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

Generalized Gluon Currents and Applications in QCD

We consider the process containing two quark lines and an arbitrary number of gluons in a spinor helicity framework. A current with two off-shell gluons appears in the amplitude. We first study this modified gluon current using recursion relations. The recursion relation for the modified gluon current is solved for the case of like-helicity gluons. We apply the modified gluon current to compute the amplitude for $q \bar q \rightarrow q \bar q gg \cdots g$ in the like-helicity gluon case.Comment: 80 pages, 2 figures (appended in pictex), CLNS 91/112

Multiphoton Production at High Energies in the Standard Model I

We examine multiphoton production in the electroweak sector of the Standard Model in the high energy limit using the equivalence theorem in combination with spinor helicity techniques. We obtain recursion relations for currents consisting of a charged scalar, spinor, or vector line that radiates $n$ photons. Closed form solutions to these recursion relations for arbitrary $n$ are presented for the cases of like-helicity and one unlike-helicity photon production. We apply the currents singly and in pairs to obtain amplitudes for processes involving the production of $n$ photons with up to two unlike helicities from a pair of charged particles. The replacement of one or more photons by transversely polarized $$Z$-bosons is also discussed.Comment: 75 pages, CLNS 91/111

Knowledge integration by thinking along

knowledge, integration

One Loop Multiphoton Helicity Amplitudes

We use the solutions to the recursion relations for double-off-shell fermion currents to compute helicity amplitudes for $n$-photon scattering and electron-positron annihilation to photons in the massless limit of QED. The form of these solutions is simple enough to allow {\it all}\ of the integrations to be performed explicitly. For $n$-photon scattering, we find that unless $n=4$, the amplitudes for the helicity configurations (+++...+) and (-++...+) vanish to one-loop order.Comment: 27 pages + 4 uuencoded figures (included), Fermilab-Pub-93/327-T, RevTe

Multigluon Helicity Amplitudes Involving a Quark Loop

We apply the solution to the recursion relation for the double-off-shell quark current to the problem of computing one loop amplitudes with an arbitrary number of gluons. We are able to compute amplitudes for photon-gluon scattering, electron-positron annihilation to gluons, and gluon-gluon scattering via a quark loop in the case of like-helicity gluons. In addition, we present the result for the one-loop gluon-gluon scattering amplitude when one of the gluons has opposite helicity from the others.Comment: 31 pages (RevTeX) + 2 uuencoded figures (included), Fermilab-Pub-93/389-

Sideband cooling while preserving coherences in the nuclear spin state in group-II-like atoms

We propose a method for laser cooling group-II-like atoms without changing the quantum state of their nuclear spins, thus preserving coherences that are usually destroyed by optical pumping. As group-II-like atoms have a $^1S_0$ closed-shell ground state, nuclear spin and electronic degrees of freedom are decoupled, allowing for independent manipulation. The hyperfine interaction that couples these degrees of freedom in excited states can be suppressed through the application of external magnetic fields. Our protocol employs resolved-sideband cooling on the forbidden clock transition, $^1S_0 \to {}^3P_0$, with quenching via coupling to the rapidly decaying $^1P_1$ state, deep in the Paschen-Back regime. This makes it possible to laser cool neutral atomic qubits without destroying the quantum information stored in their nuclear spins, as shown in two examples, $^{171}$Yb and $^{87}$Sr.Comment: 4 pages, 3 figures v4: minor changes in text, changes in the references, published versio

The Analysis of Multijet Events Produced at High Energy Hadron Colliders

We define and discuss a set of (4N - 4) parameters that can be used to analyse events in which N jets have been produced in high energy hadron-hadron collisions. These multijet variables are the multijet mass and (4N - 5) independent dimensionless parameters. To illustrate the use of the variables QCD predictions are presented for events with up to five jets produced at the Fermilab Tevatron Proton-Antiproton Collider. These QCD predictions are compared with the predictions of a model in which multijet events uniformly populate the N-body phase-space

Multi-Parton Amplitudes in Gauge Theories

In this report we review recent developments in perturbation theory methods for gauge theories. We present techniques and results that are useful in the calculation of cross sections for processes with many final state partons which have applications in the study of multi-jet phenomena in high-energy Colliders.Comment: 84 pages, 12 figures: Latex, preprint version of 1991 Physics Reports article. Scanned Figure