Model for nucleon valence structure functions at allx,allp ⊥ and allQ 2 from the correspondence between QCD and DTU

We propose a simple parametrization of the nucleon valence structure functions at allx, allp _⊥ and allQ ². We use the DTU parton model to fix the parametrization at a reference point (Q ₀ ² =3 GeV²) and we mimic the QCD evolution by replacing the dimensioned parameters of the DTU parton model by functions depending onQ ². Excellent agreement is obtained with existing data.     

The parton distribution functions of the photon and the structure functionF 2 γ (x,Q 2)

We present new parametrisations of the parton distribution functions of the photon including the first parametrisation in next-to-leading order QCD. We take into account some recent theoretical considerations pertaining to the gluon content of the photon,g ^γ. We argue that if an evolution is started at very lowQ ² and a fit to allF ₂ ^γ data performed with no constraints on the gluon distribution, then physically unreasonable gluon distributions may result. Our results support recent indications thatQ ₀ ² ≤1 GeV² is too low a value from which to start a perturbative evolution. Starting our evolution atQ ₀ ² =5.3 GeV², we evolve up inQ ² using a modified version of Rossi's Ansatz. The limited lever arm inQ ² leads to limited sensitivity to the QCD scale parameter Λ, though there is a preference for low values in the 0.1–0.2 GeV range. We also present new parametrisations of the singular asymptotic quark and gluon distribution functions of the photon which we believe are more accurate than those in current use.     

Parametrization of nuclear parton distributions

Optimum nuclear parton distributions are obtained by analysing available experimental data on electron and muon deep inelastic scattering (DIS). The distributions are given at Q ²=1 GeV² with a number of parameters, which are determined by a X ² analysis of the data. Valencequark distributions are relatively well determined at medium x, but they are slightly dependent on the assumed parametrization form particularly at small x. Although antiquark distributions are shadowed at small x, their behavior is not obvious at medium x from the F ₂ data. The gluon distributions could not be restricted well by the inclusive DIS data; however, the analysis tends to support the gluon shadowing at small x. We provide analytical expressions and computer subroutines for calculating the nuclear parton distributions, so that other researchers could use them for applications to other high-energy nuclear reactions.     

Early scaling in two photon reactions?

We show that the interpretation given by the TPC/2γ collaboration that their results for the photon structure functionF ₂ ^γ (x) indicates precocious scaling forQ ²>0.3 GeV² andx<0.1 is questionable. It appears to be a spurious effect possibly due to the fact that (i) the authors do not include two prong events (important at lowW), and (ii) in presenting the data they have averaged theW dependence in eachQ ² bin. To estimate the pointlike contribution of the offshell photon, we use the quark parton model (QPM) and find that this accounts for the data forQ ²>20 GeV² and all values ofW. This hard component is also responsible for the bulk of the cross section at lowQ ² andW<3 GeV. The soft or hadronic component is shown to dominate only at highW>6 GeV for values ofQ ²≤10 GeV².     

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.     

Possible parametrization of parton distributions incorporating singular smallx behaviour implied by QCD and its phenomenological implications for HERA

The gluon and quark distributions of the nucleon are evaluated using the Altarelli-Parisi equations with the input distributions atQ ₀ ² =5 GeV² for seaquarks and gluons modified by the factor (ax ^?0.5+b). The new parametrization is constrained to satisfy the momentum sum rule and after backward evolution (fromQ ₀ ² =5 GeV² toQ ²=1 GeV²) it is also constrained to give approximately 1/x behaviour of the sea-quark and gluon distributions in the limited region of smallx (10^?3<x<10^?2 or so). The theoretical predictions relevant for HERA for structure functionsF ₂(x, Q ²) andF _L (x, Q ²) in the region of very smallx(10^?4<x<10^?2) and largeQ ² and for the cross-sectionσ(γ^* p→ΨX) are presented. Distributions of heavy quarks (c,b,t) are also discussed.     

A model of deep inelastic polarized electroproduction

A realistic phenomenological model combining parton/QCD ideas with lower energy SU(6) constraints is proposed for the shape and evolution of the leading spin-dependent structure function G^ep(x, Q²) in polarized electroproduction. Close's broken-SU(6) ansatz is used to relate appropriately defined polarized quark-parton distribution densities to unpolarized ones at the matching momentum scale Q² = Q₀². The differences between spin and helicity distribution densities as well as the complications due to perturbative QCD and parton k_T (with related target-mass) effects are taken into account. Evolution to higher (>10 GeV²) values of Q² (where target-mass effects can be neglected) yields experimentally testable numerical predictions that are presented through various plots. The value of Q₀ is self-consistently determined to be about 0.5 GeV.     

Polarized leptoproduction and dynamically generated spin-dependent parton distributions

The first moment of the polarized parton distributions of the proton is evaluated dynamically using the assumption that at some low resolution scale the proton consists of valence quarks only. The spin carried by gluons, ΔG, at the EMC resolution scaleQ ₀ ² =10 GeV² ispredicted to be ΔG/s _p ?5 withs _p=1/2 denoting the spin of the proton. This result furthermoreexplains the dynamical origin of the recent EMC measurement of the first moment of the polarized structure functiong ₁ ^P (x, Q ²).     

Electroproduction of η mesons in the region of the resonanceS 11(1535) at momentum transfers of 2 and 3 GeV2

We report on results of η-electroproduction in the resonance region at momentum transfers ofQ ²=2 GeV² and 3 GeV². The differential cross sections obtained in the region of the second nucleon resonance strongly support the dominance of theS ₁₁(1535) in this channel. The total transverse virtual photoproduction cross section of theS ₁₁(1535) shows a flatQ ²-dependence ～e ^?0.39· Q ². Comparison with the total resonant γ _v p cross section in the second resonance region aroundW=1.5 GeV shows that theD ₁₃(1520) production decreases much faster (～e ^?1.6· Q ²). The data are not compatible with the simple harmonic oscillator quark model with spin and orbit excitation of a quark only.     

On the possibility of measuringF L (x,Q 2) at HERA using radiative events

It is shown that a significant measurement of the longitudinal structure functionF _L (x, Q ²) can be performed at HERA, forQ ²=2 GeV² andQ ²=5 GeV² and forx around 10^?4, using radiative events with hard photon emission collinear to the incident lepton beam, under the present running conditions and with an integrated luminosity of 10 pb^?1. The influence of experimental conditions is discussed.     

Nonperturbative parton distributions and the proton spin problem

The Lorentz contracted form of the static wave functions is used to calculate the valence parton distributions for mesons and baryons, boosting the rest frame solutions of the path integral Hamiltonian. It is argued that nonperturbative parton densities are due to excitedmultigluon baryon states. A simplemodel is proposed for these states ensuring realistic behavior of valence and sea quarks and gluon parton densities at Q² = 10 (GeV/c)². Applying the same model to the proton spin problem one obtains Σ₃ = 0.18 for the same Q².     

Elastic and transition form factors of light pseudoscalar mesons from QCD sum rules

We revisit F _π(Q ²) and F _Pγ(Q ²), P = π, η, η′, making use of the local-duality (LD) version of QCD sum rules. We give arguments that the LD sum rule provides reliable predictions for these form factors at Q ² ≥ 5–6 GeV², the accuracy of the method increasing with Q ² in this region. For the pion elastic form factor, the well-measured data at small Q ² give a hint that the LD limit may be reached already at relatively low values of momentum transfers, Q ² ≈ 4–8 GeV²; we therefore conclude that large deviations from LD in the region Q ² = 20–50 GeV² seem very unlikely. The data on the (η, η′) → γγ* form factors meet the expectations from the LD model. However, the BaBar results for the π ⁰ → γγ* form factor imply a violation of LD growing with Q ² even at Q ² ≈ 40 GeV², at odds with the η, η′ case and with the general properties expected for the LD sum rule.     

QCD cascade model in deep inelastic scattering

We develop a new QCD cascade model for jets in deep inelastic scattering. We use the light-like axial gauge whose gauge vector is parallel to momentum of the initial parton so that only final partons cascade. Due to this feature we can generate events for any given virtualityQ ² andx _B =Q ²/2Pq.     

How can we properly define the Q2 dependent parton distribution function in QCD?

We discuss how we can properly define the Q² dependent parton distribution functions in quantum chromodynamics within the framework of the operator product expansion and renormalization group techniques. It is proposed that the moments of the parton distribution functions at Q² should be defined as the hadronic expectation values of the twist-2 operators renormalized at Q². The integro-differential equations for the parton densities obtained by Altarelli and Parisi are reproduced in the leading logarithmic approximation. An application of our present formalism will be given in the case of a longitudinal structure function.     

Investigation of the inelastic electroproduction of J/ψ mesons at the HERA collider within the semihard QCD approach

The results of theoretical calculations within the semihard (k _T-factorization) approach are compared with the latest data obtained in the ZEUS experiment at the HERA collider for the inelastic electroproduction of J/ψ mesons in the kinematical region specified by the inequalities 2 GeV² < Q ² < 80 GeV², 50 GeV < W < 250 GeV, 0.2 < z < 0.9, and ?1.6 < y _ψlab < 1.3. The dependence of these theoretical results on the choice of parametrization among three widely used parametrizations of unintegrated gluon distributions is studied.     

Origin of the Q 2-dependence of the DIS structure functions

We consider in detail Q ²-dependence of the DIS structure functions. Very often this dependence is claimed to be originated by the Q ²-dependence of the QCD coupling. This leads to the small-x asymptotics of the structure functions with Q ²-dependent intercepts. We demonstrate that the DGLAP parametrization α _s = α _s (Q ²) is an approximation valid in the region of large x (where 2pq can be approximated by Q ²) only, providing the factorization scale is also large. Outside this region, the DGLAP parametrization fails, so α _s should be replaced by an effective coupling which is independent of Q ² at small x. As a consequence, intercepts of the structure functions are independent of Q ² . Nevertheless, the small-x asymptotics of the structure functions explicitly depend on Q ² , even when the coupling does not depend on it. We also consider the structure functions at small Q ² and give a comment on power-Q ² corrections to the structure functions at large and small Q ² .     

W 2 andQ 2 dependence of charged hadron and pion multiplicities invp and\bar vp charged current interactionscharged current interactions

Using data onvp and \(\bar vp\) charged current interactions from a bubble chamber experiment with BEBC at CERN, the average multiplicities of charged hadrons and pions are determined as functions ofW ² andQ ². The analysis is based on ～20000 events with incidentv and ～10000 events with incident \(\bar v\) . In addition to the known dependence of the average multiplicity onW ² a weak dependence onQ ² for fixed intervals ofW is observed. ForW>2 GeV andQ ²>0.1 GeV² the average multiplicity of charged hadrons is well described by〈n〉=a ₁+a ₂ln(W ²/GeV²)+a ₃ln(Q ²/GeV²) witha ₁=0.465±0.053,a ₂=1.211±0.021,a ₃=0.103±0.014 for thevp anda ₁=?0.372±0.073,a ₂=1.245±0.028,a ₃=0.093±0.015 for the \(\bar vp\) reaction.     

Electroproduction of π+ n, π- p andK + Λ,K + 2211; 0 final states above the resonance region

The reactionsΣ _v p→π⁺ n,K ⁺ Λ,K ⁺ ∑ ⁰ andΣ _v n→π⁺ n were studied at invariant hadronic masses around 2.2. GeV forQ ²=0.06, 0.28, 0.70, and 1.35 GeV². The main results are: At small |t| the π⁺ production is dominated by longitudinally polarized photons and can be described by one pion exchange. At low |t| the transverse (π⁺ n) cross section drops steeply withQ ², but remains roughly constant forQ ²≧0.5 GeV². For |t?≧0.8 GeV², (π⁺ n/dt) is almost independent ofQ ². The integrated cross section (π⁺ n) shows a similarQ ²-dependence asσ _tot (γ _v p) forQ ²≧0.28 GeV². The ratioσ(π^- p)/σ(π⁺ n) atQ ²=0.70 and 1.35 GeV² for |t|≧0.6 GeV² is smaller than in photoproduction and close to 1/4. The ratioσ(K ⁺ ∑ ⁰ decreases steeply withQ ² following roughly the predictions of the quark-parton model.     

Precise pion electroproduction in thep(e,e′ π+)n reaction at W=1125 MeV

The reactione+p →> e+π ⁺+n at c.m. energyW=1125MeV and momentum transfer Q²=0.117GeV²/c₂ has been measured. The transverse and longitudinal structure functions have been separated by varying the polarization of the virtual photon (Rosenbluth plot) with a 3 to 4% error. In addition the longitudinal-transverse interference term has been determined measuring the right-left asymmetry with an accuracy of 3%. The experimental data are compared to model calculations, and the sensitivity of the results to the axial and pion formfactors is discussed.