Color screening,absorption, and σ tot pp at LHC

We show that a growth of the proton-proton total cross section with energy can be entirely attributed to the purely perturbative mechanism. The infrared regularization at rather short distances R _c ? 0.3 fm allows extending the BFKL technique from deep inelastic to hadron-hadron scattering. With the inclusion of the absorption corrections our results are in agreement with the LHC data on σ _tot ^pp .     

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.     

Diffractive J/ψ photoproduction as a probe of the gluon density

We use perturbative QCD, beyond the leading lnQ ² approximation, to show how measurements of diffractive J/ψ production at HERA can provide a sensitive probe of the gluon density of the proton at small values of Bjorken x. We estimate both the effect of the relativistic motion of the c and $\bar c$ within the J/ψ and of the rescattering of the $c\bar c$ quark pair on the proton. We find that the available data for diffractive J/ψ photoproduction can discriminate between the gluon distributions of the most recent sets of partons.     

Quark masses and specific scaling in deep-inelastic processes

Within an operator-product expansion, the problem of the quark-mass dependence of the heavy-flavor contribution to the structure function F ₂ in the current-fragmentation region is considered at high values of the momentum transfer squared Q ². A linear combination of the structure functions F ₂ ^c and F ₂ is found that possesses a specific scaling property for Q ² → ∞ at small fixed values of the Bjorken variable x. A lower bound on the ratio F ₂ ^c /F ₂ is calculated and is compared with data obtained at the HERA collider.     

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.     

The ratio of the charm structure functions F k c (k = 2, L) at low x in deep inelastic scattering with respect to the expansion method

We study the expansion method for the gluon distribution function at low x values and calculate the charm structure functions in the LO and NLO analysis. Our results provide a compact formula for the ratio R ^c = F _L ^c /F ₂ ^c , which is approximately independent of x and the details of the parton distribution function at low x values. This ratio could be a good probe of the charm structure function F ₂ ^c in the proton deduced from the reduced charm cross sections at DESY HERA. These results show that the charm structure functions obtained are in agreement with HERA experimental data and other theoretical models.     

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.     

BFKL Pomeron in the reaction γ ⊥ * (Q 2)p→ρ ⊥ 0 p at large Q 2 and W

The reaction γ _⊥ ^* (Q ²)p→ρ _⊥ ⁰ p has been studied at large Q ² and W ²/Q ² and low momentum transfers to the nucleon, k _⊥ ² —that is, in the region where the Pomeron exchange mechanism is operative. At sufficiently large Q ², the Pomeron interacts with quarks occurring at small distances, whereby the hard component of the Pomeron is separated, so that the process is governed by the Pomeron of perturbative QCD (BFKL Pomeron). Our calculations indicate that, in vector-meson electroproduction at low k _⊥ ² , the perturbative regime cannot set in fast because, for Q ²≤100 GeV² and, accordingly, for W ²/Q ²≤10⁷, comparatively large distances of $\rho _{q\bar q} > 0.2$ fm are important.     

The BFKL Pomeron in deep inelastic diffractive dissociation neart=0

The small-t behaviour of the deep inelastic diffractive dissociation cross section in the triple Regge region is investigated, using the BFKL approximation in perturbative QCD. We show that the cross section is finite att=0, but the diffusion in lnk _t ² leads to a large contribution of small momenta at the triple Pomeron vertex. We study the dependence upon the total energy and the invariant mass. Att=0, there is a decoupling of the three BFKL singularities which is a consequence of the conservation of the conformal dimension. For large invariant masses, the four gluon state in the uppert-channel plays an important role and cannot be neglected.     

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.     

The role of screening corrections in smallx-behaviour of structure functions

We consider the influence of shadowing effects on the proton structure function in the small-x interval. The gluon-gluon shadowing are noticeable in the HERA kinematical region while the screening of the quark component of the structure function effects negligibly the gluon distribution. The only noticeable effect is the decreasing of sea quark densities at small-x. The explicit form of the gluon distribution in the proton depends significantly on the form of used boundary condition atQ ²=Q ₀ ² . We consider also difference of results obtained with the help of Kuraev-Lipatov-Fadin and Altarelli-Parisi evolution equations.     

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).     

ψψ production at collider energies

We estimate ψψ production at collider energies in the framework of perturbative QCD. TheO(α _s ² )?(α _s ⁴ ) parton cross-sections, with the non-relativistic approximation for the heavy quark bound states, are used. This first insight into the characteristics of the kinematical distributions allows predictions on the predominance of the quark, gluon orB meson production mechanisms in particular kinematical regions.     

Scaling violations and the gluon distribution of the nucleon

Using recent data on deep inelastic lepton-nucleon scattering an attempt is made to extract the gluon distributionG(x, Q ²=4 GeV²) from the observed scaling violations of structure functions. The accuracy of the data allows only for a rough determination of the gluon distribution. In particular it is found that a hard gluon distributionis consistent with present measurements. Implications of the hard gluon distribution for charm production in the gluon fusion model and for the perturbative contributions to σ _L /σ _T are further discussed. Finally, analytic parametrizations of the QCDx- andQ ²-dependence of quark and gluon distributions are presented facilitating further possible applications.     

The bootstrap condition for many reggeized gluons and the photon structure function at lowx andN c→∞

The bootstrap condition is generalized ton reggeized gluons. As a result it is demonstrated that the intercept generated byn reggeized gluons cannot be lower than the one forn=2. Arguments are presented that in the limitN _c→∞ the bootstrap condition reduces then gluon chain with interacting neighbours to a single BFKL pomeron. In this limit the contribution fromn gluons leading at high energies corresponds ton/2 non-interacting BFKL pomerons (then/2 pomeron cut). The sum overn leads to a unitaryγ*γ amplitude of the eikonal form.     

The bootstrap condition for many reggeized gluons and the photon structure function at lowx andN c����

The bootstrap condition is generalized ton reggeized gluons. As a result it is demonstrated that the intercept generated byn reggeized gluons cannot be lower than the one forn=2. Arguments are presented that in the limitN _c???? the bootstrap condition reduces then gluon chain with interacting neighbours to a single BFKL pomeron. In this limit the contribution fromn gluons leading at high energies corresponds ton/2 non-interacting BFKL pomerons (then/2 pomeron cut). The sum overn leads to a unitary??*?? amplitude of the eikonal form.     

The role of gluon-gluon shadowing in smallx-behaviour of structure functions

We consider influence of gluon shadowing effects on the proton structure function in the smallx interval. These effects are noticeable in the HERA kinematical region. The explicit form of the gluon distribution in the proton depend significantly on the form of used boundary condition atQ ²=Q ₀ ² . We consider also difference of results obtained with the help of Kuraev-Lipatov-Fadin and Altarelli-Parisi evolution equations.