Reinhard Oehme

Dispersion relations for nucleon-nucleon scattering

Abstract Dispersion relations for nucleon-nucleon scattering are presented. The general case of nonforward scattering is treated, although the majority of the discussion is confined to the limiting cases of forward scattering and the non-relativistic approximation. It is shown that in the relativistic case the dispersion relations for nucleon-nucleon scattering necessarily involve the nucleon-antinucleon amplitude. Some qualitative conclusions are drawn about the differences between the nucleon-nucleon and nucleon-antinucleon interactions. The concept of a potential in quantum field theory is discussed briefly.

Relation between effective couplings for asymptotically free models

For asymptotically free models with two independent couplings asymptotic expansions are constructed which express one effective coupling in terms of the other. The expansions involve powers (including fractional or irrational exponents) and logarithms. All orders of theβ-functions are taken into account. The expansions found are complete in the sense that they represent solutions (exact to any order) which generalize all the solutions obtained with theβ-functions approximated to second order. It is shown that higher orders are relevant since it is not possible in general to reparametrize the system such that theβ-functions become polynomials of the coupling parameters. The simplifications in case of supersymmetric models are discussed.

Construction of gauge theories with a single coupling parameter for Yang-Mills and matter fields

Abstract Massless gauge theories are considered involving matter fields coupled invariantly to a Yang-Mills field. In general renormalization induces additional couplings with independent coefficients λ j . Consistent descriptions depending only upon the gauge coupling g may be constructed by determining the functions λ j ( g ) which are independent of the normalization point and allow for an asymptotic power series in g . Two examples with four couplings are shown to result in the pure N =2, N =4 supersymmetric Yang-Mills theories. In addition, one obtains some non-supersymmetric models. Stability properties are discussed using Lyapunovs theory.

Two-channel reactions in relativistic dispersion theory

ZusammenfassungIm Rahmen der relativistischen Dispersionstheorie werden Reaktionen mit zwei gekoppelten Zwei-Teilchen-Kanälen betrachtet. Es wird gezeigt, daß die entsprechenden Partialwellen-Amplituden durch die physikalischen Verzweigungsschnitte hindurch auf eine Riemannsche Fläche mit vier Blättern analytisch fortgesetzt werden können. Die dynamischen Singularitäten werden in Betracht gezogen, und es wird der Zusammenhang zwischen den Polen in sekundären Blättern und möglichen Resonanzen der physikalischen Amplituden diskutiert. Als Modell werden die Reaktionen π+Y→π+Y,π+Y→¯K+N und ¯K + N→¯K+N benutzt, jedoch werden Komplikationen, die mit Spin und Isotopenspin zusammenhängen, weggelassen.

Renormalization group equations with vanishing lowest order of the primary β-function

Abstract The evolution equations for the effective couplings are solved for massless models with two coupling and vanishing lowest order contribution of the primary β-function. The stability and asymptotic freedom of the solutions are analyzed. A specialization to supersymmetric theories with nonvanishing Yukawa couplings of superfields shows instability for asymptotically free models and for possible cases with identically vanishing β-functions.

On superconvergence relations in quantum chromodynamics

Abstract Superconvergence relations for structure functions are considered in the exact theory and for the improved perturbation theory. The exact relations provide a link between the infrared and the ultraviolet contributions, which is of relevance for the confinement problem. They depend in important ways on the analytic properties, including the absence of Landau-type singularities, which are the dominant feature of the improved perturbation expressions.

Broken symmetries and leptonic weak interactions

Abstract The currents involved in lepton-lepton couplings generate the algebra of U(4). Corresponding U(4)-algebras can be constructed from the hadron currents; they may be considered as subalgebras of higher symmetries like U(6) × U(6), etc. The U(4)-algebras are used for the construction of two models of a universal weak coupling. One model is based upon the U(4)-algebra generated by the total hadron current involved in semileptonic interactions, and a second one is obtained by considering strangeness-changing and nonchanging currents separately. The first model involves the Cabibbo angle as a parameter and it requires this angle to be the same for all currents. The second model has no such parameter; it depends upon a possible larger manifestation of the symmetry breaking interactions to account for the damping of ΔS = 1 transitions. In both cases the neutral generators of U(4) are identified with the 1 + γ5)-projections of electromagnetic currents and of lepton number or triplet-number currents. For triplets with charges z + 1, z, z, the first model gives preference to z = 0 and the second one to z = −1. The two models are discussed briefly in connection with the phenomenological situation and with the assumption of broken SU(3)-symmetry for the hadrons. Renormalization effects are considered in detail, especially in view of the damping factor required in the second model mentioned above. The commutation relations of the hadron currents, together with the hypothesis of partially conserved axial-vector currents, give a reasonable universal damping factor λ A ∼ m π m K for axial vector matrix elements. For vector currents one obtains an analogous result only under rather restrictive assumptions. Otherwise, commutation relations, partially conserved currents, and λ V ∼ m π m K are not consistent as long as other manifestations of the symmetry breaker are considered to be small.

Duality, superconvergence and the phases of gauge theories

Abstract Results about the phase structure of certain N = 1 supersymmetric gauge theories, which have been obtained as a consequence of holomorphy and ‘electric-magnetic’ duality, are shown to be in quantitative agreement with corresponding consequences of analyticity and superconvergence of the gauge field propagator. This connection is of interest, because the superconvergence arguments for confinement are not restricted to theories with supersymmetry. The method of reduction in the space of coupling parameters is used in order to define, beyond the matching conditions, an asymptotically free, dual magnetic theory involving Yukawa couplings.

Superconvergent gluon propagator and the quark-antiquark potential

Abstract Superconvergence of the gluon propagator, together with the asymptotically negative sign of the discontinuity, imply that the structure function has a representation which corresponds to an approximately linear quark-antiquark potential, provided the number of flavors is less than ten. For more than ten flavors, there is no indication for a linear potential within this framework. The connection with metric confinement is emphasized. Possible dipole terms are considered briefly.

Application of dispersion relations to nucleon-nucleon scattering: The two-pion contribution

Abstract The two-pion contribution to the amplitude for nucleon-nucleon scattering is computed in terms of the invariant amplitudes which characterize the four-body Greens function of the pion nucleon system. The dependence of this contribution upon the momentum transfer of the two-nucleon system is completely exhibited. A general method is described for the derivation of symmetry properties for the invariant coefficients in the expansion of the scattering amplitude in spinor space.