A one-dimensional approximation for the pomeron in the dual unitarity scheme

Using a one-dimensional approximation, the pomeron in the dual unitarity scheme is examined analytically in a multiperipheral cluster model. Clusters have negative short range correlations due to the t_min effect. In dual models, the pomeron has a crossing odd part, especially in B$\text{B}$ and BB scattering. By taking all reggeon loops into account, we show explicitly in our approximation that the crossing-odd part has only lower-lying singularities in the j-plane (typically complex poles with $\text{Re}\text{α?0.2}$) whereas the crossing-even part has the leading singularity at j = α_P (we imposed α_P = 1). The dual unitarity scheme leads to a modified version of the f-dominance of the pomeron. We calculate the SU(3) breaking of the pomeron due to the SU(3) breaking among Regge trajectories without additional assumptions on the SU(3) property of the pomeron.     

Diffractive resonance production and f-dominance of the pomeron

A model for predicting diffractive production of meson resonances is presented. From a study of the s and t dependence of the available cross section and density matrix data, we deduce that the assumption of f, f′ dominance of the pomeron is violated. Relative to elastic scattering, where f, f′ dominance works well, the pomeron component in these inelastic processes appears to be about one half as strong in amplitude.     

Reggeon phases and the dual bootstrap program

Analyticity requirements lead to complex Regge vertices in multiparticle production amplitudes. Their effect is discussed within a dual, unitary and exchange-degenerate multi-Regge model. A resulting complex Regge vertex is incorporated in fixed-t model calculations of the reggeon bootstrap and the topological pomeron. The bootstrap condition for particle-particle scattering is unaffected but new j-plane singularities appear in Regge-Regge scattering amplitudes. The pomeron and reggeon intercepts determine the two parameters of our Regge vertex and admit two possible solutions: one is close to the naive phase rule (real vertex) and the other is complex and leads to a high lying non-leading pole in the pomeron channel.     

Intermediate mass distribution of the dual resonance pomeron

We determine the intermediate mass distribution of the dual resonance pomeron at the one-loop level and we show that the mass distribution obtained is remarkably similar to a suitably defined mass distribution in the dual multiperipheral model. Thus it is suggestive to identify the intermediate states of the dual resonance pomeron with multipheripheral processes.     

A non-perturbative study of regularized bosonic string amplitudes

The Wick-rotated, light-cone gauge U(n) Veneziano model of open and closed strings is examined in the limit as n → ∞, with g₀²n fixed. The amplitudes in both the “pomeron sector” (whose graphs are cylinders with holes punched out) and the “reggeon sector” (whose graphs are rectangles with holes punched out) are regularized using the lattice method of Giles and Thorn, as well as an alternative method. It is found that this string model is trivial. When the cut-off is removed, the pomeron and reggeon sector spectra are those of the free closed and open strings, respectively. This result is independent of the choice of g₀²n. A possible extension to fermionic strings, and the implications for large-n gauge theories are briefly discussed.     

Vacuum structure and diffraction scattering

A simple model of the vacuum is developed in order to explain the properties of the pomeron observed in experiments. In the model, pomeron exchange corresponds to two-gluon exchange. We explain how it can be that when the pomeron couples to a hadron, the two gluons couple predominantly to the same quark in the hadron, and how together their coupling is similar to that of aC=1 isoscalar photon.     

Spontaneous dynamical breaking of gauge symmetry in dual models

The consequences of gauge invariance are re-examined in dual models with unit intercept when the dimension of space-time has the maximum value compatible with the absence of ghosts. In that case, reggeon-reggeon bound states of zero mass are formed already at second order of perturbation theory. Gauge invariance no longer guarantees that the initially massless SU(3) singlet vector meson remains massless, and the mixing between the reggeon and pomeron sectors of the model yields a massive unitary singlet vector meson already at order g². A Lagrangian model which exhibits similar features to the dual situation is discussed.     

Impact parameter analysis of KN and πN scattering in the intermediate energy region

We have evaluated the s-channel-helicity partial-wave amplitudes for $\text{K}\text{N and πN}$ scattering as functions of the impact parameter using partial-wave data in the energy range P_L≈1.0–2.0 GeV/c. We find that the $\text{K}\text{N}$ background and resonance amplitudes exhibit features consistent with the dual absorptive picture for pomeron and f + ω and A₂ + ? exchanges. Comparison of the πN low-energy amplitude with the partial-wave decomposition of a quantitative Regge model gives evidence for local duality between the s-channel resonance and t- and u-channel Regge exchanges.     

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”.     

Inclusive Single Particle Distributions from the Dual Fermion Model

Inclusive single particle distributions are calculated from the discontinuity of a phenomenological 4π NN amplitude obtained from the Neveu-Schwarz-Ramond dual fermion model. In contrast to former calculations using the conventional Veneziano B₆-function we get a correct triple Regge behaviour at x ≈ 1 with correct pole position in the t-channel which is able to reproduce the data. The pomeron, not contained in the dual Born amplitude, is taken into account phenomenologically in the NN channel. Other pomeron contributions are subtracted from the data. We compare the inclusive pion distributions of the model in the beam fragmentation and central region with experimental data for reactions π + N → + X at 8 and 16 GeV/c.     

Dual resonance theory

It is suggested that a dual model could provide a Born approximation to a complete theory of hadrons. After reviewing various properties of Veneziano model amplitudes, including their underlying algebraic structure, more recent developments are discussed. The spectrum generating algebra is constructed and used to prove the no-ghost theorem for space-time dimension d ? 26. A modification of the Veneziano model incorporating SU(N) symmetry in a dynamical fashion is shown to have critical dimension 26?N. A detailed discussion of the dual pion model and its extension to fermions is presented. It is proved that both the meson and fermion sectors are ghost free for d ? 10. Finally, there is a discussion of nonplanar models and their possible connection with the pomeron singularities arising from nonplanar loop diagrams.     

The problem of the relation between double pomeron exchange in inclusive and exclusive experiments

The pionization region of the inclusive single-particle spectrum is accounted for by double pomeron exchange in the absorptive part of a six-point amplitude. In this paper a multiperipheral model for the six-point amplitude with double pomeron exchange is used for continuation by crossing and analyticity to the physical region of the exclusive two particle → four particle production process. The cross section for π^? p → π^?(π⁺π^?)p in the double-Regge region is then calculated and compared with the experimental analysis of Lipes, Zweig and Robertson which sets an upper bound to the strength of the double pomeron exchange coupling. This upper bound, coupled with the model for continuation to the inclusive cross section, is shown to give too small a magnitude for the double pomeron exchange in the pionization region. Further avenues for investigation are discussed.     

A theory of dual massive strings

A theory of relativistic strings with non-vanishing mechanical mass is developed. The theory involves the usual massless strings, and the main features of the massless theory are retained so that the system is dual and ghost-free. Some new features appear especially in the mass spectrum of the pomeron sector. The mode with Neveu-Schwarz spin is also considered.     

Regge extrapolation to the resonance region

The structure of dual amplitudes (beta functions) suggests that in non-exotic channels one should add to the usual Regge terms a second term which drops off as exp (?π Im α(s)) at large s but which is important for s?5 GeV². This “dual correction” multiplies the usual Regge imaginary part by an oscillating complex factor. With inclusion of such extra terms, it is possible to match πp amplitudes from phase-shift analyses significantly better than if the terms are omitted. The partial waves of a modified fit using the leading N, Δ, ?, f trajectories with a fixed-pole pomeron show much more of the correct resonant structure than do those of an unmodified fit.     

Multi-Regge limit of the Shapiro-Virasoro model; A sister for the pomeron

The structure of the four-, five-and six-point functions in the Shapiro-Virasoro model in multi-Regge and double-helicity pole limits is studied in detail. A pomeron propagator is derived along with the pomeron-particle-pomeron vertex function. The structure of both is investigated and evidence provided for the existence of a pomeron sister trajectory, related to the usual trajectory, αp, by $\text{β}\text{p}\text{=}\text{1}\text{2}\text{α}\text{p}\text{? 1}$; this is demonstrated to exist and its contribution to the full amplitude derived. Throughout, a correspondence between regions of angular integration in the Shapiro-Virasoro model and twisted configurations in the conventional dual model is emphasised.     

Probing the structure of the pomeron

We suggest that the pseudo-rapidity cut dependence of diffractive deep-inelastic scattering events at HERA may provide a sensitive test of models of diffraction. A comparison with the experimental cross section shows that the Donnachie-Landshoff model and a simple two-gluon exchange model of the pomeron model are disfavoured. However a model with a direct coupling of the pomeron to quarks is viable for a harder quark–pomeron form factor, as is a model based on the leading-twist operator contribution. We also consider a direct-coupling scalar pomeron model. We comment on the implications of these results for the determination of the partonic structure of the pomeron. Received: 5 March 1999 / Published online: 3 August 1999     

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.     

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.     

Diffractive photoproduction of jets with a direct pomeron coupling at HERA

We investigate in detail the effect of a direct pomeron coupling to quarks on the production of jets inep scattering with almost real photons. Jet production via a direct pomeron coupling is compared with the resolved-pomeron mechanism. We consider both direct and resolved photoproduction. Rapidity and transverse momentum distributions are calculated and compared with preliminary H1 and ZEUS data.