arXiv subjects
Publications and source records attributed to O. Nachtmann.
We analyse CP-violating effects in Z -> 4 jet decays, assuming the presence of a CP-violating effective triple gluon coupling. We discuss the influence of this coupling on the decay width. Furthermore, we analyse different CP-odd observables and propose strategies of a direct search for such a CP-violating GGG coupling. The present data of LEP 1 should give significant information on the coupling.
The small-x_Bj limit of deep inelastic scattering is related to the high-energy limit of the forward Compton amplitude in a familiar way. We show that the analytic continuation of this amplitude in the energy variable is calculable from a matrix element in Euclidean field theory. This matrix element can be written as a Euclidean functional integral in an effective field theory. Its effective Lagrangian has a simple expression in terms of the original Lagrangian. The functional integral expression obtained can, at least in principle, be evaluated using genuinely non-perturbative methods, e.g., on the lattice. Thus, a fundamentally new approach to the long-standing problem of structure functions at very small x_Bj seems possible. We give arguments that the limit x_Bj -> 0 corresponds to a critical point of the effective field theory where the correlation length becomes infinite in one direction.
In this article we study effects of parity nonconservation in atomic dysprosium, where one has a pair of nearly degenerate levels of opposite parity. We consider the time evolution of this two-level system within oscillatory electric and magnetic fields. These are chosen to have a periodical structure with the same period, such that a Floquet matrix describes the time evolution of the quantum states. We show that, if the states are unstable, the eigenvalues of the Floquet matrix may have contributions proportional to the square root of the parity violating interaction matrix element $H_w$ while they are almost degenerate in their parity even part. This leads to beat frequencies proportional to $\sqrt{H_w}$ which are expected to be larger by several orders of magnitude compared to ordinary P-violating contributions which are of order $H_w$. However, for the simple field configurations we considered, it still seems to be difficult to observe these P-violating beat effects, since the states decay too fast. On the other hand, we found that, within only a few Floquet cycles, very large parity violating asymmetries with respect to experimental setups of opposite chirality may be obtained. The electric and magnetic fields as well as the time intervals necessary for this are in an experimentally accessible range. For statistically significant effects beyond one standard deviation a number of about $10^7$ atoms is required. Our ideas may be applied directly to other 2-level atomic systems and different field configurations. We hope that these ideas will stimulate experimental work in this direction.
We analyse CP-violating effects in Z \to 4 jet decays, assuming the presence of CP-violating effective $Z b \bar{b} G$ and $Z b \bar{b} G G$ couplings. We discuss the influence of these couplings on the decay width. Furthermore, we propose various strategies of a direct search for such CP-violating couplings by using different CP-odd observables. The present data of LEP 1 should give significant information on the couplings.
We investigate the reaction $e p \to e PS X$ where PS denotes a pseudoscalar meson $π^0, η, η'$, or $η_c$ and X either a proton or resonance or continuum states into which the proton can go by diffractive excitation. At high energies photon and odderon exchange contribute to the reaction. The photon exchange contribution is evaluated exactly using data for the total virtual photon-proton absorption cross section. The odderon exchange contribution is calculated in nonperturbative QCD, using functional integral techniques and the model of the stochastic vacuum. For the proton we assume a quark-diquark structure as suggested by the small odderon amplitude in $pp$ and $p \bar{p}$ forward scattering. We show that odderon exchange leads to a much larger inelastic than elastic PS production cross section. Observation of our reaction at HERA would establish the soft odderon as an exchange object on an equal footing with the soft pomeron and would give us valuable insight into both the nucleon structure and the mechanism of high energy diffractive scattering.
We consider a spontaneously broken gauge theory based on the standard model (SM) group G = SU(2) x U(1) with scalar fields that carry arbitrary representations of G, and we investigate some general properties of the charged and neutral current involving these fields. In particular we derive the conditions for having real or complex couplings of the Z boson to two different neutral or charged scalar fields, and for the existence of CP-violating Z-scalar-scalar couplings. Moreover, we study models with the same fermion content as in the SM, with one SU(2) Higgs singlet, and an arbitrary number of Higgs doublets. We show that the structure of the Z-Higgs boson and of the Yukawa couplings in these models can be such that CP-violating Zb{\bar b}G form factors which conserve chirality are induced at the one-loop level.
We present a study of parity (P) violating contributions to the eigenenergies of stationary systems containing atoms in spatially inhomogeneous external electric fields. In this context the subtle interplay of P-violation and time reversal (T) invariance plays an important role. If the entire field configuration is chosen to exhibit chirality the energies are in general shifted by pseudoscalar contributions which change sign under a planar reflection of the field. To calculate the effects we use the standard model of elementary particle physics where the P-odd interaction arises through the exchange of Z-bosons between the quarks in the nucleus and the atomic electrons. We consider in detail hydrogen-like systems in unstable levels of principal quantum number n=2. The nominal order of P-violating effects is 10^-5...10^-9 Hz which is determined by the mixing of the 2S_1/2 and 2P_1/2 states. However we point out that it is possible to enhance the P-violating energy shifts dramatically! Instead of energy shifts linear in the P-violation parameters we get then shifts proportional to the square root of these parameters. Numerically we find such energy shifts to be of order 10^-5...1 Hz. Application of our technique to hydrogen-like atoms with a nucleus of spin I=1/2 yields P-violating energy shifts which are very sensitive to the nuclear spin dependent P-odd force, which receives a rather large contribution from the polarized strange quark density in polarized nuclei. Thus, a measurement of these energy shifts could provide an important tool to elucidate nuclear properties connected to the so called ``spin crisis''. We also present a method for treating degenerate perturbation theory which combines advantages of both, Kato's and Bloch's methods.
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.
On March 19-21, 1998, a workshop devoted to questions of the pomeron and the odderon in high energy scattering was held in Heidelberg. This note gives a personal account of some of the issues discussed at this workshop. Of course, misconceptions and misunderstandings are to be blamed on us, not on the other participants of the workshop. A puzzle of odderon physics is identified and a convenient reaction for its experimental study is discussed.
We investigate contributions to diffractive scattering, which are odd under C- and P-parity. Comparison of p-$\bar p$ and p-p scattering indicates that these odderon contributions are very small and we show how a diquark clustering in the proton can explain this effect. A good probe for the odderon exchange is the photo- and electroproduction of pseudo-scalar mesons. We concentrate on the pi^0 and show that the quasi elastic pi^0-production is again strongly suppressed for a diquark structure of the proton whereas the cross sections for diffractive proton dissociation are larger by orders of magnitude and rather independent of the proton structure.
Exclusive pseudoscalar meson production in ep scattering at high energies is a direct probe for a possible "odderon" exchange in soft hadronic processes. Using a simple phenomenological ansatz for the odderon, we demonstrate how it can be separated from the contribution due to photon-photon fusion, and the relevant parameters be measured. Total cross sections and differential distributions are presented for pi0, eta, eta', and eta_c production. Results are given from both a full calculation and one using the equivalent photon approximation. The accuracy of the latter is discussed.
We consider hydrogen-like atoms in unstable levels of principal quantum number n=2, confined to a finite size region in a non-homogeneous electric field carrying handedness. The interplay between the internal degrees of freedom of the atoms and the external ones of their c.m. motion can produce P-odd contributions to the eigenenergies. The nominal order of such shifts is 10^-8 Hz. Typically such energy shifts depend linearly on the small P-violation parameters delta_i similarequal 10^-12 (i=1,2), essentially the ratios of the P-violating mixing matrix elements of the 2S and 2P states over the Lamb shift, with i=1 (i=2) corresponding to the nuclear spin independent (dependent) term. We show how such energy shifts can be enhanced by a factor of similarequal 10^6 in a resonance like way for special field configurations where a crossing of unstable levels occurs, leading to P-violating effects proportional to squareroot{delta_i}. Measurements of such effects can give information concerning the ``spin crisis'' of the nucleons.
We propose to test the CP symmetry in the reactions Z -> mu+ mu- gamma and Z -> tau+ tau- gamma. The experimental analysis of angular correlations allows to determine a set of effective couplings: the electric and weak dipole moments of the muon and the tau lepton, and in particular chirality conserving 4-particle couplings, all of which can be induced by CP--violation in renormalizable theories of electroweak interactions beyond the Standard Model. We update an indirect bound on the weak dipole moment of the muon.
We show how one can measure anomalous WWZ- and WWgamma-couplings with minimal statistical error using integrated observables, without having to assume that the anomalous couplings are small. We propose a parametrisation of these couplings which is well suited for the extraction of both single and many parameters, and which leads to a very simple form of the integrated cross section, from which additional information on the couplings can be obtained.
We discuss various ideas on the nonperturbative vacuum structure in QCD. The stochastic vacuum model of Dosch and Simonov is presented in some detail. We show how this model produces confinement. The model incorporates the idea of the QCD vacuum acting like a dual superconductor due to an effective chromomagnetic monopole condensate. We turn then to high energy, small momentum transfer hadron-hadron scattering. A field-theoretic formalism to treat these reactions is developed, where the basic quantities governing the scattering amplitudes are correlation functions of light-like Wegner-Wilson lines and loops. The evaluation of these correlation functions with the help of the Minkowskian version of the stochastic vacuum model is discussed. A further surprising manifestation of the nontrivial vacuum structure in QCD may be the production of anomalous soft photons in hadron-hadron collisions. We interpret these photons as being due to `synchrotron radiation from the vacuum'. A duality argument leads us from there to the expectation of anomalous pieces proportional to $(Q^2)^{1/6}$ in the electric form factors of the nucleons for small $Q^2$. Finally we sketch the idea that in the Drell-Yan reaction, where a quark-antiquark pair annihilates with the production of a lepton pair, a `chromodynamic Sokolov-Ternov effect' may be at work. This leads to a spin correlation of the $q\bar q$ pair, observable through the angular distribution of the lepton pair.
Tests of CP violation by appropriate momentum correlations in $Z\to 3$ jets and in particular in $Z\to b\bar bX$ probe CP-violating effective couplings -- that manifest themselves as form factors -- which conserve the quark chirality and quark flavour. By giving two examples we show that such couplings can be induced at one-loop order in extensions of the Standard Model with CP violation beyond the Kobayashi-Maskawa phase. In one of the models we compute the chirality-conserving part of the CP-violating $Zb{\bar b}$-gluon amplitude for massless $b$ quarks, determine the resulting effective dimension $d=6$ couplings in the local limit, and discuss the possible size of the effects. Finally we show that in models with excited quarks the chiral-invariant CP-violating effective interactions could be quite large if appropriate couplings are of a size characteristic of a strong interaction
We discuss the reaction $e p \to e \tilde{p} X$ in the one-photon exchange approximation, where it is in essence the reaction $γ^{*} p \to \tilde{p} X$. A large rapidity gap is required between the particle or particles of the proton remnant $\tilde{p}$ and those of $X$. We define a suitable azimuthal angle $φ$ between a leptonic and a hadronic plane. The dependence of the cross section on $φ$ is given explicitly and can be used to extract cross sections and interference terms for the reaction $γ^{*} p \to \tilde{p} X$ corresponding to the various helicities of the virtual photon $γ^{*}$. The interference terms can be used to test models for the large rapidity gap events in a sensitive way. We discuss in detail models with factorizing Pomeron exchange and in particular the Donnachie-Landshoff Pomeron model. We make some remarks on soft colour exchange models and on possible effects of QCD background vacuum fields. We conclude with a suggestion to look for Odderon exchange in exclusive deep inelastic high energy reactions like $γ^{*} p \to \tilde{p} π^{0}$ and $γ^{*} p \to \tilde{p} η$.
We discuss some issues arising in the search for CP violation in the decays Z -> tau+ tau- and Z -> b \bar b X. The form-factor and the effective Lagrangian approach to parametrize CP-violating effects are compared. We emphasize the interest to study both real and imaginary parts of CP-violating form factors like the weak dipole moment form factor d_tau^Z(m^2_Z) of the tau-lepton. We propose an 'optimal' way to search for CP violation when Z -> b \bar b X events have to be selected on a statistical basis from the total number of Z hadronic decays.