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 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 dipole picture of high energy scattering,the BFKL equation and many gluon compound states

The relationship and equivalence between the BFKL and dipole equation kernels are investigated by means of explicit calculations in light-cone perturbation theory. A dipole equation, equivalent to the usual equation, for interactions between four reggeized gluons is given in the large N_c limit. The leading trajectory of the four-gluon system is bounded by 2αp − 1 with αp the BFKL pomeron intercept.     

On the multipomeron exchange and the BKP equation in the high colour limit

The interaction of reggeized gluons is discussed in the high-colour limit. It is argued that the dominant contributions from the diagrams with a topology of a cylinder sum into a single BFKL pomeron. It is also shown that the BKP equation should be supplemented with terms which change the number of gluons, after which it can be solved in a trivial manner. In the high energy limit the theory reduces to that of noninteracting BFKL pomerons.     

The system of four reggeized gluons and the three-pomeron vertex in the high colour limit

The amplitude for 4 interacting reggeized gluons is studied in the high-colour limit. The leading order amplitude is explicitly shown to reduce to a pair of reggeons, i.e to a single BFKL pomeron. The next-to-leading order diffractive amplitude is found to split into a double pomeron exchange and triple pomeron contribution. The obtained three-pomeron vertex is different from the originally proposed in [2]. Received: 26 June 1997 / Revised version: 28 February 1998 / Published online: 3 September 1998     

On the inclusive gluon jet production from the triple pomeron vertex in the perturbative QCD

Single and double inclusive cross-sections for gluon jet production from within the triple pomeron vertex are studied in the reggeized gluon technique in the QCD with N_c→∞. It is shown that to satisfy the AGK rules the vertex has to be fully symmetric in all four reggeized gluons which form the two final pomerons. The single inclusive cross-sections are found for different cuttings of the triple pomeron vertex. They sum to the expression obtained by Kovchegov and Tuchin in the color dipole picture. The found double inclusive cross-sections satisfy the AGK rules.     

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     

Conformal properties of the odderon in QCD

We construct, in the framework of QCD, the conformally invariant functional whose maximal value gives the J-plane location of the leading singularity of the t-channel partial waves in LLA for diagrams with n reggeized gluons. In the case of the odderon the wave function in impact-parameter space depends on only one anharmonic ratio and the corresponding functional is significantly simplified. We discuss in the variational approach the relation between the odderon and the pomeron in QCD. A semiquantitative argument is given that the intercept of the odderon in LLA is probably bigger than 1.     

Shadowing effects in nuclear parton distributions for small values ofx

The shadowing corrections to gluon and quark distributions in nuclei in the region of small values ofx are discussed. They are related to parton distributions in a pomeron which are in principle measurable in hard diffractive processes on the nucleon target. Multiple scattering corrections to shadowing are considered in a model dependent way. The perturbative QCD evolution of shadowing is also taken into account. Various possibilities of the partonic content of a pomeron are considered. It is shown in particular that the conventional parametrizations of parton distributions in a pomeron which are based on the assumption that it consists mostly of gluons imply substantial nuclear shadowing in gluon distributions in heavy nuclei. Possible phenomenological implications of shadowing corrections in nuclear parton distributions for various semi-hard processes with nuclear targets are briefly discussed.     

Leading logarithmic approximation in QCD

The leading logarithmic approximation (LLA) for the scattering amplitudes in QCD is reviewed. The double-logarithmic asymptotics of scattering amplitudes is obtained as a solution to nonlinear evolution equations in the infrared cutoff. The DGLAP equation describes an evolution of parton distributions with increasing parton virtuality. The evolution of the amplitudes with respect to the scale in the longitudinal subspace is given by the BFKL equation. The gluon and quarks in QCD lie on the Regge trajectories calculable in perturbation theory. Mesons and baryons are composite states of Reggeized quarks. Similarly the Pomeron and Odderon are colorless ground states of Reggeized gluons. In the case of multicolor QCD, the Reggeon field theory in LLA is completely integrable. The Reggeon interactions in QCD are derived from a gauge-invariant effective action. In particular, next-to-leading corrections to the BFKL equation in QCD and in supersymmetric gauge models are obtained in this way.     

NLO corrections to the kernel of the BKP-equations

We present results for the NLO kernel of the BKP-equations for composite states of three reggeized gluons in the Odderon channel, both in QCD and in N=4$N=4$ SYM. The NLO kernel consists of the NLO BFKL kernel in the color octet representation and the connected 3→3$3\to 3$ kernel, computed in the tree approximation.     

Search for large-rapidity-gap events in e+e− annihilation

We investigate the cross section for the production of a low-mass colour-singlet cluster ine ⁺ e ^? annihilation with a large rapidity gap between the colour-singlet cluster and the other jets. It is argued that such events are the cross-channel analogue of large-rapidity-gap events in deep-inelastic scattering, and therefore could in principle be used to investigate the analytic continuation of the BFKL pomeron to the positive-t kinematic regime, where one would expect the trajectory to pass through glueball states. The cross section can be calculated in perturbative QCD, so that the infrared scale arising from non-perturbative effects, which prevents an exponential fall-off with rapidity gap in the case of deep-inelastic scattering, is absent ine ⁺ e ^? annihilation. Correspondingly, the cross section for such events decreases rapidly with increasing rapidity gap.     

Diffractive production of dijets at HERA

We investigate the production of a quark-antiquark pair in diffractive photon-proton scattering, approximating soft pomeron exchange by the exchange of two nonperturbative gluons. In deep inelastic scattering at HERA, events with two jets and the scattered proton in the final state are predicted to be observable, with an important contribution from charm production. For photoproduction of light quark jets with high transverse momentum we find that both exchanged gluons must have a large invariant mass, so that the cross section is very small, whereas for charm quarks it is quite appreciable. From our calculation we also extract the quark structure function of the pomeron for the scaling variablez no too close to 0 or 1, finding a strong flavour dependence and a behaviour somewhat harder thanz(1?z) for light quarks.     

Integrabilty of the BFKL dynamics and Pomeron trajectories in a thermostat

We consider scattering amplitudes in QCD at high energies $\sqrt s $ and fixed momentum transfers $q = \sqrt { - t} $ with a non-zero temperature T in the t-channel. In the s-channel the temperature leads to a compactification of the impact parameter plane. We find that the thermal BFKL Hamiltonian in the leading logarithmic approximation proceeds to have the property of the holomorphic separability. Moreover, there exists an integral of motion allowing one to construct the Pomeron wave function for arbitrary T in the coordinate and momentum representations. The holomorphic Hamiltonian for n-reggeized gluons at T ≠ 0 in the multicolour limit N _c → ∞ turns out to be equal to the local Hamiltonian for an integrable Heisenberg spin model. Further, the two-gluon Baxter function coincides with the corresponding wave function in the momentum representation. We calculate the spectrum of the Pomeron Regge trajectories at a finite temperature with taking into account the QCD running coupling. The important effect of the t-channel temperature is the appearence of a confining potential between gluons.     

QCD corrections to γγ→ZZ at small scattering angles

QCD corrections to the electroweak cross section of γγ→ZZ at high energies and small scattering angles have been calculated. The dominant contributions are due to t-channel gluon exchange, i.e., photons dissociate into quark–antiquark pairs giving rise to two colour dipoles which interact through gluons. Corrections resulting from the leading log BFKL amplitude are of the order of a few percent close to the forward region already at the 1 TeV energy range and are rising with the scattering energy. We also considered the helicity non-conserving cases in which the QCD corrections in comparison to the electroweak part of the amplitude strongly grow with energy. The helicity non-conserving scattering process is of particular interest since it is sensitive to the Higgs sector.     

On inclusive gluon jet production off the nucleus in perturbative QCD

In the perturbative QCD approach single and double inclusive cross-sections for gluon production off the nucleus are studied by the relevant reggeized gluon diagrams. Various terms corresponding to emission of gluons from the triple pomeron vertex are found. Among them the term derived by Kovchegov and Tuchin emerges as a result of the transition from the diffractive to effective high-energy vertex. However it does not exhaust all the vertex contributions to the inclusive cross-section. In the double inclusive cross-section a contribution violating the naive AGK rules is found in which one gluon is emitted from the vertex and the other from one of the two pomerons below the vertex. But then this contribution is subdominant at high energies and taking it into account seems to be questionable.Received: 6 March 2005, Revised: 5 May 2005, Published online: 8 June 2005     

Pomeron structure function and diffraction dissociation of virtual photons in perturbative QCD

We study scaling properties of the diffraction dissociation of virtual photons in a deep inelastic scattering. We concentrate on the total diffraction dissociation rate, diffraction excitation mass spectrum and the pomeron structure function to the lowest order in perturbative QCD. We calculate the valence structure function and the strangeness and charm content of the pomeron and estimate the ocean structure function using the pomeron factorization property. We find that quarks carry ≈ 10% of pomeron's momentum. Differential cross section of the (virtual) photon-pomeron scattering is found to exhibit features typical of the hadronic two-body reactions, supporting a treatment of the Pomeron as a particle, whereas the flavor dependence of structure functions does not support the particle treatment of the pomeron. Diffraction dissociation of photons is predicted to make ≈ 15% of the total deep inelastic scattering rate at smallx and largeQ ². Detailed predictions for the mass spectrum and angular distribution of jets produced on the valence component of the pomeron are presented.     

Color dipole BFKL-Regge factorization and high-energy photon-photon scattering

Based on the color dipole representation, we investigate consequences for the γ*γ*, γ *γ scattering of the finding by Fadin, Kuraev, and Lipatov that the incorporation of asymptotic freedom into the BFKL equation 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 the γ *γ*, γ*γ scattteirng and the deep inelastic scattering on protons. Numerical predictions based on our early work on the color dipole BFKL phenomenology of the deep inelastic scattering on protons gives a good agreement with the recent experimental data from OPAL and L3 experiments at LEP200. We discuss the role of nonperturbative dynamics and predict a pronounced effect of the Regge-factorization breaking due to large unfactorizable nonperturbative corrections to the perturbative vacuum exchange. We comment on the salient features of the BFKL-Regge expansion for the γ*γ*, γ*γ scattering including the issue of the decoupling of subleading BFKL poles and the soft plus rightmost hard BFKL pole dominance.     

Comparison of moments from the valence structure function with QCD predictions

We present moments (both ordinary and Nachtmann) of the nucleon valence structure function measured in high Q²_νFE scattering, supplemented by data from deep inelastic eD scattering. These data seem to agree with QCD predictions for vector gluons. The QCD parameter Λ is found to be of the order 0.5 GeV.