Determination of resonance couplings and high energy amplitudes in γN → πN using fixed-t dispersion relations

The real parts of the amplitudes are generated entirely from their imaginary parts via d.rs., and essentially all available data is included at all energies with momentum transfer |t| < 1 GeV². A total of 46 resonance couplings and 50 high energy parameters are varied to fit all the data simultaneously with a χ² of 4.8 per data point.     

Optimized computation of the voigt and complex probability functions

Methods for computing the complex probability function w(z) = e^?z2 erfc (?iz), which is related to the Voigt spectrum line profiles, are developed. The basic method is a rational approximation, minimizing the relative error of the imaginary part on the real axis. It is complemented by other methods in order to increase efficiency and to overcome the inevitable failure of any rational approximation near the real axis. The procedures enable one to evaluate both real and imaginary parts of w(z) with high relative accuracy. The methods are simple, as demonstrated by a sample FORTRAN program.     

Single decay-lepton angular distributions in polarizede + e − →\overline {tt} and simple angular asymmetries as a measure of CP-violating top dipole couplingsand simple angular asymmetries as a measure of CP-violating top dipole couplings

In the presence of an electric dipole coupling of $\overline {tt} $ to a photon, and an analogous ‘weak’ dipole coupling to the Z, CP violation in the process e⁺e^? → $\overline {tt} $ results in modified polarization of the top and the anti-top. This polarization can be analyzed by studying the angular distributions of decay charged leptons when the top or anti-top decays leptonically. Analytic expressions are presented for these distributions when eithert or $\overline t $ decays leptonically, including $\mathcal{O}$ (α_s) QCD corrections in the soft-gluon approximation. The angular distributions are insensitive to anomalous interactions in top decay. Two types of simple CP-violating polar-angle asymmetries and two azimuthal asymmetries, which do not need the full reconstruction of thet or $\overline t $ , are studied. Independent 90% CL limits that may be obtained on the real and imaginary parts of the electric and weak dipole couplings at a linear collider operating at √ s = 500 GeV with integrated luminosity 500 fb^? and also at √s = 1000 GeV with integrated luminosity 1000 fb^? have been evaluated. The effect of longitudinal electron and/or positron beam polarizations has been included.     

CP violation and strong phases from penguins in B±→PP and B±→VP decays

We calculate direct CP-violating rate asymmetries in chargedB→PP andB→VP decays arising from the interference of amplitudes with different strong and CKM phases. The perturbative strong phases develop at order α _s from absorptive parts of one-loop matrix elements of the next-to-leading logarithm corrected effective Hamiltonian. CPT constraints are maintained. Based on this model, we find that partial rate asymmetries between charge conjugateB ^± decays can be as high as 20% for certain channels with branching ratios in the 10^?6 range. Because the $c\bar c$ threshold lies so close to the physical momentum scale, the asymmetries depend sensitively on the model assumptions used to evaluate the imaginary parts of the matrix elements, in particular, on the internal momentum transfer. The charge asymmetries of partial rates would provide unambiguous evidence for direct CP violation.     

An efficient method for evaluation of the complex probability function: The Voigt function and its derivatives

An efficient method is developed to evaluate the function w(z)=e^-z2(1+(2i/√π)∫^z₀e^t2dt) for the complex argument z = x + iy. The real part of w(z) is the Voigt function describing spectral line profiles; the imaginary part can be used to compute derivatives of the spectral line shapes, which are useful, e.g. in least-squares fitting procedures. As an example of the method a simple and fast FORTRAN subroutine is listed in the Appendix from which w(z) in the entire y ? 0 half-plane can be calculated, the maximum relative error being less than 2 × 10^-6 and 5 × 10^-6 for the real and imaginary parts, respectively.     

Effect of complex coupling in inelastic cross sections,asymmetries and spin flip in the DWA

The effects of adding an effective imaginary part to real inelastic microscopic form factors in DWA are investigated. Calculations are compared to data for the proton differential cross sections and asymmetries of the lowest-lying states of ¹²⁰Sn, ⁵⁸Ni, and ²⁰⁸Pb. Proton spin flip is calculated for ¹²⁰Sn. Both collective imaginary and effective microscopic imaginary contributions were considered. The most substantial improvements were in fits to asymmetry data. Collective-model calculations indicate the effects of complex coupling are comparable to those of the deformed spin-orbit well.     

CP-violation in the production of $\tau$-leptons at TESLA with beam polarization

We study the prospects of discovering CP-violation in the production of leptons in the reaction at TESLA, an e ⁺ e ^- linear collider with center-of-mass energies of 500 or even 800 GeV. Non-vanishing expectation values of certain correlations between the momenta of the decay products of the two leptons would signal the presence of CP-violation beyond the standard model. We study how longitudinal beam polarization of the electron and positron beams will enhance these correlations. We find that T-odd and T-even vector correlations are well suited for the measurements of the real and imaginary parts of the electric dipole form factors. We expect measurements of the real part with a precision of roughly 10^-20 e cm and of the imaginary part of 10^-17 Received: 13 June 2002 / Revised version: 17 October 2002 / Published online: 20 December 2002     

Anomalous top magnetic couplings

The real and imaginary parts of the one-loop electroweak contributions to the left and right tensorial anomalous couplings of the tbW vertex in the Standard Model (SM) are computed.     

Single-spin asymmetries in the Bethe-Heitler process e − + p → e − + γ + p induced by loop corrections

The single-spin beam and target asymmetries in the hard electroproduction process e ⁻ + p → e ⁻ + γ + p induced by the loop radiative corrections to the vertex part of lepton interaction are considered. The physical reason for the appearance of such asymmetries is the nonzero imaginary part of the amplitude (on the level of radiative corrections) caused by diagrams with photon radiation from the outgoing electron. We calculate the single-spin beam and target asymmetries at a longitudinally polarized electron beam or at arbitrary polarizations of the target proton for the CLAS and HERMES experimental conditions. The text was submitted by the authors in English.     

Finding the 3-gluon vertex from 4-jet events ine + e − annihilation

General properties of single transversee ^± beam polarization asymmetries (cos ? or sin ? azimuthal distributions and their forward-backward asymmetries) are established. These asymmetries are genuine ways of analyzing the structure of chirality violating amplitudes at high energy. Several examples of chirality violating processes are considered and their asymmetries computed. Constraints due tog _e ?2,d _e andm _e are obtained in the form of sum rules and their physical consequences are discussed.     

High energy pion photoproduction amplitudes from fixed-t dispersion relations and duality

Contributions to the high energy imaginary parts of the charged and neutral pion photoproduction amplitudes from degenerate ? and A₂ exchanges and ω and B exchanges are parametrized similarly to the dual absorptive model. These contributions together with the imaginary parts of the amplitudes found at low energies from partial-wave analyses are then used to evaluate the high energy real parts of the photoproduction amplitudes from fixed-t dispersion relations. A fit is made to data on pion photoproduction at 3.4 and 16 GeV incident photon energies, for momentum transfers up to ?1(GeV/c)². It is shown that much of the data is reproduced both qualitatively and quantitatively by our model. The high energy imaginary parts of the photoproduction amplitudes given by the fit are shown to be in accord with their average low energy behaviour.     

Final state photon bremsstrahlung ine + e −→Z 0→hadrons as a tool for a precise measurement of the weak quark couplings

We discuss for the processe ⁺ e ^?→Z ⁰→q \(\bar q\) how final state photons can be used to disentangle the weak couplings of up and down type quarks. Since the flavour composition of multihadronic events with final state photons is different from that of all multihadrons, a combination of observables from the two samples allows the couplings to be determined. Both theZ ⁰ width and the forward-backward charge asymmetry at centre-of-mass energies aroundM _Z0 can be used to constrain the weak couplings. Taking into account the theoretical uncertainties a precision for the sum of the square axial and vector couplings of δ(v ²+a ²)～4% for up and down type quarks separately seems feasible for 10⁶ Z ⁰'s. The precision from asymmetry measurements will be less significant.     

The optical potential in the Green's function approach

Utilizing the so-calledλ ⁰⁰-approximation the effective single-particle potential (“mass operator”) is investigated with respect to its energy and momentum dependence. For the nucleon-nucleon interaction a localS-wave potential matching the experimental phase shifts is used. The dispersion behaviour of the real and imaginary parts of the generalized optical potential is studied. The potential on the energy-shell is in satisfactory agreement with the phenomenological fits.     

Surface and volume contributions to real and imaginary parts of the heavy-ion optical potential

Starting from the Feshbach expression for the optical potential, explicit formulae for the real and the imaginary parts of the optical potential between two heavy ions (HI's) are obtained. They are each composed of a volume and a surface term. The contributions to the volume term are calculated in two nuclear Fermi liquids which flow through each other starting from the realistic Reid soft core nucleon-nucleon (NN) interaction. Since the Fermi surface is formed by two spheres one obtains a complex Brueckner reaction matrix which is approximated by a complex, effective local interaction. It is used in a fully antisymmetrized double folding procedure to obtain the volume terms of the optical potential between the two HI's. The surface contributions are directly calculated in the collision of the two finite HI's. The collective surface vibrations (3^? octupole state and 2⁺, 4⁺ (T = 0) giant resonances for the ¹⁶O?¹⁶O collision) are included as intermediate states. This yields especially an imaginary contribution at the surface which reduces the transparency found with the volume terms alone. The method is applied to ¹⁶O?¹⁶O scattering at 83 and 332 MeV laboratory energy. The local approximations to the real and imaginary parts obtained in this way agree well with phenomenological fits. The surface terms improve the agreement of the differential cross section at 80 MeV where experimental data are available.     

Can one test technicolour?

We estimate the couplings to ordinary particles of the lightest bound states in technicolour theories and discuss the resulting phenomenology. We compute their couplings to light gauge bosons through axial anomalies and also estimate their non-anomalous couplings at low energies. We estimate their couplings to fermions under the general simplifying assumption that each fermion acquires its mass from a unique technifermion condensate (“monophagy”), in which case they are naturally flavour conserving and relatively well-defined. We find that the classic Higgs search experiments (ttoponium → H⁰ + γ, e⁺e^? → H⁺H^?, e⁺e^? → Z⁰ + H⁰) enable one to make a decisive discrimination between elementary and composite models of spontaneous symmetry breaking. We also emphasize the interest of improving experimental limits on K_L⁰ → μe in the context of dynamical symmetry breaking models.     

Leptonic polarization asymmetries ate + e − colliders inE 6 theories

We examine the left-right and azimuthal polarization asymmetries of lepton pairs produced ine ⁺ e ^? ande ^? e ^? interactions as probes of new physics resulting fromE ₆ theories. The asymmetries are calculated and compared for the processese ⁺ e ^?→µ ⁺ µ ^?,e ⁺ e ^?→e ⁺ e ^?,e ^? e ^?→e ^? e ^?, ande ⁺ e ^?→L ⁺ L ^? whereL is either anE ₆ exotic, mirror, or fourth generation heavy lepton. Our results show that lepton polarization asymmetries can be used to easily distinguish differentE ₆ models and can be used to distinguish among possible new heavy leptonsL.     

Nucleus-nucleus scattering in the high-energy approximation and optical folding potential

A microscopic complex folding-model potential that reproduces the scattering amplitude of Glauber-Sitenko theory in its optical limit is obtained. The real and imaginary parts of this potential are dependent on energy and are determined by known data on the nuclear-density distributions and on the nucleon-nucleon scattering amplitude. For the real part, use is also made of a folding potential involing effective nucleon-nucleon forces and allowing for the nucleon-exchange term. Three forms of semimicroscopic optical potentials where the contributions of the template potentials—that is, the real and the imaginary folding-model potential—are controlled by adjusting two parameters are constructed on this basis. The efficiency of these microscopic and semimicroscopic potentials is tested by means of a comparison with the experimental differential cross sections for the elastic scattering of heavy ions ¹⁶O on nuclei at an energy of E ～ 100 MeV per nucleon.     

Weak asymmetries in e+e− -annihilation at high energies

We study the effects of neutral weak currents in high energy e⁺e^? -annihilation into hadrons with polarized incident beams. It is shown that in current gauge models considerable weak asymmetries arise from q ≈ 28 GeV.     

An effective theory of a compositeZ

It is shown that the experimental value of sin² θ_w can be obtained if theZ is a bound state of two haplons provided that the haplons carry a new hypercolour quantum number in addition to colour. This approach also leads to the prediction that the electromagnetic couplings of theZ are substantially larger than they are in standard electroweak theory. It may be possible to observe these anomalous couplings in the processe ⁺ e ^? →Zγ at LEP 200 where theZ is longitudinally polarised.