Multiple parton scattering in nuclei: twist-four nuclear matrix elements and off-forward parton distributions

Multiple parton scatterings inside a large nucleus generally involve higher-twist nuclear parton matrix elements. The gluon bremsstrahlung induced by multiple scattering depends not only on direct parton matrix elements but also on momentum-crossed ones, due to the Landau–Pomeranchuk–Migdal interference effect. We show that both types of twist-four nuclear parton matrix elements can be factorized approximately into the product of twist-two nucleon matrix elements in the limit of extremely large nuclei, A→∞, as assumed in previous studies. Due to the correlative nature of the twist-four matrix elements under consideration, it is actually the off-forward parton distributions that appear naturally in this decomposition, rather than the ordinary diagonal distributions probed in deeply-inelastic scattering. However, we argue that the difference between these two distribution classes is small in certain kinematic regimes. In these regions, the twist-four nuclear parton matrix elements are evaluated numerically and compared to the factorized form for different nuclear sizes within a schematic model of the two-nucleon correlation function. The nuclear size dependence is found to be A^4/3 in the limit of large A, as expected. We find that the factorization is reasonably good when the momentum fraction carried by the gluon field is moderate. The deviation can be more than a factor of 2, however, for small gluon momentum fractions, where the gluon distribution is very large.     

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.     

Semi-exclusive production of photons at HERA

We study the feasibility of measuring the semi-exclusive photon production at HERA. The cross section of photons produced at large transverse momenta, recoiling off an inclusive system Y of limited mass, can without photon isolation cuts simply be expressed in terms of hard PQCD subprocesses and standard target parton distributions. With the help of event generators we identify the kinematic region where quark and gluon fragmentation processes can be neglected. The cross section in this semi-exclusive region is large enough to be measured with an upgraded HERA luminosity of . The subprocesses of lowest order in are suppressed at low recoil masses , compared to higher order gluon exchange, i.e. BFKL contributions. The distinct -dependence makes it possible to determine experimentally the kinematic range where the higher order processes dominate. Received: 27 March 2000 / Revised version: 6 June 2000 / Published online: 9 August 2000     

Diffractive vector mesons beyond the s-channel helicity conservation

We derive a full set, and determine the twist, of helicity amplitudes for diffractive production of light to heavy vector mesons in deep inelastic scattering. For large Q ² all helicity amplitudes but the double-flip are calculable in perturbative QCD and are proportional to the gluon structure function of the proton at a similar hardness scale. We find a substantial breaking of the s-channel helicity conservation, which must persist in real photoproduction also. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 9, 667–673 (10 November 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Regge-pole description of γN→πN backward-scattering data

Baryon Regge-pole contributions to u-channel helicity amplitudes for the γN→πN processes are derived, with attention to kinematic singularities and threshold conditions. An N, Nγ and Δδ Regge-exchange model is proposed that describes the backward scattering data on γp→π^op and γp→π⁺n at high energy. The N and Nγ trajectories are found to be nearly degenerate, with residues in the ratio β(Nγ)/β(N)≈0.6. Structure in the differential cross sections is explained as dominance at small u giving way to dominance at large u. An isoscaar-isovector admixture for the γ-coupling to is required by the fits. The solution extrapolates through the mean γp→π^op 180^o differential cross section at intermediate energies, as required by duality.     

Classification and asymptotic scaling of the light-cone wave-function amplitudes of hadrons

We classify the hadron light-cone wave-function amplitudes in terms of parton helicity, orbital angular momentum, and quark-flavor and color symmetries. We show in detail how this is done for the pion, meson, nucleon, and delta resonance up to and including three partons. For the pion and nucleon, we also consider four-parton amplitudes. Using the scaling law derived previously, we show how these amplitudes scale in the limit that all parton transverse momenta become large.Received: 16 October 2003, Published online: 29 January 2004     

Multiple collisions and induced gluon bremsstrahlung in QCD

Induced soft gluon bremsstrahlung associated with multiple collisions is calculated via perturbative QCD. We derive the non-abelian analog of the Landau-Pomeranchuk effect that suppresses induced soft radiation with formation times exceeding the mean free path. The dependence of the suppression effect on the SU(N) representation of the jet parton as well as the kinematic variables is expressed through a radiation formation factor. The soft radiation with k < μ, where μ is the infrared screening scale in the medium, is shown to lead to an approximately constant radiative energy loss per unit length.     

Global analysis of helicity parton densities and their uncertainties

We present a new analysis of the helicity parton distributions of the nucleon. The analysis takes into account the available data from inclusive and semi-inclusive polarized deep inelastic scattering, as well as from polarized proton-proton (p-p) scattering at RHIC. For the first time, all theoretical calculations are performed fully at next-to-leading order (NLO) of perturbative QCD, using a method that allows incorporation of the NLO corrections in a very fast and efficient way in the analysis. We find evidence for a rather small gluon polarization in the nucleon, over a limited region of momentum fraction, and for interesting flavor patterns in the polarized sea.     

Collinear limits of one-loop helicity amplitudes in QCD

We point out that for QCD subprocesses involving multiple quark pairs, it is useful to investigate the collinear limits of full helicity amplitudes. We study the recently calculated one-loop $0 \to \bar q\bar QQqg$ helicity amplitudes and confirm the results found by Bern, Dixon, Dunbar and Kosower for the loop splitting amplitudes.     

Dijet and photon-jet correlations in proton-proton collisions at RHIC

We discuss correlations in azimuthal angle as well as correlations in two-dimensional space of transverse momenta of two jets as well as photon and jet. Some k_t-factorization subprocesses are included for the first time in the literature. Different unintegrated gluon/parton distributions are used in the k_t-factorization approach. The results depend on UGDF/UPDF used. The collinear NLO 2 ↦3 contributions dominate over k_t-factorization cross section at small relative azimuthal angles as well as for asymmetric transverse momentum configurations.     

Generalized coherent state for soft gluon emission

By using a recursive soft insertion technique, many gluon emission amplitudes are computed to all orders in α_s and leading infrared accuracy. The resulting correlation structure is systematically exponentiated to yield a generalized coherent state operator which satisfies an integral equation where virtual corrections occur as a Sudakov matrix for many parton states. Infrared cancellations for physical quantities, including Drell-Yan processes, are derived on the basis of the unitarity relation for the coherent state. By further assuming strong ordering in emission angles, all known results on coherent effects and multiplicity distributions are easily recovered.     

Theoretical models for deuteron photodisintegration in the energy range between 250 MeV and 800 MeV

Two theoretical models of γd → pn are developed to study the differential cross-section and'the proton polarization data in a coherent way. The first model is an extension of conventional diagrammatic summations of Born terms and isobar excitation terms. The second model is novel in that the isobar excitation terms are replaced by experimentally determined _γN → N_π helicity amplitudes. The second model allows us to extend to higher energies with the introduction of only one arbitrary parameter. The differential cross-section data are fairly well reproduced in the whole energy range, while the proton polarization data are very far removed from the calculations.     

Asymptotic freedom in parton language

A novel derivation of the Q² dependence of quark and gluon densities (of given helicity) as predicted by quantum chromodynamics is presented. The main body of predictions of the theory for deep-inleastic scattering on either unpolarized or polarized targets is re-obtained by a method which only makes use of the simplest tree diagrams and is entirely phrased in parton language with no reference to the conventional operator formalism.     

The singular behavior of one-loop massive QCD amplitudes with one external soft gluon

We calculate the one-loop correction to the soft-gluon current with massive fermions. This current is process independent and controls the singular behavior of one-loop massive QCD amplitudes in the limit when one external gluon becomes soft. The result derived in this work is the last missing process-independent ingredient needed for numerical evaluation of observables with massive fermions at hadron colliders at the next-to-next-to-leading order.     

QCD coherence in the structure function and associated distributions at small x

We recall the origin of angular ordering in soft parton emission and show that at small x this coherent structure is masked in the structure function while it can be detected in the associated distributions. This is due to the fact that collinear singularities cancel completely in the structure function at fixed transverse momentum for x → 0. In this limit the dependence on the hard scale is lost, the angular ordered region becomes equivalent to the multi-Regge region in which all transverse momenta are of the same order, and one derives the BFKL equation. For the associated distributions at small x such a complete cancellation of collinear singularities does not hold in general, thus large singular contributions are neglected if angular ordering is replaced by multi-Regge phase space. The deduction of these features requires an analysis without any collinear approximations which is done by extending to small x the soft gluon factorization techniques typically used in the region of large x. Since the coherent structure of parton emission is the same in the small and large x regions, one can formulate a unified evolution equation for the structure function, a unified coherent branching and jet algorithm which allows the calculation of associated distributions in all x regions. Such a unified formulation, valid for all x, is presented and compared with usual treatments.     

On Timelike Compton Scattering at Medium and High Energies

We emphasize the complementarity of timelike and spacelike studies of deep exclusive processes, taking as an example the case of timelike Compton scattering (TCS) i.e. the exclusive photoproduction of a lepton pair with large invariant mass, versus deeply virtual Compton scattering i.e. the exclusive leptoproduction of a real photon. Both amplitudes factorize with the same generalized parton distributions (GPDs) as their soft parts and coefficient functions which differ significantly at next to leading order in α _s . We also stress that data on TCS at very high energy should be available soon thanks to the study of ultraperipheral collisions at the LHC, opening a window on quark and gluon GPDs at very small skewness.     

The role of the quark and gluon GPDs in hard vector-meson electroproduction

Electroproduction of light vector mesons is analyzed on the basis of handbag factorization. The required generalized parton distributions are constructed from the CTEQ6 parton distributions with the help of double distributions. The partonic subprocesses are calculated within the modified perturbative approach. The present work extends our previous analysis of the longitudinal cross section to the transverse one and other observables related to both the corresponding amplitudes. Our results are compared to recent experimental findings in detail.     

The use of QCD in OZI violating radiative decays of vector mesons

The spin parity (J^P) of the hadronic system produced in OZI violating vector decays V → γ + h is analyzed in the lowest order QCD approach. While the predicted rates for 0^± states agree with the data, theoretically unacceptable anomalies occur for even J ≠ 0, P = +1, channels. Experimental consequences are drawn. We argue that the rate for gluon jet emission in V → γ + 2 gluons is substantially smaller than previously stated.     

Final-state interactions and single-spin asymmetries in semi-inclusive deep inelastic scattering

Recent measurements from the HERMES and SMC Collaborations show a remarkably large azimuthal single-spin asymmetries A_UL and A_UT of the proton in semi-inclusive pion leptoproduction γ^*(q)p→πX. We show that final-state interactions from gluon exchange between the outgoing quark and the target spectator system lead to single-spin asymmetries in deep inelastic lepton–proton scattering at leading twist in perturbative QCD; i.e., the rescattering corrections are not power-law suppressed at large photon virtuality Q² at fixed x_bj. The existence of such single-spin asymmetries requires a phase difference between two amplitudes coupling the proton target with J^z_p=±1/2 to the same final-state, the same amplitudes which are necessary to produce a nonzero proton anomalous magnetic moment. We show that the exchange of gauge particles between the outgoing quark and the proton spectators produces a Coulomb-like complex phase which depends on the angular momentum L^z of the proton's constituents and is thus distinct for different proton spin amplitudes. The single-spin asymmetry which arises from such final-state interactions does not factorize into a product of distribution function and fragmentation function, and it is not related to the transversity distribution δq(x,Q) which correlates transversely polarized quarks with the spin of the transversely polarized target nucleon.     

Energy flow along the medium-induced parton cascade

We discuss the dynamics of parton cascades that develop in dense QCD matter, and contrast their properties with those of similar cascades of gluon radiation in vacuum. We argue that such cascades belong to two distinct classes that are characterized respectively by an increasing or a constant (or decreasing) branching rate along the cascade. In the former class, of which the BDMPS, medium-induced, cascade constitutes a typical example, it takes a finite time to transport a finite amount of energy to very soft quanta, while this time is essentially infinite in the latter case, to which the DGLAP cascade belongs. The medium induced cascade is accompanied by a constant flow of energy towards arbitrary soft modes, leading eventually to the accumulation of the initial energy of the leading particle at zero energy. It also exhibits scaling properties akin to wave turbulence. These properties do not show up in the cascade that develops in vacuum. There, the energy accumulates in the spectrum at smaller and smaller energy as the cascade develops, but the energy never flows all the way down to zero energy. Our analysis suggests that the way the energy is shared among the offsprings of a splitting gluon has little impact on the qualitative properties of the cascades, provided the kernel that governs the splittings is not too singular.