231 research outputs found
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
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-
One Loop Multiphoton Helicity Amplitudes
We use the solutions to the recursion relations for double-off-shell fermion
currents to compute helicity amplitudes for -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 -photon scattering, we find
that unless , 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
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 () or unequal spins () are derived. The imposed conditions are that the amplitudes should have
the lowest possible dimension, have propagators of dimension , 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
Exact Results on e+ e- --> e+ e- + 2 Photons at SLC/LEP Energies
We use the spinor methods of the CALKUL collaboration, as realized by Xu,
Zhang and Chang, to calculate the differential cross section for e+ e- --> e+
e- + 2 photons for c.m.s. energies in the SLC/LEP regime. An explicit complete
formula for the respective cross section is obtained. The leading log
approximation is used to check the formula. Applications of the formula to high
precision luminosity calculations at SLC/LEP are discussed.Comment: 16 pages(LaTeX), UTHEP-92-0601 (contains corrected figures
Amplitudes With Different Helicity Configurations Of Noncommutative QED
The amplitudes of purely photonic and photon{2-fermion processes of non-
commutative QED (NCQED) are derived for different helicity configurations of
photons. The basic ingredient is the NCQED counterpart of Yang-Mills recursion
relations by means of Berends and Giele. The explicit solutions of recursion
relations for NCQED photonic processes with special helicity configurations are
presented.Comment: 23 pages, 2 figure
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
Two-photon mediated resonance production in e+e- collisions: cross sections and density matrices
Earlier described model amplitudes are used in this paper to evaluate both
cross sections and density matrices for two-photon mediated resonance
production in e^+e^- collisions. All 25 q\bar{q} low-lying ^1S_0, ^3P_J and
^1D_2 resonances can thus be treated. Two independent methods are described to
obtain the resonance production density matrices and cross sections. These
density matrices combined with a resonance decay density matrix give the
detailed angular distributions of the resonance decay products. For two
particular decays, \chi_{c2},\chi_{c1}\to\gamma J/\psi the details are given.
Several numerical results are presented as well.Comment: 27 pages, 4 figure
Analytical and numerical methods for massive two-loop self-energy diagrams
Motivated by the precision results in the electroweak theory studies of
two-loopFeynman diagrams are performed. Specifically this paper gives a
contribution to the knowledge of massive two-loop self-energy diagrams in
arbitrary and especially four dimensions.This is done in three respects firstly
results in terms of generalized, multivariable hypergeometric functions are
presented giving explicit series for small and large momenta. Secondly the
imaginary parts of these integrals are expressed as complete elliptic
integrals.Finally one-dimensional integral representations with elementary
functions are derived.They are very well suited for the numerical evaluations.Comment: 24 page
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