QCD Pomeron Research Articles

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.

Energy spectrum of the electroweak Pomeron

In this paper we study the high energy behaviour of Electroweak Standard Model for a nonzero Weinberg angle $\theta_{W}$. We evaluate the spectrum of the electroweak pomeron and demonstrate that the leading intercept is given by $\alpha _{\rm e.w.}4 \ln 2$ and does not depend on the mixing angle $\theta_{W}$. Due to its very small numerical value, we conclude that the high energy behaviour of electroweak theory cannot be discussed without including the QCD Pomeron which, at sufficiently large energies, will dominate.

Stringy (holographic) Pomeron with extrinsic curvature

We model the soft pomeron in QCD using a scalar Polyakov string with extrinsic curvature in the bottom-up approach of holographic QCD. The overall dipole-dipole scattering amplitude in the soft pomeron kinematics is shown to be sensitive to the extrinsic curvature of the string for finite momentum transfer. The characteristics of the diffractive peak in the differential elastic $pp$ scattering are affected by a small extrinsic curvature of the string.

QCD pomeron from AdS/CFT Quantum Spectral Curve

Using the methods of the recently proposed Quantum Spectral Curve (QSC) originating from integrability of ${\cal N}=4$ Super--Yang-Mills theory we analytically continue the scaling dimensions of twist-2 operators and reproduce the so-called pomeron eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation. Furthermore, we recovered the Faddeev-Korchemsky Baxter equation for Lipatov's spin chain and also found its generalization for the next-to-leading order in the BFKL scaling. Our results provide a non-trivial test of QSC describing the exact spectrum in planar ${\cal N}=4$ SYM at infinitely many loops for a highly nontrivial non-BPS quantity and also opens a way for a systematic expansion in the BFKL regime.

Stretched string with self-interaction at high resolution: Spatial sizes and saturation

We model the (holographic) QCD Pomeron as a long and stretched (fixed impact parameter) transverse quantum string in flat $D_\perp=3$ dimensions. After discretizing the string in $N$ string bits, we analyze its length, mass and spatial distribution for large $N$ or low-x ($x=1/N$), and away from its Hagedorn point. The string bit distribution shows sizable asymmetries in the transverse plane that may translate to azimuthal asymmetries in primordial particle production in the Pomeron kinematics, and the flow moments in minimum bias $pp$ and $pA$ events. At moderately low-x and relatively small string self-interactions $g_s\approx \alpha_s$ (the gauge coupling), a pre-saturation phase is identified whereby the string transverse area undergoes a sharp transition from a large diffusive growth to a small fixed size area set by few string lengths $l_s$. For lower values of $x$ the transverse string bit density is shown to increase as $1/x$ before saturating at the Bekenstein bound of one bit per Planck area with the Planck length $l_P/l_s\approx \alpha_s^{2/3}$. We argue that the effects of the AdS$_5$ curvature on the interacting string maybe estimated using an effective transverse dimension between the interacting string bits. The result is a smoother transition with a transverse string bit density increasing as $1/x^{0.31}$.

Matching the Discrete BFKL Pomeron to DGLAP

The discrete BFKL formalism which accounts for the running of the coupling and incorporates information about the phase of the oscillations at small transverse momentum, arising from the infrared properties of QCD, leads to a QCD pomeron consisting of a set of discrete Regge poles. Here we discuss under what circumstances this discrete pomeron leads to an amplitude which matched the prediction of a DGLAP analysis in the double leading logarithm limit.

Secondary hadron distributions in a two component model

Inclusive charged hadron cross sections, $d\ensuremath{\sigma}/d\ensuremath{\eta}$, and the mean transverse momenta, $⟨{p}_{T}⟩$, are considered within the two component model, which combines the powerlike and the exponential terms in ${p}_{T}$. The observed dependences of the spectra shape on energy and the event multiplicity qualitatively agree with that expected from the Regge theory with the perturbative QCD Pomeron. Finally, the dependences observed are used to make predictions on the mean transverse momenta, $⟨{p}_{T}⟩$, as function of multiplicity at LHC energies, which are tested on available experimental data.

Exclusive vector mesons at high energies: from photon-proton to proton-proton and nucleus-nucleus collisions

Photoproduction of vector mesons has been studied since the 1960's and was instrumental in establishing the hadronic structure of the photon and the concept of vector- meson dominance. More recently our knowledge on vector meson photoproduction has been furthered by experiments at the HERA accelerator. Total cross sections ans well as a number of kinematical distributions have been measured from light to heavy vector mesons. These experiments have been a testbed of ideas on the production mechanism, the QCD Pomeron exchange. In particular in varying the mass of the vector meson we can study the Pomeron exchange from the soft to the perturbatively hard regimes. The production mechanism also contains information on the quark-antiquark wave function of the produced meson. High energy protons or ions are the source of a flux of Weizs ¨ Williams photons, which can be utilized to study the photoproduction of vector mesons also at the Tevatron and LHC colliders. We discuss how information on the small-x gluon distribution in protons in nuclei can be obtained. Besides this intrinsic interest in vector meson production, a precise knowledge thereof is also necessary for odderon searches. In this regard, we discuss also transverse momentum distributions including absorption effects.

BFKL pomeron propagator in the external field of the nucleus

It is shown by numerical calculations that the convoluted QCD pomeron propagator in the external field created by a solution of the Balitsky–Kovchegov equation in the nuclear matter vanishes at high rapidities. This may open a possibility to apply the perturbative approach for the calculation of pomeron loops.

Large t diffractive [formula omitted] photoproduction with proton dissociation in ultraperipheral pA collisions at LHC

We evaluate the large momentum transfer J/ψ photoproduction with rapidity gaps in ultraperipheral proton–ion collisions at the LHC which provides an effective method of probing dynamics of large t elastic hard QCD Pomeron interactions. It is shown that the experimental studies of this process would allow to investigate the energy dependence of cross section of elastic scattering of a small cc¯ dipole off the gluon over a wide range of invariant energies 103<scc¯-gluon<106 GeV2. The accessible energy range exceeds the one reached in γp at HERA by a factor of 10 and allows the kinematic cuts which improve greatly sensitivity to the Pomeron dynamics as compared to the HERA measurements. The cross section is expected to change by a factor ⩾20 throughout this interval and our estimates predict quite reasonable counting rates for this process with the several of the LHC detectors.

Boundary conditions in the QCD nucleus–nucleus scattering problem

In the framework of the effective field theory for interacting BFKL pomerons, applied to nucleus–nucleus scattering, boundary conditions for the classical field equations are discussed. Correspondence with the QCD diagrams at the boundary rapidities requires pomeron interaction with the participating nuclei to be exponential and non-local. Commonly used ‘eikonal’ boundary conditions, local and linear in fields, follow in the limit of small QCD pomeron–nucleon coupling. Numerical solution of the classical field equations, which sum all tree diagrams for central gold–gold scattering, demonstrates that corrected boundary conditions lead to substantially different results, as compared to the eikonal conditions studied in earlier publications. A breakdown of projectile–target symmetry for particular solutions discovered earlier in [S. Bondarenko, L. Motyka, Phys. Rev. D 75 (2007) 114015] is found to occur at roughly twice lower rapidity. Most important, due to a high non-linearity of the problem, the found asymmetric solutions are not unique but form a family growing in number with rapidity. The minimal value for the action turns out to be much lower than with the eikonal boundary conditions and saturates at rapidities around 10.

Diffractive dissociation including Pomeron loops in zero transverse dimensions

We have recently studied the QCD pomeron loop evolution equations in zero transverse dimensions [Phys. Rev. D 73, 094014 (2006)]. Using the techniques developed in [Phys. Rev. D 73, 094014 (2006)] together with the AGK cutting rules, we present a calculation of single, double and central diffractive cross sections (for large diffractive masses and large rapidity gaps) in zero transverse dimensions in which all dominant pomeron loop graphs are consistently summed. We find that the diffractive cross sections unitarise at large energies and that they are suppressed by powers of ${\ensuremath{\alpha}}_{s}$. Our calculation is expected to expose some of the diffractive physics in hadron-hadron collisions at high energy.

ELASTIC SCATTERING AND THE PROTON FORM FACTOR

We use the QCD pomeron model proposed by Landshoff and Nachtmann to compute the differential and the total cross-sections for pp scattering in order to discuss a QCD-based approach to the proton form factor. This model is quite dependent on the experimental electromagnetic form factor, and it is not totally clear why this form factor gives good results even at moderate transferred momentum. We exchange the electromagnetic form factor by the asymptotic QCD proton form factor determined by Brodsky and Lepage (BL) plus a prescription for its low energy behavior dictated by the existence of a dynamically generated gluon mass. We fit the data with this QCD inspired form factor and a value for the dynamical gluon mass consistent with the ones determined in the literature. Our results also provide a determination of the proton wave function at the origin, which appears in the BL form factor.

Initial condition for evolution of the perturbative QCD Pomeron in a nucleus

We show that subdominant terms obtained using the reggeized gluon diagram technique, which should be added to Pomeron fan diagrams with the triple-Pomeron interaction, can be taken into account exactly if the initial condition for the evolution is chosen in the Glauber form. This demonstrates the complete equivalence of the dipole picture and the reggeized gluon technique in the high-energy limit not only in the leading order but also in the next order.

Non-linear evolution of pomeron and odderon in momentum space

The small x evolution of the QCD pomeron and the QCD odderon is investigated in the mean field limit of the color glass condensate. The resulting system of coupled non-linear evolution equations is transformed to the momentum space and analyzed at a very small momentum transfer. The main properties of the C-even and C-odd dipole densities in momentum space are obtained analytically. The critical scaling dimension is found for the odderon and the universal asymptotic behavior of the solutions is determined for small and large gluon momenta. We find that the same saturation scale characterizes both the pomeron and the odderon and both densities depend on the momentum only through the geometric scaling variable. The absorptive effects are found to cause a strong suppression of the odderon exchange amplitude for momenta below saturation scale and only a moderate suppression for larger momenta.

The QCD pomeron in ultraperipheral heavy ion collisions: V. Double vector meson production in the BFKL approach

In this work the double vector meson production in ultraperipheral heavy ion collisions is investigated within the BFKL approach. The integrated cross sections and event rates for the processes AA --> V1 V2 AA (V_i = rho, omega, phi, J/Psi, Upsilon) are computed and theoretical estimates for scattering on both light and heavy nuclei are given for energies of RHIC and LHC.

Vector meson production in ultraperipheral heavy ion collisions

Ultraperipheral heavy ion collisions (UPCs) are an important alternative for studying QCD dynamics until the next generation of e+e−/ep/eA colliders becomes a reality. Due to the coherent action of all the protons in the nucleus, the electromagnetic field is very strong and the resulting flux of equivalent photons is large, which allows us to study two-photon as well as photonuclear interactions at high energies. In this paper we present a brief review of the vector meson production in UPCs at high energies using the QCD colour dipole approach to describe their photonuclear production and the perturbative QCD Pomeron (BFKL dynamics) to describe the double meson production in photon–photon processes. Predictions for rates and integrated cross sections are presented for energies of RHIC and LHC.

HIGH ENERGY PHOTON–PHOTON COLLISIONS AT A LINEAR COLLIDER

High intensity back-scattered laser beams will allow the efficient conversion of a substantial fraction of the incident lepton energy into high energy photons, thus significantly extending the physics capabilities of an e-e± linear collider. The annihilation of two photons produces C = + final states in virtually all angular momentum states. An important physics measurement is the measurement of the Higgs coupling to two photons. The annihilation of polarized photons into the Higgs boson determines its fundamental H0γγ coupling as well as determining its parity. Other novel two-photon processes include the two-photon production of charged pairs τ+τ-, W+W-, [Formula: see text], and supersymmetric squark and slepton pairs. The one-loop box diagram leads to the production of pairs of neutral particles such as γγ → Z0Z0, γZ0, and γγ. At the next order one can study Higgstrahlung processes, such as γγ → W+W-W-H. Since each photon can be resolved into a W+W- pair, high energy photon-photon collisions can also provide a remarkably background-free laboratory for studying possibly anomalous WW collisions and annihilation. In the case of QCD, each photon can materialize as a quark anti-quark pair which interact via multiple gluon exchange. The diffractive channels in photon-photon collisions allow a novel look at the QCD pomeron and odderon. The C = - odderon exchange contribution can be identified by looking at the heavy quark asymmetry. In the case of eγ → e′ collisions, one can measure the photon structure functions and its various components. Exclusive hadron production processes in photon-photon collisions provide important tests of QCD at the amplitude level, particularly as measures of hadron distribution amplitudes which are also important for the analysis of exclusive semi-leptonic and two-body hadronic B-decays.

Triple-pomeron dynamics: valence vs. glue

Three pomerons are known to couple via the gluon loop and interactions of this kind, which are responsible for high-mass diffraction, are described in terms of the gluonic structure function of the QCD pomeron. We show that the triple-pomeron coupling via the light quark loop associated with the “valence” in the pomeron is of the same strength as the purely gluonic coupling. The large Q 2 behavior of this new contribution is described by the DLLA evolution from the non-perturbative f f ¯ valence state of the pomeron. Numerical estimates of the high-mass diffraction structure functions based on the consistent account of both couplings are in good agreement with experimental data.

The QCD pomeron in ultraperipheral heavy ion collisions: IV. Photonuclear production of vector mesons

The photonuclear production of vector mesons in ultraperipheral heavy ion collisions is investigated within the QCD color dipole picture, with particular emphasis on the saturation model. The integrated cross section and the rapidity distribution for the A + A --> V + A + A (V = rho, omega, phi, J/Psi) process are computed and theoretical estimates for scattering on both light and heavy nuclei are given for energies of RHIC and LHC. A comparison with the recent STAR data on coherent production of rho mesons is also presented. Furthermore, we calculate the photoproduction of vector mesons in proton-proton collisions at RHIC, Tevatron and LHC energies.