1,097 research outputs found
Initial-Final-State Interference in the Z line-shape
The uncertainty in the determination of the Z line-shape parameters coming
from the precision of the calculation of the Initial-State Radiation and
Initial--Final-State Interference is 2 10**(-4) for the total cross section
sigma zero(had) at the Z peak, 0.15 MeV for the Z mass M Z, and 0.1 MeV for the
Z width Gamma Z. Corrections to Initial--Final-State Interference beyond
\Order{\alpha^1} are discussed.Comment: 10 pages LaTeX including 2 PostScript figure
Minimal Gauge Invariant Classes of Tree Diagrams in Gauge Theories
We describe the explicit construction of groves, the smallest gauge invariant
classes of tree Feynman diagrams in gauge theories. The construction is valid
for gauge theories with any number of group factors which may be mixed. It
requires no summation over a complete gauge group multiplet of external matter
fields. The method is therefore suitable for defining gauge invariant classes
of Feynman diagrams for processes with many observed final state particles in
the standard model and its extensions.Comment: 13 pages, RevTeX (EPS figures
The analytic value of the sunrise self-mass with two equal masses and the external invariant equal to the third squared mass
We consider the two-loop self-mass sunrise amplitude with two equal masses
and the external invariant equal to the square of the third mass in the
usual -continuous dimensional regularization. We write a second order
differential equation for the amplitude in and show as solve it in
close analytic form. As a result, all the coefficients of the Laurent expansion
in of the amplitude are expressed in terms of harmonic polylogarithms
of argument and increasing weight. As a by product, we give the explicit
analytic expressions of the value of the amplitude at , corresponding to
the on-mass-shell sunrise amplitude in the equal mass case, up to the
term included.Comment: 11 pages, 2 figures. Added Eq. (5.20) and reference [4
Numerical evaluation of the general massive 2-loop sunrise self-mass master integrals from differential equations
The system of 4 differential equations in the external invariant satisfied by
the 4 master integrals of the general massive 2-loop sunrise self-mass diagram
is solved by the Runge-Kutta method in the complex plane. The method, whose
features are discussed in details, offers a reliable and robust approach to the
direct and precise numerical evaluation of Feynman graph integrals.Comment: 1+21 pages, Latex, 5 ps-figure
Weyl-van-der-Waerden formalism for helicity amplitudes of massive particles
The Weyl-van-der-Waerden spinor technique for calculating helicity amplitudes
of massive and massless particles is presented in a form that is particularly
well suited to a direct implementation in computer algebra. Moreover, we
explain how to exploit discrete symmetries and how to avoid unphysical poles in
amplitudes in practice. The efficiency of the formalism is demonstrated by
giving explicit compact results for the helicity amplitudes of the processes
gamma gamma -> f fbar, f fbar -> gamma gamma gamma, mu^- mu^+ -> f fbar gamma.Comment: 24 pages, late
Counting loop diagrams: computational complexity of higher-order amplitude evaluation
We discuss the computational complexity of the perturbative evaluation of
scattering amplitudes, both by the Caravaglios-Moretti algorithm and by direct
evaluation of the individual diagrams. For a self-interacting scalar theory, we
determine the complexity as a function of the number of external legs. We
describe a method for obtaining the number of topologically inequivalent
Feynman graphs containing closed loops, and apply this to one- and two-loop
amplitudes. We also compute the number of graphs weighted by their symmetry
factors, thus arriving at exact and asymptotic estimates for the average
symmetry factor of diagrams. We present results for the asymptotic number of
diagrams up to 10 loops, and prove that the average symmetry factor approaches
unity as the number of external legs becomes large.Comment: 27 pages, 17 table
The lowest order inelastic QED processes at polarized photon-electron high energy collisions
The compact expressions for cross sections of photoproduction of a pair of
charged particles ; ; as
well as the double Compton scattering process are given. The explicit analytic
expressions for the case of polarized photon and the initial electron in the
kinematics when all the particles can be considered as a massless ones are
presented. The photon polarization is described in the terms of Stokes
parameters.Comment: LaTeX2e, 9 page
Numerical evaluation of the general massive 2-loop 4-denominator self-mass master integral from differential equations
The differential equation in the external invariant p^2 satisfied by the
master integral of the general massive 2-loop 4-denominator self-mass diagram
is exploited and the expansion of the master integral at p^2=0 is obtained
analytically. The system composed by this differential equation with those of
the master integrals related to the general massive 2-loop sunrise diagram is
numerically solved by the Runge-Kutta method in the complex p^2 plane. A
numerical method to obtain results for values of p^2 at and close to thresholds
and pseudo-thresholds is discussed in details.Comment: Latex, 20 pages, 7 figure
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