225 research outputs found
One-loop leading logarithms in electroweak radiative corrections: II. Factorization of collinear singularities
We discuss the evaluation of the collinear single-logarithmic contributions
to virtual electroweak corrections at high energies. More precisely, we proof
the factorization of the mass singularities originating from loop diagrams
involving collinear virtual gauge bosons coupled to external legs. We discuss,
in particular, processes involving external longitudinal gauge bosons, which
are treated using the Goldstone-boson equivalence theorem. The proof of
factorization is performed within the 't Hooft--Feynman gauge at one-loop order
and applies to arbitrary electroweak processes that are not mass-suppressed at
high energies. As basic ingredient we use Ward identities for Green functions
with arbitrary external particles involving a gauge boson collinear to one of
these. The Ward identities are derived from the BRS invariance of the
spontaneously broken electroweak gauge theory.Comment: 28 pages, late
One-loop leading logarithms in electroweak radiative corrections, I. Results
We present results for the complete one-loop electroweak logarithmic
corrections for general processes at high energies and fixed angles. Our
results are applicable to arbitrary matrix elements that are not
mass-suppressed. We give explicit results for 4-fermion processes and
gauge-boson-pair production in electron-positron annihilation.Comment: 35 pages, latex, 4 postscript figures, some misprints correcte
On-the-fly reduction of open loops
Building on the open-loop algorithm we introduce a new method for the
automated construction of one-loop amplitudes and their reduction to scalar
integrals. The key idea is that the factorisation of one-loop integrands in a
product of loop segments makes it possible to perform various operations
on-the-fly while constructing the integrand. Reducing the integrand on-the-fly,
after each segment multiplication, the construction of loop diagrams and their
reduction are unified in a single numerical recursion. In this way we entirely
avoid objects with high tensor rank, thereby reducing the complexity of the
calculations in a drastic way. Thanks to the on-the-fly approach, which is
applied also to helicity summation and for the merging of different diagrams,
the speed of the original open-loop algorithm can be further augmented in a
very significant way. Moreover, addressing spurious singularities of the
employed reduction identities by means of simple expansions in rank-two Gram
determinants, we achieve a remarkably high level of numerical stability. These
features of the new algorithm, which will be made publicly available in a
forthcoming release of the OpenLoops program, are particularly attractive for
NLO multi-leg and NNLO real-virtual calculations.Comment: v2 as accepted by EPJ C: extended discussion of the triangle
reduction and its numerical stability in section 5.4.2; speed benchmarks for
2->5 processes included in section 6.2.1; ref. adde
A unified NLO description of top-pair and associated Wt production
We present an NLO simulation of WWbb production with massive b-quarks at the
LHC. Off-shell and non-resonant contributions associated with top-pair and
single-top channels and with leptonic W-boson decays are consistently taken
into account using the complex-mass scheme. Thanks to the finite b-quark mass,
WWbb predictions can be extended to the whole b-quark phase space, thereby
including Wt-channel single-top contributions that originate from collinear
g->bb splittings in the four-flavour scheme. This provides a consistent NLO
description of tt and Wt production and decay, including quantum interference
effects. The simulation is also applicable to exclusive 0- and 1-jet bins,
which is of great importance for Higgs-boson studies in the H->WW channel and
for any other analysis with large top backgrounds and jet vetoes or jet bins.Comment: 8pp. Minor revision, results unchange
Precise numerical evaluation of the two loop sunrise graph Master Integrals in the equal mass case
We present a double precision routine in Fortran for the precise and fast
numerical evaluation of the two Master Integrals (MIs) of the equal mass
two-loop sunrise graph for arbitrary momentum transfer in d=2 and d=4
dimensions. The routine implements the accelerated power series expansions
obtained by solving the corresponding differential equations for the MIs at
their singular points. With a maximum of 22 terms for the worst case expansion
a relative precision of better than a part in 10^{15} is achieved for arbitrary
real values of the momentum transfer.Comment: 11 pages, LaTeX. The complete paper is also available via the www at
http://www-ttp.physik.uni-karlsruhe.de/Preprints/ and the program can be
downloaded from http://www-ttp.physik.uni-karlsruhe.de/Progdata
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