclusive neutral current ep cross sections is studied. Over most of the kinematic range, this ratio shows no significant dependence on Q² at fixed x_IP and x or on x at fixed Q² and β.     

Diffraction at HERA, Color Opacity and Nuclear Shadowing in DIS off nuclei

The QCD factorization theorem for diffractive processes in DIS is used to derive formulae for the leading twist contribution to the nuclear shadowing of parton distributions in the low thickness limit (due to the coherent projectile (photon) interactions with two nucleons). Based on the current analyzes of diffraction at HERA we find that the average strength of the interactions which govern diffraction in the gluon sector at x≤ 10⁻³, Q ₀= 2 GeV is ∼50mb. This is three times larger than in the quark sector and suggests that applicability of DGLAP approximation requires significantly larger Q ₀ in the gluon sector. We use this information on diffraction to estimate the higher order shadowing terms due to the photon interactions with N≥ 3 nucleons which are important for the scattering of heavy nuclei and to calculate nuclear shadowing and Q ² dependence of gluon densities. For the heavy nuclei the amount of the gluon shadowing: G _A(x,Q ₀ ²) /AG _N(x,Q ₀ ²)_{|x ≤ 10−3}∼ 0.25–0.4 is sensitive to the probability of the small size configurations within wave function of the gluon “partonometer” at the Q ₀ scale. At this scale for A∼ 200 the nonperturbative contribution to the gluon density is reduced by a factor of 4–5 at x≤ 10⁻³ unmasking PQCD physics in the gluon distribution of heavy nuclei. We point out that the shadowing of this magnitude would strongly modify the first stage of the heavy ion collisions at the LHC energies, and also would lead to large color opacity effects in eA collisions at HERA energies. In particular, the leading twist contribution to the cross section of the coherent J/ψ production off A≥ 12 nuclei at s ⁻²≥ 70 GeV is strongly reduced as compared to the naive color transparency expectations. The Gribov black body limit for F _2A(x,Q ²) is extended to the case of the gluon distributions in nuclei and shown to be relevant for the HERA kinematics of eA collisions. Properties of the final states are also briefly discussed. Received: 12 March 1999     

Inclusive Jet Production in γp and γγ Processes: Direct and Resolved Photon Cross Sections in Next-To-Leading Order QCD

The production of jets in low Q² ep scattering (photoproduction) and in low Q² ey⁺ey⁻ scattering (γγ scattering) allows for testing perturbative QCD and for measuring the proton and photon structure functions. This requires exact theoretical predictions for one- and two-jet cross sections. We describe the theoretical formalism, giving sufficient details, for calculating the direct and resolved processes in γp and γγ reactions in next-to-leading order QCD. We present the complete analytical results for the Born terms, the virtual, and the real corrections. To separate singular and regular regions of phase space we use the phase space slicing method with an invariant mass cut-off. In this way, all soft and collinear singularities are either canceled or absorbed into the structure functions. Using a flexible Monte Carlo program, we evaluate the cross sections numerically and perform various tests and comparisons with other calculations. We consider the scale dependence of our results and compare them to data from the experiments H1 and ZEUS at HERA and OPAL at LEP.