John Polkinghorne

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.

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.

High‐Energy Behavior in Perturbation Theory

Contributions to the asymptotic behavior of Feynman integrals are evaluated which correspond to pinches in the interior of the hypercontour of integration. It is shown that they give the Gribov‐Pomeranchuk phenomenon and Regge cuts. A set of diagrams is investigated which gives a Regge cut on the physical sheet.

Partons and duality in deep inelastic lepton scattering

Abstract The parton approach, with the partons identified as quarks, is combined with a dual model to describe deep inelastic lepton scattering. The partons are introduced through a non-perturbative field-theory formalism, which is shown to reproduce many of the results of more phenomenological approaches. Duality is imposed by assuming that exotic states correspond to a purely diffractive contribution, and by constructing a Veneziano-like model for the non-diffractive contribution. It is found that the difference between the cross sections on proton and neutron is just less than one third of the experimental cross section for electro-production on the proton. The proton cross section is well explained by assuming that the diffractive contribution is small.

The scaling law for deep inelastic scattering in a few Veneziano-like amplitude

Abstract A new Veneziano-like amplitude is constructed for two currents. It satisfies the Fubini-Gell-Mann sum rule with the same form factor as is obtained from the factored residue on the leading trajectory. This form factor can be given any desired rate of decrease at large momentum transfer. The Bjorken scaling law is satisfied and the amplitude can be used to construct a simple model for deep inelastic electron scattering on protons. The result is in qualitive agreement with experiment and the parameters of the model can be chosen to give a fair quantitative fit to the data. A more intricate version of the model is also developed which incorporates some of the effects of current conservation. A feature of these models is that they correlate the behaviour of the structure function νW 2 near ω = 1 with the rate of decreaseof the form factor for large momentum transfer.

Two high energy processes involving detected final state particles

Abstract Two processes are discussed: (a) semi-inclusive electroproduction experiments; (b) heavy-lepton pair production in hadronic collisions. The non-perturbative approach to the parton model is used to evaluate scaling properties and to consider extra contributions due to wee partons. These latter have not been previously discussed and are found to be important for process (b), but absent in process (a). Quantitative agreement is obtained for process (b), including an explanation of the observed shoulder in the differential cross section.

ON THE CLASSIFICATION OF FUNDAMENTAL PARTICLES

SummaryA new four-dimensional isotopic spin formalism is developed for the heavy fundamental particles. All particles correspond to singlevalued representations of the rotation group and there is complete symmetry between the isotopic properties of fermions and bosons. The resulting classification is similar to Gell-Mann’s except that the degeneracy in the classification of the K-mesons is removed. The forms of the strong interactions are given explicitly. The physical consequences of the theory are discussed in detail. In particular it predicts the existence of a neutral K-meson of lifetime ∼ 10−19 s. A new experimental technique for detecting this particle is suggested.RiassuntoSi sviluppa per le particelle pesanti fondamentali un nuovo formalismo assumendo lo spin isotopico quadridimensionale. Tutte le particelle corrispondono a rappresentazioni ad un unico valore del gruppo rotazionale e si ha completa simmetria tra le proprietà isotopiche dei fermioni e dei bosoni. La classificazione risultante è simile a quella di Gell-Mann, salvo che scompare la degenerazione nella classificazione dei mesoni K. Le forme dell’interazione forte sono date esplicitamente. Si discutono dettagliatamente le conseguenze fisiche della teoria. In particolare questa predice l’esistenza di un mesone K neutro di vita media ∼ 10−19 s. Si suggerisce una nuova tecnica sperimentale per la scoperta di questa particella.

Acnodes and Cusps on Landau Curves

It is shown that the Landau curve for a reduced sixth‐order diagram can acquire acnodes and real cusps as the masses are varied. They are associated with complex singularities that under certain conditions are in the physical sheet and cause a breakdown of the Mandelstam representation. The problem of obtaining general criteria for acnodes and cusps is discussed.

Ethical issues in biotechnology.

New ethical questions have arisen from our ability to intervene in the structure of the genome. Responsible use of this technique requires ethical evaluation in which experts, potential beneficiaries and the general public should all participate. The examples of genetically modified food and of human genetics help to illustrate the issues involved.

The Complete High‐Energy Behavior of Ladder Diagrams in Perturbation Theory

The Mellin‐transform method for obtaining the high‐energy behavior of Feynman integrals is modified and applied to the set of ladder diagrams. The complete set of terms of the form s−1(ln s)n is summed, and gives an equation for the trajectory function which is analogous to that obtained by Fredholm methods for a Yukawa potential. A perturbation expansion for α(t) valid for t large is given, and the threshold behavior investigated. The results confirm the reliability of the perturbation‐theory method of investigation. They also exhibit directly the connection between high‐energy behavior and the poles of the scattering amplitude.