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.     

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.     

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.     

On the two-reggeon-two-particle amplitude at large momentum transfer

The role of sister trajectories in the fixedangle limit of reggeon amplitudes is analyzed. The conventional α-sector of the two-reggeon-two-particle scattering amplitude has been proved to be negligeable, in the non-Regge asymptotic limit, as compared to the unconventional β-sector, which behaves as exp{?β(s)f(θ)}. It is conjectured that the fixed-angle limit of a general reggeon amplitude is dominated by the less sloped sister trajectory exchanged in the Regge region.     

Diffractive scattering in the dual model

A method is suggested for calculating the elastic amplitude as the shadow of multiparticle processes. This does not require explicit formulae for the production amplitudes, but depends only on the following assumptions: (a) Regge behaviour, (b) semi-local duality, (c) exchange degeneracy. The system is multiperipheral in general structure but because of the assumption (a)-(c), it incorporates such features as the clustering of final particles and provides a proper treatment of quantum numbers, phases, and resonance spins. As a result, the unitarity sum separates automatically into two components corresponding respectively to pomeron and ordinary reggeon exchange, each of which is seen to have the correct qualitative dependence on the quantum numbers, the energy s, and the momentum transfer t. Quantitatively, the elastic amplitude is given in terms of a triple-Regge vertex, for which we suggest a simple parametization based on a detailed study of existing experiment and the Veneziano model. The method is then applied to calculate the elastic amplitudes for π^±p, K^±p and pp within the range 6 < s < 50 and 0 > t > ?0.5 GeV². Semi-quantitative agreement is obtained with experiment with essentially no free parameter. Although the investigation is restricted at present to elastic scattering as the shadow of only the non-diffractive component satisfying (a)-(c), the method is believed to apply also to other diffractive processes, and may be regarded as the first step in an iterative solution of the full unitarity equation.     

Pomerons and BCFW recursion relations for strings on D-branes

We derive pomeron vertex operators for bosonic strings and superstrings in the presence of D-branes. We demonstrate how they can be used in order to compute the Regge behavior of string amplitudes on D-branes and the amplitude of ultrarelativistic D-brane scattering. After a lightning review of the BCFW method, we proceed in a classification of the various BCFW shifts possible in a field/string theory in the presence of defects/D-branes. The BCFW shifts present several novel features, such as the possibility of performing single particle momentum shifts, due to the breaking of momentum conservation in the directions normal to the defect. Using the pomeron vertices we show that superstring amplitudes on the disc involving both open and closed strings should obey BCFW recursion relations. As a particular example, we analyze explicitly the case of 1→1$1\to 1$ scattering of level one closed string states off a D-brane. Finally, we investigate whether the eikonal Regge regime conjecture holds in the presence of D-branes.     

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.     

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.     

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.     

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.     

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.     

Check of the gluon-reggeization condition in the next-to-leading order: Quark part

The bootstrap condition for gluon production in multi-Regge kinematics is considered in the next-to-leading order. Bootstrap conditions follow fromthe requirement that the Regge formof amplitudes in QCD be consistent with s-channel unitarity and are nonlinear relations between the Reggeized-gluon trajectory and vertex functions. Their fulfillment ensures the Reggeization of gluons—that is, the Regge form of both elastic and inelastic amplitudes. This condition is the only one that has not yet been verified. The demonstration of its fulfillment is the ultimate step in proving the Reggeization of gluons in the next-to-leading logarithmic approximation. In the present article, this is done for the quark part of the bootstrap condition.     

Regge theory for multiparticle amplitudes

The asymptotic behavior of multiparticle scattering amplitudes is discussed and reviewed with an emphasis on the analytic structure of the amplitudes as a function of the channel invariants. Single and multiple asymptotic limits of the Regge and helicity type are defined and a recipe is given for obtaining the asymptotic behavior of amplitudes in these limits controlled by exchanges of factorizable Regge poles and constrained by analyticity requirements. Applications to inclusive cross sections and the decoupling theorems for a pomeron Regge pole are reviewed as illustrative consequences of unitarity for multi-Regge theory. The present understanding of the relationship of cuts in angular momentum to unitarity is also described and suggestions given for further research. An effort has been made to keep the discussion pedagogical, while at the same time providing an entree to the literature.     

A laboratory scale fundamental time?

In the Regge kinematics the amplitude for gluon production off three scattering centers is found in the Lipatov effective action technique. The vertex for gluon emission with the reggeon splitting in three reggeons is calculated and its transversality is demonstrated. It is shown that in the sum of all contributions terms containing principal value singularities are canceled and substituted by the standard Feynman poles. These results may be used for calculation of the inclusive cross section for gluon production on two nucleons in the nucleus.     

General features of the reggeon calculus with α > 1

We discuss some general properties of the reggeon calculus with input intercept greater than one, in an attempt to formulate a model yielding indefinitely rising cross sections which is consistent with t-channel unitarity. In general the leading behaviour of the amplitude always factorises. If interactions between reggeons are ignored the scattering is equivalent to that from a grey absorbing disk of radius O (ln s). Diagrams involving such interactions are subject to large-scale cancellations. These enable the model to give sensible results for inclusive cross sections. In quantum number exchange reactions, factorisation of the Regge pole residues is weakly broken in the model.     

Exploiting the equivalence of reggeon field theory in zero transverse dimensions and reaction–diffusion processes

The reggeon field theory in zero transverse dimensions is investigated. Two versions of the theory are considered: one that allows for at most triple pomeron interactions and the other that embodies an additional 2→2 quartic reggeon coupling. The behavior of the scattering amplitude at asymptotic rapidities is obtained in both cases. In an s-channel picture of the high energy scattering both models can be viewed as reaction–diffusion processes. We derive known results in reggeon field theory rather easily using the reaction–diffusion formalism. We find that some results which are surprising from the reggeon field theory point of view turn out to have a simple interpretation from the reaction–diffusion point of view.     

Flavouring the Gribov process

The exchange of flavour carrying trajectories is studied in the non-covariant parton interpretation of reggeon field theory. While pomeron exchange is described by wee partondensities, i.e. diagonal elements of the density matrix of a fast hadron, meson exchange is described by density matrix elements which are diagonal in parton number but off-diagonal in flavour. The reggeon field theory “hamiltonian” describes a markoffian evolution of this block-diagonal density matrix during a boost. This interpretation is possible both if there are two distinctf and ? trajectories and in case of ? identity. The meson trajectories are superpositions of odd and even signature trajectories.