Perturbative Pomeron Research Articles

Jets separated by a large pseudorapidity gap at the Tevatron and at the LHC

We present a phenomenological analysis of events with two high transverse momentum (pT) jets separated by a large (pseudo-)rapidity interval void of particle activity, also known as jet-gap-jet events. In the limit where the collision energy sqrt{s} is much larger than any other momentum scale, the jet-gap-jet process is described in terms of perturbative pomeron exchange between partons within the Balitsky-Fadin-Kuraev-Lipatov (BFKL) limit of perturbative quantum chromodynamics (QCD). The BFKL pomeron exchange amplitudes, with resummation at the next-to-leading logarithmic approximation, have been embedded in the PYTHIA8 Monte Carlo event generator. Standard QCD dijet events are simulated at next-to-leading order in αs matched to parton showers with POWHEG+PYTHIA8. We compare our calculations to measurements by the CDF, D0, and CMS experiments at center-of-mass energies of 1.8, 7 and 13 TeV. The impact of the theoretical scales, the parton densities, final- and initial-state radiation effects, multiple parton interactions, and pT thresholds and multiplicities of the particles in the rapidity gap on the jet-gap-jet signature is studied in detail. With a strict gap definition (no particle allowed in the gap), the shapes of most distributions are well described except for the CMS azimuthal-angle distribution at 13 TeV. The survival probability is surprisingly well modelled by multiparton interactions in PYTHIA8. Without multiparton interactions, theoretical predictions based on two-channel eikonal models agree qualitatively with fits to the experimental data.

Towards a single scale-dependent Pomeron in holographic light-front QCD

The Pomeron Regge trajectory underlies the dynamics dependence of hadronic total cross sections and diffractive reactions at high energies. The physics of the Pomeron is closely related to the gluon distribution function and the gluon gravitational form factor of the target hadron. In this article we examine the scale dependence of the nonperturbative gluon distribution in the nucleon and the pion, which was derived in a previous article [G. F. de T\'eramond, H. G. Dosch, T. Liu, R. S. Sufian, S. J. Brodsky, and A. Deur, Gluon matter distribution in the proton and pion from extended holographic light-front QCD, Phys. Rev. D 104, 114005 (2021)] in the framework of holographic light-front QCD and the Veneziano model. We argue that the QCD evolution of the gluon distribution function $g(x,\ensuremath{\mu})$ to large ${\ensuremath{\mu}}^{2}$ leads to a single scale-dependent Pomeron. The resulting Pomeron trajectory ${\ensuremath{\alpha}}_{P}(t,\ensuremath{\mu})$ not only depends on the momentum transfer squared $t$, but also on the physical scale $\ensuremath{\mu}$ of the amplitude, such as the virtuality ${Q}^{2}$ of the interacting photon in inclusive diffractive electroproduction, thus unifying the soft and the perturbative Pomeron. This can explain not only the ${Q}^{2}$ evolution of the proton structure function ${F}_{2}(x,{Q}^{2})$ at small $x$, but also the observed energy and ${Q}^{2}$ dependence of high energy diffractive processes involving virtual photons up to LHC energies.

High |t| diffractive vector meson production at the EIC

We investigate the prospects of the diffractive production of $J/\psi$ mesons at large momentum transfer $|t|$ at the future Electron Ion Collider in electron-proton collisions. In particular, we focus on the measurements of the rapidity gap size. The model used for the calculations is based on the diffractive exchange of the Balitsky-Fadin-Kuraev-Lipatov perturbative Pomeron. Calculations for the cross section and the estimates for the rates assuming integrated luminosity of $10 \, \rm fb^{-1}$ are provided. Two experimental strategies were considered. First, measuring the rapidity gap size directly, by observing the activity in the forward part of the central detector, and second by putting a lower limit on the rapidity gap size in the case when the detector cannot measure forward activity. We find that, it is possible to measure at the EIC the dependence of the cross section on rapidity gap interval up to four units in rapidity. This should allow to measure the change of the cross section by a factor 1.6 expected due to the BFKL exchange. This is possible with the present setup of the detector which projects the coverage up to 3.5 units of rapidity. We conclude however, that the extension of the detector up to higher rapidity, for example to 4.5 would be desirable and provide even better lever arm for testing rapidity gap physics at the EIC.

DGLAP versus perturbative Pomeron in large momentum transfer hard diffractive processes at HERA and LHC

We evaluate within the LO DGLAP approximation the dependence on energy of the cross section of the photo(electro)production of vector meson V (V=J/ψ,…) in the hard elastic processes off a parton γ∗+g→V+g as the function of momentum transfer t=(qγ−pV)2. We demonstrate that in the limit −t⩾mV2+Q2 the cross section does not contain double logarithmic terms in any order of the DGLAP approximation leading to the energy independent cross section. Thus the energy dependence of cross section γ∗+p→J/ψ+rapidity gap+X is governed at large t by the gluon distribution within a proton, i.e. it is unambiguously predicted within the DGLAP approximation including the stronger WγN dependence at larger −t. This prediction explains recent HERA data. The calculations which follow perturbative Pomeron logic predict opposite trend of a weaker WγN dependence at larger t. We explain that at the HERA energies double logarithmic terms characteristic for DGLAP approximation dominate in the hard processes as the consequence of the constraints due to the energy–momentum conservation. We give predictions for the ultraperipheral hard diffractive processes at the LHC and show that these processes are well suited for looking for the contribution of the single logarithmic terms due to the gluon emission in the multi-Regge kinematics. We also comment on the interrelation between energy and t dependence of the cross sections of the hard exclusive processes.

The energy dependence of the hard exclusive diffractive processes in pQCD as the function of momentum transfer

We predict the dependence on energy of photo (electro) production processes: γ(γ*)+p→V+X with large rapidity gap at small x and large momentum −t transferred to V in pQCD. Here V is a heavy quarkonium (J/ψ,ϒ) or longitudinally polarized light vector meson (in the electroproduction processes), etc. In the kinematics of HERA we calculate the dependence on energy of cross sections of these processes as the function of momentum transfer t, photon virtuality Q2 and/or quarkonium mass. In the kinematical region \(Q_{0}^{2}\le -t\ll Q^{2}+M^{2}_{V}\) the nontrivial energy dependence of the cross section for the vector meson production due to the photon scattering off a parton follows within QCD from the summing of the double logarithmic terms. In the second regime \(-t\ge Q^{2}+M^{2}_{V}\) within DGLAP approximation in all orders of perturbation theory the \(q\bar{q}\)-parton elastic cross section is energy independent. We show that the correct account of the double logarithmic terms and of the gluon radiation including kinematical constraints removes the disagreement between pQCD calculations and recent HERA experimental data. The explicit formula for the dependence of the differential cross section \(\frac{d^{2}\sigma}{dt\,dx_{J}}\) of these processes on \(s_{\gamma^{*}N}\) is obtained. We show that perturbative Pomeron type behavior may reveal itself only at energies significantly larger than those available at HERA. In addition we evaluate the energy dependence of DVCS processes.

Diffractive parton distributions from perturbative QCD

The asymptotic collinear factorisation theorem, which holds for diffractive deep-inelastic scattering, has important modifications in the sub-asymptotic HERA regime. We use perturbative QCD to quantify these modifications. The diffractive parton distributions are shown to satisfy an inhomogeneous evolution equation. We emphasise that it is necessary to include both the gluonic and sea-quark t-channel components of the perturbative Pomeron. The corresponding Pomeron-to-parton splitting functions are derived in the Appendix.

Simultaneous QCD analysis of diffractive and inclusive DIS data

We present a novel analysis of diffractive DIS data, in which the input parton distributions of the Pomeron are parameterised using perturbative QCD expressions. In addition to the usual two-gluon model for the perturbative Pomeron, we allow for the possibility that it may be made from two sea quarks. In particular, we treat individually the components of the Pomeron of different size. This property allows the absorptive corrections to the inclusive DIS structure function F 2 to be calculated using the AGK cutting rules. The absorptive effects are found to enhance the size of the gluon distribution of the proton at small x .

A QCD analysis of diffractive deep-inelastic scattering data

We perform a novel type of analysis of diffractive deep-inelastic scattering data, in which the input parton distributions of the Pomeron are parameterised using the perturbative QCD expressions. In particular, we treat individually the components of the Pomeron of different size. We are able to describe simultaneously both the recent ZEUS and H1 diffractive data. In addition to the usual two-gluon model for the perturbative Pomeron, we allow for the possibility that it may be made from two sea quarks.

The effect of higher order corrections to the BFKL equation on the perturbative pomeron

We discuss the significance of the next-to-leading order term in the BFKL equation on the energy dependence of diffractive processes controlled by the perturbative QCD pomeron. It is shown that whereas the large negative corrections do indeed reduce the rate of growth of diffractive amplitudes with increasing energy, this reduction is considerably less than previously expected.

The soft pomeron and HERA

The standard phenomenology of the soft pomeron in hadron - hadron interactions is recalled briefly. The model is confronted with the HERA data for the total photoproduction cross section, deep inelastic scattering, diffractive vector meson photoproduction and diffractive electroproduction of vector mesons. Although much of the data can be explained by the model, there are some aspects of the HERA data which require a more rapid variation with energy than can be incorporated. It is argued that the perturbative (BFKL) pomeron cannot give a sufficiently large contribution to explain these observations. Possible non-perturbative solutions to this problem are indicated.

T-channel approach to Reggeon interactions in QCD.

Starting from the multi-Regge effective action for high-energy scattering in QCD a $t$-channel approach can be developed which is similar to the approach by White based on general Regge arguments. The BFKL kernel of reggeized gluon interaction, contributions to the $2 \rightarrow 4 $ reggeized gluon vertex function and the one-loop correction to the BFKL kernel are considered. The conditions are discussed under which this approach can provide a simple estimante of the next-to-leading logarithmic corrections to the BFKL perturbative pomeron intercept.

Deep inelastic onium scattering

Using the colour dipole approach of the QCD perturbative (BFKL) Pomeron exchange in onium-onium scattering, we compute the cross section for small but hierarchically different onium sizes. A specific term dependent on the size-ratio is generated. In deep inelastic onium scattering it appears as a scaling-violation contribution to the quark structure function near the BFKL singularity. We find that the extension of the formalism for deep inelastic onium scattering to the proton structure function provides a remarkably good 3-parameter fit to HERA data at small x with a simple physical interpretation in terms of the dipole formulation.

Semi-hard parton rescatterings in nuclear collisions at very high energies

Representing the semi-hard partonic interactions by the exchange of Lipatov's perturbative Pomeron, we express the semi-hard nuclear cross section as a self shadowing cross section. With the help of a generating functional technique, we obtain average numbers of multiple semi-hard partonic collisions without any need of using explicit expressions for the multi-parton distributions. The average number of semi-hard interactions of a given projectile parton against a target nucleus is estimated quantitatively and it is shown to grow very rapidly above one with increasing the c.m. energy. (Figures available on request)

Production of jet pairs at large relative rapidity in hadron-hadron collisions as a probe of the perturbative pomeron

The production of jet pairs with small transverse momentum and large relative rapidity in high energy hadron-hadron collisions is studied. The rise of the parton-level cross section with increasing rapidity gap is a fundamental prediction of the BFKL “perturbative pomeron” equation of Quantum Chromodynamics. However, at fixed collider energy it is difficult to disentangle this effect from variations in the cross section due to the parton distributions. It is proposed to study instead the distribution in the azimuthal angle difference of the jets as a function of the rapidity gap. The flattening of this distribution with increasing dijet rapidity gap is shown to be a characteristic feature of the BFKL behaviour. Predictions for the Fermilab p p collider are presented, and comparisons with a non-perturbative model calculation are made.

Photoproduction of jet pairs at HERA as a probe of the perturbative pomeron

The photoproduction of minijet pairs with small transverse momentum and large relative rapidity at the HERA electrophoton collider is studied. We examine, in particular, the prospects for measuring a rise in the cross section with increasing rapidity gap at fixed transverse momentum, as predicted by the BFKL ‘perturbative pomeron’ of QCD. We show that the distribution in the azimuthal angle difference of the jets is particularly sensitive to the BFKL resummation, and its therefore more likely to provide a distinct signature than the minijet cross section itself.

Parton-parton elastic scattering and rapidity gaps at very high energies

The theory of the perturbative pomeron, due to Lipatov and collaborators, is used to compute the probability of observing parton-parton elastic scattering and rapidity gaps between jets in hadron collisions at very high energies.

Exploring the Lipatov equation

Properties of the Lipatov equation for the small x behaviour in deep inelastic scattering are explored. In particular, the effect of imposing upper and lower cutoffs on the transverse momentum integral in the equation is analysed. The lower cutoff, needed to avoid integration over momenta where the gluon propagators are nonperturbative, does not change the output power. Imposing both a lower and an upper cutoff, so as to take account of kinematic limitations at subasymptotic values of Q 2, has an important effect even at HERA energies. This will make it difficult to separate the perturbative pomeron from the nonperturbative one seen already in soft hadronic collisions.

Gluonic regge singularities and anomalous dimensions in QCD

The Regge calculus results on the perturbative pomeron are applied to deep inelastic scattering. Explicit expressions are given for the anomalous dimensions γ GG n and γ GF n at n ≅ 1 to the lowest order in α and all orders in α/( n − 1).