4,335 research outputs found
How to prove that the LHC did not discover dark matter
If the LHC is able to produce dark matter particles, they would appear at the
end of cascade decay chains, manifesting themselves as missing transverse
energy. However, such "dark matter candidates" may decay invisibly later on. We
propose to test for this possibility by studying the effect of particle widths
on the observable invariant mass distributions of the visible particles seen in
the detector. We consider the simplest non-trivial case of a two-step two-body
cascade decay and derive analytically the shapes of the invariant mass
distributions, for generic values of the widths of the new particles. We
demonstrate that the resulting distortion in the shape of the invariant mass
distribution can be significant enough to measure the width of the dark matter
"candidate", ruling it out as the source of the cosmological dark matter.Comment: 5 pages, 5 figure
Distribution of PageRank Mass Among Principle Components of the Web
We study the PageRank mass of principal components in a bow-tie Web Graph, as
a function of the damping factor c. Using a singular perturbation approach, we
show that the PageRank share of IN and SCC components remains high even for
very large values of the damping factor, in spite of the fact that it drops to
zero when c goes to one. However, a detailed study of the OUT component reveals
the presence ``dead-ends'' (small groups of pages linking only to each other)
that receive an unfairly high ranking when c is close to one. We argue that
this problem can be mitigated by choosing c as small as 1/2
Resolving Combinatorial Ambiguities in Dilepton Event Topologies with Constrained Variables
We advocate the use of on-shell constrained variables in order to
mitigate the combinatorial problem in SUSY-like events with two invisible
particles at the LHC. We show that in comparison to other approaches in the
literature, the constrained variables provide superior ansatze for the
unmeasured invisible momenta and therefore can be usefully applied to
discriminate combinatorial ambiguities. We illustrate our procedure with the
example of dilepton events. We critically review the existing
methods based on the Cambridge variable and MAOS-reconstruction of
invisible momenta, and show that their algorithm can be simplified without loss
of sensitivity, due to a perfect correlation between events with complex
solutions for the invisible momenta and events exhibiting a kinematic endpoint
violation. Then we demonstrate that the efficiency for selecting the correct
partition is further improved by utilizing the variables instead.
Finally, we also consider the general case when the underlying mass spectrum is
unknown, and no kinematic endpoint information is available
Testing Invisible Momentum Ansatze in Missing Energy Events at the LHC
We consider SUSY-like events with two decay chains, each terminating in an
invisible particle, whose true energy and momentum are not measured in the
detector. Nevertheless, a useful educated guess about the invisible momenta can
still be obtained by optimizing a suitable invariant mass function. We review
and contrast several proposals in the literature for such ansatze: four
versions of the M_T2-assisted on-shell reconstruction (MAOS), as well as
several variants of the on-shell constrained M_2 variables. We compare the
performance of these methods with regards to the mass determination of a new
particle resonance along the decay chain from the peak of the reconstructed
invariant mass distribution. For concreteness, we consider the event topology
of dilepton ttbar events and study each of the three possible subsystems, in
both a ttbar and a SUSY example. We find that the M_2 variables generally
provide sharper peaks and therefore better ansatze for the invisible momenta.
We show that the performance can be further improved by preselecting events
near the kinematic endpoint of the corresponding variable from which the
momentum ansatz originates.Comment: 38 pages, 15 figure
Edge Detecting New Physics the Voronoi Way
We point out that interesting features in high energy physics data can be
determined from properties of Voronoi tessellations of the relevant phase
space. For illustration, we focus on the detection of kinematic "edges" in two
dimensions, which may signal physics beyond the standard model. After deriving
some useful geometric results for Voronoi tessellations on perfect grids, we
propose several algorithms for tagging the Voronoi cells in the vicinity of
kinematic edges in real data. We show that the efficiency is improved by the
addition of a few Voronoi relaxation steps via Lloyd's method. By preserving
the maximum spatial resolution of the data, Voronoi methods can be a valuable
addition to the data analysis toolkit at the LHC.Comment: 6 pages, 7 figure
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