Hadron–nucleus scattering in the local reggeon model with pomeron loops for realistic nuclei

The contribution of the simplest loops for hadron–nucleus scattering cross-sections is studied in Local Reggeon Field Theory with a supercritical pomeron. It is shown that inside the nucleus the supercritical pomeron transforms into a subcritical one, so that perturbative treatment becomes possible. The pomeron intercept becomes complex, which leads to oscillations in the cross-sections.     

On the d<Subscript>T</Subscript>=0 toy model in reggeon field theory

Reggeon field theory with zero transverse dimensions is critically reanalyzed in the Hamiltonian formulation for both a sub- and a supercritical pomeron. Different mathematical aspects of the model, starting from the scalar products in the space of quantum states, are discussed. The probabilistic picture is addressed in the absence of pomeron merging. The issue of the large loop approximation is discussed in terms of the Hamiltonian evolution and its relation to the probabilistic picture recalled. A perturbative treatment, based on the PT symmetry of the model, is proposed that may be useful for more realistic models. Finally, we present numerical calculations for the various parameters of the models, α(0)-1=μ and the triple-pomeron coupling constant λ, which help one to understand some mathematical aspects and the different approximation regimes. They show that the triple-pomeron interaction always makes amplitudes fall with rapidity, irrespective of the value of the intercept. The smaller the values of the ratio λ/μ, the higher are the rapidities y at which this fall starts, so that at small values of λ it begins at asymptotically high rapidities (for λ/μ<1/4 the fall is noticeable only at μy>100). No visible singularity is seen for the critical pomeron.     

f-pole corrections to the critical parameters of the pomeron

A reggeon field theory with two vacuum quantum numbers Regge poles, the pomeron and the f-reggeon is presented. In such a theory only one stable fixed point appears which is sensibly different from that governing a RFT with the pomeron alone. This fact is responsible for the modifications of the critical parameters of the pomeron. In particular, the intercept of the bare pomeron increases and approaches the phenomenological value.     

Pomeron factorization in general dual models

We demonstrate that in each ghost-free dual model with one minor restriction, there exists a critical dimensionality of space-time in which the pomeron singularity becomes a factorizable Regge pole. In each model when this dimensionality is chosen, the pomeron emerges with twice the intercept and half the slope of the leading secondary (f) trajectory. We explicitly construct the pomeron propagator and the operator coupling the pomeron to the reggeon sector for the general dual model, including the lower-lying negative-G-parity pomeron in the Neveu-Schwarz model. Gauge identities and physical states in the pomeron sector are also investigated. In all of the dual models the pomeron form factors exhibit a generalized f dominance and modified Wu-Yang behavior.     

J-plane structure of the “cylinder”; slope and intercept of the bare pomeron

We derive and investigate an integral equation for the “cylinder” with full t-dependence. In contrast to the pure pole planar model, the “cylinder” contains, in addition to the bare pomeron pole, also a Reggeon-Reggeon cut. The strongly correlated slope and intercept of the bare pomeron have the correct observed values. We also briefly comment on the concept of “asymptotic planarity”.     

Conformally invariant pomeron interaction in perturbative QCD with large Nc

An effective non-local quantum field theory is constructed, which describes the interaction of pomerons in high-colored QCD. The theory includes both splitting and merging triple pomeron vertexes and diagrams with pomeronic loops. The Schwinger–Dyson equations for the ‘physical’ pomeron are written. Conformal invariance allows one to reduce the theory to the old-fashioned Gribov pomeron theory with an infinite number of pomerons, one of which is supercritical.     

Existence of a phase transition in reggeon field theory in two transverse dimensions

We show that a reggeon field theory, in the physical number of dimensions, with a linear bare trajectory and a constant triple-pomeron coupling, undergoes a phase transition as the bare pomeron intercept is increased through a certain critical value.     

Odderon with a running coupling constant

The running coupling is introduced into the equation for the odderon via the bootstrap relation. It is shown that the previously found odderon state with a maximal intercept, which is constructed from an antisymmetric pomeron wave function, continues to exist in the running coupling case. Its intercept is found to remain equal to unity independent of the behaviour assumed for the running coupling at low momenta.     

On the triple-Pomeron vertex in perturbative QCD

We estimate the size of the triple-pomeron vertex in perturbative QCD and compare with the phenomenological value extracted from Regge fits to the experimental data. For simplicity, the results of the QCD analysis are taken in the large-N_c limit. We find that the perturbative triple-pomeron coupling is of the same order of magnitude as the observed one. We also estimate the size of the pomeron self-energy and its contribution to the renormalization of the pomeron intercept. The effect is very small, in agreement with previous non-perturbative estimates. Received: 9 October 2002 / Published online: 20 December 2002     

The content of unitarity constraints on a pomeron pole of intercept one

We present a consistent picture of a pomeron pole with intercept one, together with its cuts, which evades the decoupling arguments. We use the reggeon cut discontinuity formulae to introduce Gribov's reggeon calculus as an exact solution of multiparticle t-channel unitarity. We show how, within the calculus, two-pomeron iterations of a singular kernel can be responsible for the zero in the triple-pomeron vertex. Using the concept of a bare pomeron pole as a multiperipheral production process which is subsequently renormalised by other effects, we apply the reggeon calculus analysis to inclusive cross sections. We find that the inclusive sum rule decoupling arguments are avoided because of the addition of enhanced absorptive corrections to the conventional Regge pole contributions. However, we show that in this picture the combined pole and two-pomeron cut contribution to the total cross section factories to order (ln s)^?2.We also show that, when the correct helicity structure of the pomeron is taken into account, the s-channel unitarity condition for pomeron scattering amplitudes does not lead to any serious decouplings.     

Problems with spontaneous breakdown in reggeon field theories

We prove a theorem which states that if a reggeon field theory undergoes spontaneous breakdown as a result of the pomeron intercept being above one, then the shifted Lagrangian must in general develop terms which are non-canonical from the point of view of reggeon Lagrangians. We discuss the interpretation of these terms and point out some of the problems associated with them.     

The bare parameters of Gribov's lagrangian in a simple t-dependent dual bootstrap model

In the context of the “$\text{1}\text{N}$ Dual Unitarization” scheme, we present an explicit dynamical study of the triple bare pomeron mechanism which governs the interaction term in Gribov's lagrangian. Together with the previously established bare pomeron slope and intercept, controlling respectively, the kinetic and mass terms in Gribov's lagrangian, this work demonstrates the viability of the “$\text{1}\text{N}$ Dual Unitarization” approach for a field theory of interaction bare pomerons.     

\gamma^* \gamma^* reactions at high energies

The total hadronic cross sections at high energy are calculated as a function of energy and photon virtuality in a model combining Reggeon exchange, the quark box diagram (a fixed pole in Regge language) and soft and hard pomeron exchanges evaluated in the context of dipole-dipole scattering. Good agreement is obtained with the data for the real cross section and for the real photon structure function . However the model prediction for the cross section is too small. This is attributed to an incorrect extrapolation of the dependence of the hard pomeron adopted here. Parametrising it independently shows that the hard part of the cross section can be well represented by a simple Regge pole with intercept . Received: 19 August 1999 / Published online: 3 February 2000     

QCD instantons and the soft pomeron

We study the rôle of semiclassical QCD vacuum solutions in high-energy scattering by considering the instanton contribution to hadronic cross sections. We propose a new type of instanton-induced interactions (“instanton ladder”) that leads to the rising with energy cross section σs^Δ of Regge type (the pomeron). We argue that this interaction may be responsible for the structure of the soft pomeron. The intercept Δ>0 is calculated. It has a nonanalytic dependence on the strong coupling constant, allowing a nonsingular continuation into the nonperturbative region. We derive the pomeron trajectory, which appears to be approximately linear in some range of (negative) momentum transfer t, but exhibits a curvature at small t. Possible rôle of instantons in multiparticle production is also discussed.     

Effect of glueball exchange in DTU

The inclusion of glueball exchange within the DTU program is known to replace the P-f identity scheme by the standard P + f scheme. We show that the output pomeron and reggeon parameters easily get realistic values when the glueball is a strongly coupled object of Regge intercept near 0.6.     

The intercept of the BFKL pomeron from forward jets at HERA

Recently the H1 and ZEUS collaborations have presented cross sections for DIS events with a forward jet. The BFKL formalism is able to produce an excellent fit to these data. The extracted intercept of the hard pomeron suggests that when all higher order corrections are taken into account the cross section will still rise very rapidly as expected for low x dynamics.     

Scattering off nuclei when the pomeran is supercritical

A recent parton interpretation of the supercritical pomeron is applied to scattering off nuclei. Predictions are made for elastic and inelastic diffraction, inclusive densities and correlations, and for hard scattering.     

Building a cylinder in the topological expansion

Usual cylinder construction neglect planar analyticity and the resulting cylinder is contaminated by j-plane cuts. Beginning with input planar amplitudes that are manifestly consistent with a pole-to-pole planar bootstrap, a three-dimensional cylinder equation is formulated, incorporating planar analyticity. The output cylinder is now free of j-plane cuts. The bare pomeron is a simple pole with trajectory intercept slightly above one.     

Calculation of critical pomeron intercept with block-spin methods

The single-site energy eigenvalues and field matrix elements of reggeon field theory are accurately calculated. Using the block-spin approximation with realistic parameters, the phase transition is studied in one and two dimensions using different methods. In one dimension, the use of blocks with one site and one link gives a critical temperature in agreement with that predicted by the high-temperature expansion. In two dimensions, the methods with critical temperature around the high-temperature expansion result, give a critical pomeron intercept larger than 1.05 in the physical range.     

Phenomenological Behavior of the Hard Pomeron Intercept

The hard pomeron intercept value is determined by the decoupling solutions of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations at low-x. The unpolarized proton structure functions at next-to-next-to-leading order (NNLO) analysis are calculated and compared with new Hadron-Electron Ring Accelerator (HERA) data.