Discriminative deep inelastic tests of strong interaction field theories

It is demonstrated that recent measurements of ∫¹₀F₂(x, Q²)dx eliminate already all strong interaction field theories except QCD. A detailed study of scaling violations of F₂(x, Q²) in QCD shows their insensitivity to the gluon content of the hadron at presently measured values of Q².     

The longitudinal structure function F L(x, Q 2) and the gluon distribution G(x, Q 2) at low x

We obtain a relation between the longitudinal structure function F _L(x, Q ²), F ₂(x, Q ²) and G(x, Q ²) at small x, using the formalism recently reported by one of the authors [2]. We also obtain a relation between F _L(x, Q ²), F ₂(x, Q ²) and its slope (dF ₂(x, Q ²))/(dlnQ ²). This provides us with the determination of the longitudinal structure function F _L(x, Q ²) from F ₂(x, Q ²) data and hence extract the gluon distribution G(x, Q ²).     

Total cross sections and nucleon structure functions in the gargamelle SPS neutrino/antineutrino experiment

Total neutrino and antineutrino cross sections in the energy range 15 to 150 GeV, and the nucleon structure functions, F₂(x, Q²) and xF₃(x, Q²) in the Q² range 0.5 to 50 (GeV/c)² have been measured using a data sample of 3000 neutrino and 3800 antineutrino events. The structure functions show a weak Q² dependence at different x values.     

Deep-inelastic scattering in κ factorization and the anatomy of the differential gluon structure function of the proton

The differential gluon structure function of the proton, ?(x, Q ²), introduced by Fadin, Kuraev, and Lipatov in 1975 is extensively used in small-x QCD. We report here the first determination of ?(x, Q ²) from experimental data on the small-x proton structure function F _2p (x, Q ²). We give convenient parametrizations for ?(x, Q ²) based partly on the available DGLAP evolution fits (GRV, CTEQ, and MRS) to parton distribution functions and on realistic extrapolations into the soft region. We discuss the impact of soft gluons on various observables. The x dependence of the so-determined ?(x, Q ²) varies strongly with Q ² and does not exhibit simple Regge properties. Nonetheless, the hard-to-soft diffusion is found to give rise to a viable approximation of the proton structure function F _2p (x, Q ²) by the soft and hard Regge components with intercepts Δ_soft=0 and Δ_hard ～ 0.4.     

Scaling and non-scaling in a rest frame quark-parton model of the proton

Electron-proton deep inelastic scattering is treated as the incoherent scattering of electrons by bound Dirac partons in the proton rest frame. An approximate bound state wave function is used for the initial parton, while the final parton is considered free. A good fit is obtained to the structure function F₁(x,Q²) in the range x > 0.15, Q² > 2 GeV. The subsequent prediction for F₂(x,Q²) is not as good, indicating a small additional contribution by longitudinal photons for W < 2.5 GeV. The parton momentum distribution is found to contain transverse momentum of 400–600 MeV, increasing with x.     

QCD analysis of twist-4 contributions to the g i structure functions

We analyze the twist-4 contributions to Bjorken and Ellis-Jaffe sum rules for spin-dependent structure function g ₁(x, Q ²). We investigate the anomalous dimensions of the twist-4 operators which determine the logarithmic correction to the 1/Q ² behavior of the twist-4 contribution by evaluating off-shell Green’s functions in both flavor non-singlet and singlet case. It is shown that the operators which are proportional to the equation of motion play an important role to extract the anomalous dimensions of physical operators. The calculations to solve the operator mixing of higher-twist operators are given in detail     

A measurement of the proton structure function F2(x,Q2)

A measurement of the proton structure function F₂(x, Q²) is reported for momentum transfers squared Q² between 4.5 GeV² and 1600 GeV² and for Bjorken x between 1.8 × 10⁻¹⁴ and 0.13 using data collected by the HERA experiment H1 in 1993. It is observed that F₂ increases significantly with decreasing x, confirming our previous measurement made with one tenth of the data available in this analysis. The Q² dependence is approximately logarithmic over the full kinematic range covered. The subsample of deep inelastic events with a large pseudo-rapidity gap in the hadronic energy flow close to the proton remnant is used to measure the “diffractive” contribution to F₂.     

Constraints on gluon evolution at smallx

The BFKL and the unified angular-ordered equations are solved to determine the gluon distribution at smallx. The impact of kinematic constraints is investigated. Predictions are made for observables sensitive to the gluon at smallx. In particular comparison is made with measurements at the HERA electron-proton collider of the proton structure functionF ₂(x, Q ²) as a function of lnQ ², the charm componentF _c ² (X, Q ²) and diffractiveJ/Ψ photoproduction.     

Constraints on gluon evolution at smallx

The BFKL and the unified angular-ordered equations are solved to determine the gluon distribution at smallx. The impact of kinematic constraints is investigated. Predictions are made for observables sensitive to the gluon at smallx. In particular comparison is made with measurements at the HERA electron-proton collider of the proton structure functionF ₂(x, Q ²) as a function of lnQ ², the charm componentF _c ² (X, Q ²) and diffractiveJ/?? photoproduction.     

The effect of screening on the x and Q2 behaviour of F2 slopes

A systematic study of ϖF₂(x, Q²)/ϖ ln Q² and ϖ ln F₂(x, Q²)/ϖ ln(1/x) is carried out in pQCD taking screening corrections into account. The result of calculations, which are different from the non-screened DGLAP prediction, are compared and shown to agree with the available experimental data as well as a pseudo data base generated from the ALLM'97 parameterization. This pseudo data base allows us to study in detail our predictions over a wider kinematic region than is available experimentally, and allows us to make suggestions for future experiments. Our results are compared with the GRV'94 parameterization (which is used as an input for our calculations) as well as the recently proposed MRST structure functions.     

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.     

How to measure the charm density in the proton

We study two experimental ways to measure the heavy-quark content of the proton: using the Callan-Gross ratio R(x, Q ²) = F _L /F _T and/or the azimuthal cos(2φ) asymmetry in DIS. Our approach is based on the following observations. First, the ratio R(x, Q ²) = F _L /F _T and azimuthal cos(2φ) asymmetry in heavy-quark leptoproduction are stable, both parametrically and perturbatively, within pQCD. Second, both these quantities are sensitive to resummation of the mass logarithms of the type α_sln(Q ²/m ²). We conclude that the heavy-quark densities in the nucleon can, in principle, be determined from high-Q ² data on the Callan-Gross ratio and/or the azimuthal asymmetry. In particular, the charm content of the proton can be measured in future studies at the proposed Large Hadron-Electron (LHeC) and Electron-Ion (EIC) Colliders.     

F 2 c at low x

We study the heavy-quark contributions to the proton structure function F ₂(x,Q ²) at next-to-leading order using compact formulas at small values of Bjorken??s x variable. The formulas provide a good agreement with the modern HERA data for F ₂ ^c (x,Q ²).     

Inclusive measurement of diffractive deep-inelastic ep scattering

A measurement is made of the cross section for the process ep → eXY in deep-inelastic scattering with the H1 detector at HERA. The cross section is presented in terms of a differential structure function F ₂ ^D(3) (x _P, β,Q ²) of the proton over the kinematic range 4.5 < Q ² < 75 GeV². The dependence of F ₂ ^D(3) on x _P is found to vary with β, demonstrating that a factorisation of F ₂ ^D(3) with a single diffractive flux independent of β and Q ² is not tenable. An interpretation in which a leading diffractive exchange and a subleading reggeon contribute to F ₂ ^D(3) reproduces well the x _P dependence of F ₂ ^D(3) with values for the pomeron and subleading reggeon intercepts of α_P (0) = 1.203±0.020(stat.)±0.013(sys.) _-0.035 ^+0.030 (model) and α _R (0) = 0.50 ± 0.11(stat.) ± 0.11(sys.) _-0.10 ^+0.09 (model), respectively. A fit is performed of the data using a QCD motivated model, in which parton distributions are assigned to the leading and subleading exchanges. In this model, the majority of the momentum of the pomeron must be carried by gluons in order for the data to be well described.     

Measurement of the longitudinal structure function and the smallx gluon density of the proton

At HERA energies the smallx region (x?10^?2) can be explored atQ ² values large enough that leading twist QCD calculations are valid. We show how measurement of the longitudinal structure function,F _L (x,Q ²), can lead to accurate measurement of the gluon structure function at such smallx values. Experimental systematic errors are discussed fully and requirements for the measurement outlined. We conclude that it should be possible to distinguish between the widely varying gluon distributions which are currently allowed.     

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.     

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.     

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.     

NLO predictions for the growth ofF 2 at smallx and comparison with experimental data

We present parametrizations for the proton structure functionF ₂ in the next to leading order in perturbative QCD. We consider that the dominant term toF ₂(x, Q ²) should grow asx ^?ψ _s for smallx values, with the exponentλ _S being essentially independent ofQ ². Comparisons with the most recent H1 and ZEUS data confirm the valueλ _S ～0.35 obtained previously from fits to low energy data.