69 research outputs found
Final-state QED Multipole Radiation in Antenna Parton Showers
We present a formalism for a fully coherent QED parton shower. The complete
multipole structure of photonic radiation is incorporated in a single branching
kernel. The regular on-shell 2 to 3 kinematic picture is kept intact by
dividing the radiative phase space into sectors, allowing for a definition of
the ordering variable that is similar to QCD antenna showers. A modified
version of the Sudakov veto algorithm is discussed that increases performance
at the cost of the introduction of weighted events. Due to the absence of a
soft singularity, the formalism for photon splitting is very similar to the QCD
analogon of gluon splitting. However, since no color structure is available to
guide the selection of a spectator, a weighted selection procedure from all
available spectators is introduced.Comment: 33 pages, 12 figures. Added subsection 4.3 and some comments and
references per reviewer request. Version accepted by JHE
Competing Sudakov Veto Algorithms
We present a way to analyze the distribution produced by a Monte Carlo
algorithm. We perform these analyses on several versions of the Sudakov veto
algorithm, adding a cutoff, a second variable and competition between emission
channels. The analysis allows us to prove that multiple, seemingly different
competition algorithms, including those that are currently implemented in most
parton showers, lead to the same result. Finally, we test their performance and
show that there are significantly faster alternatives to the commonly used
algorithms.Comment: 16 pages, 1 figur
Discrepancy-based error estimates for Quasi-Monte Carlo. III: Error distributions and central limits
In Quasi-Monte Carlo integration, the integration error is believed to be
generally smaller than in classical Monte Carlo with the same number of
integration points. Using an appropriate definition of an ensemble of
quasi-randompoint sets, we derive various results on the probability
distribution of the integration error, which can be compared to the standard
Central Limit theorem for normal stochastic sampling. In many cases, a Gaussian
error distribution is obtained.Comment: 15 page
Singular Cross Sections in Muon Colliders
We address the problem that the cross section for the collisions of unstable
particles diverges, if calculated by standard methods. This problem is
considered for beams much smaller than the decay length of the unstable
particle, much larger than the decay length and finally also for pancake-
shaped beams. We find that in all cases this problem can be solved by taking
into account the production/propagation of the unstable particle and/or the
width of the incoming wave packets in momentum space.Comment: 12 pages, 3 figures. References corrected. Removed one sentence about
a fact that was known. Added explaination why one of our graphs is different
as compared to one of the references. Clearified explaination in sec. 3.
Amplitudes, recursion relations and unitarity in the Abelian Higgs Model
The Abelian Higgs model forms an essential part of the electroweak standard
model: it is the sector containing only Z and Higgs bosons. We present a
diagram-based proof of the tree-level unitarity of this model inside the
unitary gauge, where only physical degrees of freedom occur. We derive
combinatorial recursion relations for off-shell amplitudes in the massless
approximation, which allows us to prove the cancellation of the first two
orders in energy of unitarity-violating high-energy behaviour for any
tree-level amplitude in this model. We describe a deformation of the amplitudes
by extending the physical phase space to at least 7 spacetime dimensions, which
leads to on-shell recursion relations a la BCFW. These lead to a simple proof
that all on-shell tree amplitudes obey partial-wave unitarity.Comment: 15 page
CAMORRA: a C++ library for recursive computation of particle scattering amplitudes
We present a new Monte Carlo tool that computes full tree-level matrix
elements in high-energy physics. The program accepts user-defined models and
has no restrictions on the process multiplicity. To achieve acceptable
performance, CAMORRA evaluates the matrix elements in a recursive way by
combining off-shell currents. Furthermore, CAMORRA can be used to compute
amplitudes involving continuous color and helicity final states.Comment: 22 page
A fast algorithm for generating a uniform distribution inside a high-dimensional polytope
We describe a uniformly fast algorithm for generating points \vec{x}
uniformly in a hypercube with the restriction that the difference between each
pair of coordinates is bounded. We discuss the quality of the algorithm in the
sense of its usage of pseudo-random source numbers, and present an interesting
result on the correlation between the coordinates.Comment: 7 pages, cpu-time table added to illustrate efficienc
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