Otto Nachtmann

Considerations concerning diffraction scattering in quantum chromodynamics

Abstract A model for diffractive, especially elastic hadron-hadron scattering at high c.m. energies squared s and small momentum transfer squared |t| is developed, based on quantum chromodynamics (QCD). First the scattering of hadron constituents, partons, is considered. In this paper we study mainly the scattering of quarks and antiquarks. The s-dependence of the amplitudes is treated by analytical means using a functional integral approach and an eikonal approximation. The t-dependence of the amplitudes is then shown to be governed by a certain correlation function of gluon string operators. A calculation of this function by non-perturbative methods in the framework of lattice OCD or in the stochastic vacuum field model should be feasible. The transition from the parton to the hadron level is accomplished by constructing an effective S-operator in terms of local tensor operators. In this way we avoid dealing explicitly with hadronic wave functions. In our approach the bound state nature of the hadrons enters through matrix elements of the local operators, where information from deep inelastic lepton-hadron scattering exists. The resulting expression for the elastic hadron-hadron scattering amplitude is discussed and is shown to lead to an understanding of various phenomenological findings. The physical picture emerging is one where single partons of the hadrons interact at a time, i.e., the “Pomeron” couples to single partons. This was suggested previously by phenomenological analyses of experiments and by theoretical investigations of an abelian gluon model.

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.

Stability and symmetry breaking in the general two-Higgs-doublet model

A method is presented for the analysis of the scalar potential in the general two-Higgs-doublet model. This allows us to give the conditions for the stability of the potential and for electroweak symmetry breaking in this model in a very concise way. These results are then applied to two different Higgs potentials in the literature, namely the MSSM and the two-Higgs-doublet potential proposed by Gunion et al. The known results for these models follow easily as special cases from the general results. In particular, for the potential of Gunion et al. we can clarify the stability and symmetry-breaking properties of the model with our method.

Angular correlations and distributions for searches of CP violation in top quark production and decay

Abstract Investigation of the t t system at future colliders will offer an excellent opportunity to test the CP symmetry at high energies; viz. to search for CP -violating interactions beyond the Kobayashi-Maskawa mechanism. Here we demonstrate this for t t production in e + e − annihilation. We propose various CP -odd correlations involving the momenta of the charged leptons and/or b ( b ) jets which originate from t ( t ) decay. Possible CP -violating effects in t t production and decay are taken into account in a model-independent way using form factors. In particular we show that there are several correlations which allow us to disentangle possible effects in t t production from those in t and t decay. From a calculation of these correlations and their fluctuations we estimate the statistical sensitivities with which several CP -violating form factors will be measurable for a given number of t t events.

A color dielectric model for the nucleus

Abstract An effective color dielectric quark model is applied to the nucleus. It generates nuclear binding via a spread of the quark wavefunctions in the nucleus of the nucleus. Σ and Λ hyperons have a mean potential W Λ,Σ ≅ 2 3 W N . A nonvanishing color dielectric constant in the nucleus allows color modes which extend over the whole nucleus.

CP violation in the general two-Higgs-doublet model: a geometric view

We discuss the CP properties of the potential in the general two-Higgs-doublet model (THDM). This is done in a concise way using real gauge invariant functions built from the scalar products of the doublet fields. The space of these invariant functions, parametrising the gauge orbits of the Higgs fields, is isomorphic to the forward light cone and its interior. CP transformations are shown to correspond to reflections in the space of the gauge invariant functions. We consider CP transformations where no mixing of the Higgs doublets is taken into account as well as the general case where the Higgs basis is not fixed. We present basis independent conditions for explicit CP violation which may be checked easily for any THDM potential. Conditions for spontaneous CP violation, that is CP violation through the vacuum expectation values of the Higgs fields, are also derived in a basis independent way.

Production of Higgs particles in diffractive hadron-hadron collisions

Abstract Diffractive Higgs production in proton-proton collisions due to the pomeron-pomeron interaction is analysed. The inclusive production cross section can be calculated with some reliability and turns out to be of the order of 0.2 pb for 10 TeV proton on proton (20 TeV CM energy) and m H =100 GeV and 0.7 pb for 40 TeV CM energy. This is large enough to be observable at the proposed colliders LHC and SSC. We also discuss briefly heavy-ion collisions at LHC or SSC energies, which have been proposed as a way to search for Higgs particles in the mass range of 50–200 GeV produced in diffractive electromagnetic processes. We estimate the pomeron contribution to be comparable to the electromagnetic one, but we give some arguments why we think such heavy ion experiments to be difficult.

CP violation andZ boson decays

We present a general discussion ofCP-violating effects in the following two and three body decays of theZ boson:Z→l+l−,Z→l+l−γ, wherel=e, μ, τ andZ→2 jets,Z→ 2 jets+γ, andZ→ 3 jets. Experimental observables sensitive toCP violation in these decays are discussed systematically for the case that polarizations of final state particles are not observed. It is shown that the standard model predicts only extremely smallCP-violating effects for the above decays. PossibleCP-violating interactions beyond the standard model are parametrized in terms of aCP-odd effective Lagrangian containing coupling constants proportional to ΛP-1 and ΛP-2. Here ΛCP is the mass scale associated with the assumed new interactions. We give estimates of the bounds obtainable for ΛCP in experiments at LEP1.

A test for the gluon selfcoupling in the reactionse+e−→4 jets andZ0→4 jets

We consider the reactionse+e−→γ*→4 jets andZo→4 jets with the 4 jets coming in two pairs of essentially back to back jets of high and low energy. We calculate the angular distribution of the low energy jet axis with respect to the high energy jet axis in QCD, in an abelian gluon model “QED” and a phase space model (PS). Using simple helicity arguments we show that our angular distribution is very sensitive to the triple gluon coupling in QCD. This is then confirmed by a complete calculation. Our correlation offers, therefore, a direct test for QCD as a non-abelian gauge theory.

Differential cross-sections for high-energy elastic hadron hadron scattering in nonperturbative QCD

Abstract. Total and differential cross sections for high energy and small momentum transfer elastic hadron-hadron scattering are studied in QCD using a functional integral approach. The hadronic amplitudes are governed by vacuum expectation values of lightlike Wegner-Wilson loops, for which a matrix cumulant expansion is derived. The cumulants are evaluated within the framework of the Minkowskian version of the model of the stochastic vacuum. Using the second cumulant, we calculate elastic differential cross sections for hadron-hadron scattering. The agreement with experimental data is good.