Analytic calculation of feynman amplitudes

A new method is proposed for calculating amplitudes of processes involving spin-1/2 fermions. The method is based on the use of the isotropic-vierbein vectors in Minkowski space and the basis spinors associated with them. The amplitudes for the electron-positron interaction processes e^?e⁺ → ff and e^?e⁺ → W^?W⁺ and the amplitude for one of the possible diagrams for the process e⁺e^? → e⁺e^?e⁺e^?e⁺e^? are calculated in order to test and illustrate the potential of the method.     

QED to lowest order ine + e −→e + e −γγγ

We calculate the cross-section for the production ofe ⁺ e ^?γγγ ine ⁺ e ^? annihilation. The results are in agreement with the first observation of such a process by the ASP experiment at SLAC. The calculation also provides another example of the power of ‘spinor techniques’ in calculating Feynman amplitudes.     

Hard bremsstrahlung amplitudes fore + e − collisions with polarized beams at LEP/SLC energies

Cross sections are presented for the processese ⁺ e ^?→e ⁺ e ^?γ ande ⁺ e ^?→f \(\bar f\) γ (wheref is any light fermion) in the form of helicity amplitudes in which all complex phase information is kept. Owing to a spcial choice of the bremsstrahlung polarization and the use of spinor techniques the resultant expressions are extremely compact and lend themselves to fast numerical evaluation. An algorithm is given to obtain from the helicity amplitudes the cross section for arbitrary polarization of the incominge ⁺ e ^? beams. Special attention is given to the case of bremsstrahlung at very small angles to the beams, where a complicated dependence on the electron mass has to be taken into account.     

Anomalous effects ine + e − annihilation into boson pairs I.e + e −→W + W −

We present a phenomenological analysis of the various kinds of anomalous effects which can apper either in the leptonic or in the bosonic sector of the reactionse ⁺ e ^?→V V′(V V′=W ^±,Z ⁰ or γ). A general descritpin of invariant amplitudes and helicity amplitudes is given. Applications are made with non standar couplings, new intermediate states, residuale ⁺ e ^? VV′ contact interactions. In this first part results are given fore ⁺ e ^?→W ⁺ W ^? in view of LEP 200 and future linear colliders in the TeV range.     

Production of excited electrons ine + e − interactions

We present a complete lowest order calculation of the processe ⁺ e ^?→(e ^*)→e ⁺ e ^? ρ based on a phenomenological Lagrangian where interference with “standard” amplitudes and spin correlation effects are considered. The calculation has been implemented in a Monte Carlo generator of unweighted events and can be used to study interactions with polarized beams as well as the effects of other excited fermions.     

Impact of space-time extra dimensions on μ+μ− and W + W − angular distributions in e + e − collisions

The effects on μ⁺μ^? and W ⁺ W ^? angular distribution in e ⁺ e ^? collisions, due to the exchange of massive gravitons in space-time with large extra dimensions are considered. It is shown that under beam and detector conditions at TESLA, these effects would be discovered or the constraints on string scale ～4.5 TeV from below would be achieved at 20 fb^?1 of the integrated luminosity and √s = 500 GeV.     

The π N → e +e−N reaction close to the vector-meson production threshold

The π^? p→e ⁺ e ^? n and π⁺ n→e ⁺ e ^? p reaction cross sections are calculated below and in the vicinity of the vector-meson (?⁰,ω) production threshold. These processes are largely responsible for the emission of e ⁺e^? pairs in pion-nucleus reactions and contribute to the dilepton spectra observed in relativistic heavy ion collisions. They are dominated by the decay of low-lying baryon resonances into vector-meson-nucleon channels. The vector mesons materialize subsequently into e ⁺ e^? pairs. Using πN→?⁰ N and πN→ωN, amplitudes calculated in the center of mass energy interval 1.4 < √s<1.8 GeV, we compute the π^? p→e ⁺ e ^? n and π⁺ n→e ⁺ e ^? p reaction cross sections in these kinematics. Below the vector-meson production threshold, the π⁰?ω interference in the e ⁺ e^? channel appears largely destructive for the π^? p→e ⁺ e ^? n cross section and constructive for the π⁺ n→e ⁺ e ^? p cross section. The pion beam and the HADES detector at GSI offer a unique possibility to measure these effects. Such data would provide strong constraints on the coupling of vector-meson-nucleon channels to low-lying baryon resonances.     

Semi-classical models for gluon jets and leptoproduction based on the massless relativistic string

Based upon the dynamics of a massless relativistic string we propose a semi-classical model for a gluon jet. We also show a close but non-trivial similarity between a jet obtained in a leptoproduction event and the quark jets frome ⁺ e ^?-annihilation.     

Polarization amplitudes fore + e − →W + W − ande + e − →ZZ

The main purpose of this work is to study the three weak boson vertex. We give explicit formulae for all polarization amplitudes of the processese ⁺ e ^? →W ⁺ W ^? ande ⁺ e ^? →ZZ, with arbitrary couplings between the various intermediate vector bosons. Using these expressions we discuss possible signatures ofC, P andT violation in the three vector boson coupling, as well as the effects of anomalous magnetic dipole and electric quadrupole moments ofW ^±. The amplitudes for the above processes in any SU(2) × U(1) and SU(2)_L × SU(2)_R × U(1) gauge theory are also given, while the special case of the Weinberg-Salam model is studied in detail.     

Ultra-relativistic heavy ion collisions in a multi-string model

We present a model for ultra-relativistic heavy ion collisions based on color string formation and subsequent independent string fragmentation. Strings are formed due to color exchange between quarks at each individual nucleon nucleon collision. The fragmentation is treated as ine ⁺ e ^? or lepton nucleon scattering. Calculation forpp, pA, andAA were carried out using the Monte Carlo code VENUS for Very Energetic NUclear Scattering (version 1.0).     

Gluonic contributions to the exclusive amplitudes

The contributions from gluonic wave functions to the amplitudes of meson production ine ⁺ e ^? annihilation, quarkonium decays and twophoton processes are calculated.     

Production of pion and muon pairs in e±e− colliding beams. Extension of the equivalent photon approximation

The reactions e^?e^?→e^?e^?π⁺π^?(μ⁺μ^?) are considered here in the situation where only pions (muons) are recorded and k_⊥ (total transverse momentum of the pair) is not too small (roughly speaking m_e²?k_⊥²?m_π²); this domain gives the main contribution to the cross section. In this paper the differential cross sections have been obtained to an accuracy of (Ink_⊥²/me²)^?1k_⊥/m_π. The amplitudes with one scalar photon have to be taken into account in this approximation. Also the charge asymmetry appears due to the interference of the two-photon and bremsstrahlung diagrams. It is shown what information on amplitudes of the reaction γγ→π⁺π^? and on the pion electromagnetic form factor can be obtained from an experiment in the given set-up.     

Bose Einstein symmetrisation,coherence and chaos; with particular application toe + e − annihilation

The phenomenon of Bose-Einstein correlation within the debris of hadronic final states is discussed in simple terms, with particular attention to the nature of coherent and chaotic sources. The Artru-Mennessier string is taken as a model for the pion source ine ⁺ e ^? annihilation and the predicted Bose-Einstein correlations between like pion pairs evaluated. The results are in good accord with such data as exist.     

Z boson effects in electron positron scattering at epic energies at 14 GeV

We discuss the problem of testing the intermediate vector boson effects in the reactions e^?e⁺ → e^?e⁺ + hadrons, e^?e⁺ → e^?e⁺ + μ^?μ⁺, e^?p → e^?x with the next generation of accelerators, and conclude that these reactions must be considered. The differential cross sections for the one lepton at large four-momentum transfer are obtained, and a significant contribution of Z effects is found.     

Screening effect of the coulomb interaction on the energy levels of atomic and molecular systems

The energies of atomic and molecular systems with a screened Coulomb interaction are expressed in terms of properties of the system with a conventional Coulomb interaction to the third order in the screening constant. The energy levels of an H atom, an H^? ion, and nonadiabatic systems, namely, the positronium ion e ⁺ e ^? e ^? and the positronium molecule e ⁺ e ⁺ e ^? e ^?, are calculated for screened Coulomb interactions of charged particles. It is demonstrated that, as the screening constant of the Coulomb interaction increases, the stability of the hydrogen atom, the H^? ion, and the positronium molecule e ⁺ e ⁺ e ^? e ^? decreases, whereas the stability of the positronium ion e ⁺ e ^? e ^? increases after a slight decrease.     

Approximations for high-energy photon-photon scattering in two-photon processes and double bremsstrahlung

Presented are some approximation formulae for the processese ⁺ e ^? →e ⁺ e ^?γ^*γ^* →e ⁺ e ^?γγ (e ⁺ e ^?) scattering with intermediate γγ scattering) ande ⁺ e ^?→e ⁺ e ^?γγ (double bremsstrahlung) at high energies for forwarde ⁺ e ^? scattering, using not only the usual equivalent-photon approximation method but also direct approximations under certain kinematic conditions. In both cases the outgoing photons can be polarized. Their numerical check is examined by comparing these results with those of the exact calculations obtained in a recent paper. The agreement of both results is quite satisfactory if the required conditions are satisfied.     

Study of some rare decays of the K+ meson

In a search for very rare decays of the K⁺ meson we observed the K⁺→μ⁺νe⁺e^? and K⁺→e⁺ν e⁺e^? modes with branching ratios of (10±3) ×10^?7 and (2⁺²_?2)×10^?7 respectively. We also put new limits on a decay allowed by the alternate scheme of lepton conservation K⁺→π^?μ⁺e⁺, on a decay with double charged weak current K⁺→π^? e⁺e⁺ and on other forbidden decays K⁺→μ^?νe⁺e⁺ and K⁺→π⁺μ^±e^±.     

Hard photon corrections for Bhabha scattering

Numerical results for the α³ differential cross section for e⁺e^? → e⁺e^? are presented for the case of e⁺e^? colliding beams. Special care is given to the hard photon corrections. Acoplanarity distributions for e⁺e^? → e⁺e^?γ are also presented. Attention is drawn to experimental conditions which require the calculation of still higher order corrections.     

The muon spectra from decays ofW- andZ-bosons produced ine + e −-collisions

The muon spectra from the decays ofW-andZ-bosons, produced ine ⁺ e ^?→W ⁺ W ^?,e ⁺ e ^?→Zγ,e ⁺ e ^?→ZZ ande ⁺ e ^?→ZH reactions have been obtained (H is the Higgs boson). It has been shown (in terms of Glashow-Weinberg-Salam theory) that the main source of muons are thee ⁺ e ^?→Zγ ande ⁺ e ^?→W ⁺ W ^? processes (over theW-boson production threshold). The contribution of thee ⁺ e ^?→ZZ ande ⁺ e ^?→ZH reactions to the inclusive muon spectra is small. It has been also shown, that it is possible to distinguish contributions of thee ⁺ e ^?→Zγ ande ⁺ e ^?→W ⁺ W ^? reactions if the decay muons move at a small angle to the initial electron momentum.     

Optimal Hamiltonian of internal motion of an atomic-molecular system in a magnetic field

The effect of a uniform magnetic field on the state of an atomic-molecular system considered as a united system of N particles (without separation of the motion of acoelightac and particles) is analyzed. It is shown that the Hamiltonian of the internal motion of the system in the magnetic field contains (N-1)(N-2)/2 arbitrary parameters corresponding to the coefficients of the gauge transformation of the vector potential. A method of calculation of the optimal values of these coefficients based on the requirement for the minimum diamagnetic correction to the energy is proposed. New formulas for the diamagnetic susceptibility of atomic-molecular systems are obtained that take into account the simultaneous perturbing effect of the magnetic field on the motion of all particles. The theory is applied for calculation of the diamagnetic susceptibilities of the H, He, Li, and Be atoms; the muonic analogues of helium atoms ^∞He²⁺µ^? e ^?,⁴He²⁺µ^? e ^?, and ³He²⁺µ^? e ^?; and the positron-containing systems t ⁺ e ⁺ e ^? e ^?, d ⁺ e ⁺ e ^? e ^?, p ⁺ e ⁺ e ^? e ^?, µ⁺ e ⁺ e ^? e ^?, and e ⁺ e ⁺ e ^? e ^?, with regard for the motion of all particles.