P.V. Landshoff

Total cross sections

Abstract Regge theory provides a very simple and economical description of all total cross sections.

Elastic Scattering and Diffraction Dissociation

Abstract High-energy elastic and inelastic scattering at small t are discussed in terms of pomeron and (where relevant) double-pomeron exchange. The similarity between pomeron exchange and photon exchange allows an almost parameter-free description of various elastic process, a and diffraction dissociation, in good agreement with experiment.

A non perturbative parton model of current interactions

A formulation of the parton picture of current interactions is given without recourse to perturbation theory. In deep inelastic electron scattering the structure functions W1 and νW2 scale but the corresponding functions W1and νW2 for electron-positron annihilation processes at high energy are likely to be divergent. Form factors for particles other than the partons themselves go to zero at infinite momentum transfer. The relation between the rate of decrease of the nucleon form factors and the behaviour of νW2 near ω = 1 is shown to depend upon further specific properties of parton-nucleon dynamics and so to be model dependent. Some similarities between the parton picture and a recently proposed Veneziano-like amplitude are discussed. A difference is that the parton picture permits the incorporation of the pomeron.

Small x: two pomerons!

Abstract Regge theory provides a very simple and economical description of data for (i) the proton structure function with x Q 2 values, (ii) the charm structure function, and (iii) γ p→J/ψ p . The data are all in agreement with the assumption that there is a second pomeron, with intercept about 1.4 . They suggest also that the contribution from the soft pomeron is higher twist. This means that there is an urgent need to make perturbative evolution compatible with Regge theory at small and not-so-small x , and to reassess the magnitude of higher-twist contributions at quite small x .

Dynamics of elastic scattering

Abstract If the energy scale of the long-range interaction is determined by the string tension and not by the nucleon mass, our previous dynamical model for high-energy pp and p p scattering is in excellent agreement with the data, both from the CERN ISR and the CERN Collider. Thus the interpretation of these data does not require any novel dynamical mechanism.

Exclusive rho production in deep inelastic scattering

Abstract While for many purposes the pomeron behaves like a C =1 isoscalar photon, the observed small- x behaviour of inclusive deep inelastic scattering requires it to have an “effective radius” of about 1 6 fm . This is tested in a zero-parameter calculation of the exclusive process γ ∗ p→ϱ p . Our results compare well with recent data from the EMC Collaboration, and raise certain questions about these data.

Diffractive deep inelastic lepton scattering

Abstract We calculate the structure function for deep inelastic lepton scattering events in which the target proton emerges isolated in rapidly and has its momentum changed very little by the scattering. This measures “the structure function of the pomeron”. We find that such events make up a few per cent of the total inclusive cross section at small values of the Bjorken variable x, so that it should be possible to measure the structure function at HERA.

A non-analytic S-matrix

Abstract A study is made of theories having the unusual analyticity properties recently proposed by Lee and Wick. A prescription is given for setting up a covariant perturbation-theory expansion of the scattering amplitudes, based on Feynman graphs. It is found that the presence of a complex pole in the upper half plane of the physical sheet leads to points of non-analyticity in the physical region, such that the values of the amplitude to either side of the point are not related by analytic continuation. It is shown how this is compatible with unitarity. The nature of the non-analyticity is not fully determined by unitarity. Neither, in the case of the more complicated graphs, is it fully determined by the perturbation-theory prescription, and some extra constraint must be imposed on the theory to remove the ambiguity. It is shown that the prescription of Lee and Wick has an exactly similar ambiguity, but for their prescription different results are obtained in different Lorentz frames. An estimate is made of the extent to which the theory violates causality, and is found to be too small to measure.

Hard diffraction: Production of high pT jets, W or Z, and Drell-Yan pairs

We have previously calculated the quark content of the pomeron. This determines the diffractive structure function of the proton, which may be measured in deep inelastic lepton scattering at HERA. We now apply it to two hard diffractive pp or pp reactions. In these reactions, one initial proton or antiproton has its momentum changed very little by the interaction, and emerges isolated in rapidity. Our predicted cross sections for hard diffractive high pT jet production at SPS collider energy are between one and two orders of magnitude smaller than previous estimates. At this energy the cross section rises very rapidly with energy even for only moderately high pT. At SSC energy, of the order of 1% of jet events will be diffractive, over a wide range of pT. For W and Z production, the fraction of events that are diffractive at this energy will be about 10%, and for continuum dilepton production such a fraction will be achieved when the energy ✓s is greater than about 30mll.

pp and pp elastic scattering

Abstract We present an analysis of pp and p p elastic scattering in terms of various exchanges. Three-gluon exchange dominates at large t , and single-pomeron exchange at small t . The dip seen in high-energy pp scattering is provided by the interference of both of these with double-pomeron exchange. We predict that this dip will not be found in high-energy p p scattering. The dip that is seen in low-energy p p scattering is the result of the additional presence of reggeon-pomeron exchange.