On the Construction of Scattering Amplitudes for Spinning Massless Particles

In this paper the general form of scattering amplitudes for massless particles with equal spins s ($s s \to s s$) or unequal spins ($s_a s_b \to s_a s_b$) are derived. The imposed conditions are that the amplitudes should have the lowest possible dimension, have propagators of dimension $m^{-2}$, and obey gauge invariance. It is shown that the number of momenta required for amplitudes involving particles with s > 2 is higher than the number implied by 3-vertices for higher spin particles derived in the literature. Therefore, the dimension of the coupling constants following from the latter 3-vertices has a smaller power of an inverse mass than our results imply. Consequently, the 3-vertices in the literature cannot be the first interaction terms of a gauge-invariant theory. When no spins s > 2 are present in the process the known QCD, QED or (super) gravity amplitudes are obtained from the above general amplitudes.Comment: 19 pages, Late

Navigating Around the Algebraic Jungle of QCD: Efficient Evaluation of Loop Helicity Amplitudes

A method is developed whereby spinor helicity techniques can be used to simplify the calculation of loop amplitudes. This is achieved by using the Feynman-parameter representation where the offending off-shell loop momenta do not appear. Background Feynman gauge also helps to simplify the calculations. This method is applicable to any Feynman diagram with any number of loops as long as the external masses can be ignored, and it is at least as efficient as the string technique in the special circumstances when the latter can be used. In order to minimize the very considerable algebra encountered in non-abelian gauge theories, graphical methods are developed for most of the calculations. This enables the large number of terms encountered to be organized visually in the Feynman diagram without the necessity of having to write down any of them algebraically. A one-loop four-gluon amplitude in a particular helicity configuration is computed explicity to illustrate the method.Comment: 22 pages of text in PLAIN TEX, plus 14 figures in 10 pages stored in a POSTSCRIPT file (attached to the end of the PLAIN TEX file); McGill preprint no. McGill/92-3

BHAGEN-1PH: A Monte Carlo event generator for radiative Bhabha scattering

BHAGEN-1PH is a FORTRAN program providing fast Monte Carlo event generation of the process $e^+ e^- \to e^+ e^- \gamma$, within electroweak theory, for both unpolarized beams and also for the longitudinally polarized electron beam. The program is designed for final leptons outside a small cone around the initial leptons direction and has a new algorithm allowing also for a fast generation of non collinear initial and final emission, as well as for asymmetric and different angular cuts for final leptons.Comment: 23 pages, plain Tex, no figure

Emission of Two Hard Photons in Large-Angle Bhabha Scattering

A closed expression for the differential cross section of the large-angle Bhabha $e^+ e^-$ scattering which explicitly takes into account the leading and next-to-leading contributions due to the emission of two hard photons is presented. Both collinear and semi-collinear kinematical regions are considered. The results are illustrated by numerical calculations.Comment: 13 pages, LaTeX, 1 PostScript figure, submitted to Nucl. Phys.

Simulation of the process e+e−↦e+e−γe^+ e^- \mapsto e^+ e^- \gamma within electroweak theory with longitudinally polarized initial electrons

We present simple analytic expressions for the distributions of the Bhabha scattering process with emission of one hard photon, including weak boson exchanges, and with longitudinal polarization of the initial electron. The results from the Monte Carlo generator BHAGEN-1PH, based on these expressions, are presented and compared, for the unpolarized case, with those existing in literature.Comment: 9 pages, plain Tex, no figures, small change in Table

All electroweak four fermion processes in electron-positron collisions

This paper studies the electroweak production of all possible four fermion states in e+ e- collisions. Since the methods employed to evaluate the complete matrix elements and phase space are very general, all four fermion final states in which the charged particles are detected can be considered. Also all kinds of experimental cuts can be imposed. With the help of the constructed event generator a large number of illustrative results is obtained, which show the relevance of backgrounds to a number of signals. For LEP 200 the W-pair signal and its background are discussed, for higher energies also Z-pair and single W and Z signals and backgrounds are presented.Comment: INLO-PUB-1/94,NIKHEF-H/94-08, LaTeX, uses axodraw.sty (appended to end of TeX file), 45 page

Higgs production in e+e−→llˉqqˉe^+ e^- \to l{\bar l} q{\bar q} at LEP and NLC

Predictions for Higgs production with processes of the type $e^+ e^- \rightarrow \mu{\bar \mu}\;b\bar b$ at LEP~2 and the NLC are calculated. Short analytical formulae describe the double differential distribution in the invariant masses of the $\mu \bar \mu$ and $b \bar{b}$ pairs. The total cross section may be got with two numerical integrations. The various Higgs-background interferences vanish either identically or are small. The background contributions depend strongly on cuts applied on the invariant masses.Comment: 8 pages (LaTeX), 5 figures ( 3 of them not included, a uuencoded file containing the LaTeX and all postscript files is available via anonymous ftp at ftp://ftp.ifh.de/pub/preprint/desy95-057.uu

Massive Spin-5/2 Fields Coupled to Gravity: Tree-Level Unitarity vs. the Equivalence Principle

I show that the gravitational scattering amplitudes of a spin-5/2 field with mass $m\ll M_{Pl}$ violate tree-level unitarity at energies $\sqrt{s}\approx\sqrt{mM_{Pl}}$ if the coupling to gravity is minimal. Unitarity up to energies $\sqrt{s}\approx M_{Pl}$ is restored by adding a suitable non-minimal term, which gives rise to interactions violating the (strong) equivalence principle. These interactions are only relevant at distances d\lequiv 1/m.Comment: 6 pages, NYU-TH.93/01/01, (a misprint corrected, minor modifications of the text

Cross section of the processes e++e−→e++e−(γ)e^++e^-\to e^++e^-(\gamma), →π++π−(γ)\to \pi^++\pi^-(\gamma), μ++μ−(γ) \mu^++\mu^-(\gamma), γ+γ(γ) \gamma+\gamma(\gamma) in the energy region 200 MeV ≤2E≤\le 2E\le 3 GeV

The cross section for different processes induced by $e^+e^-$ annihilation, in the kinematical limit $\beta_{\mu}\approx\beta_{\pi}=(1-m_{\pi}^2/\epsilon^2)^{1/2}\sim 1$, is calculated taking into account first order corrections to the amplitudes and the corrections due to soft emitted photons, with energy $\omega\le\Delta E\le \epsilon$ in the center of mass of the $e^+e^-$ colliding beams. The results are given separately for charge--odd and charge--even terms in the final channels $\pi^+\pi^-(\gamma)$ and $\mu^+\mu^-(\gamma)$. In case of pions, form factors are taken into account. The differential cross sections for the processes: $e^++e^-\to e^++e^-(+\gamma)$, $\to \pi^++\pi^-(\gamma)$, $\to \mu^++\mu^-(\gamma),\to \gamma\gamma(\gamma)$ have been calculated and the corresponding formula are given in the ultrarelativistic limit $\sqrt{s}/2= \epsilon \gg m_{\mu}\sim m_{\pi}$ . For a quantitative evaluation of the contribution of higher order of the perturbation theory, the production of $\pi^+\pi^-$, including radiative corrections, is calculated in the approach of the lepton structure functions. This allows to estimate the precision of the obtained results as better than 0.5% outside the energy region corresponding to narrow resonances. A method to integrate the cross section, avoiding the difficulties which arise from singularities is also described.Comment: 25 pages 3 firgur

Multiloop String-Like Formulas for QED

Multiloop gauge-theory amplitudes written in the Feynman-parameter representation are poised to take advantage of two important developments of the last decade: the spinor-helicity technique and the superstring reorganization. The former has been considered in a previous article; the latter will be elaborated in this paper. We show here how to write multiloop string-like formulas in the Feynman-parameter representation for any process in QED, including those involving other non-electromagnetic interactions. The general connection between the Feynman-parameter approach and the superstring/first-quantized approach is discussed. In the special case of a one-loop multi-photon amplitude, these formulas reduce to the ones obtained by the superstring and the first quantized methods. The string-like formulas exhibits a simple gauge structure which makes the Ward-Takahashi identity apparent, and enables the integration-by-parts technique of Bern and Kosower to be applied, so that gauge-invariant parts can be extracted diagram-by-diagram with the seagull vertex neglected.Comment: 25 pages in Plain Tex, plus four figures in a postscript file; McGill/92-5