29,564 research outputs found
Perturbativity Constraints in BSM Models
Phenomenological studies performed for non-supersymmetric extensions of the
Standard Model usually use tree-level parameters as input to define the scalar
sector of the model. This implicitly assumes that a full on-shell calculation
of the scalar sector is possible - and meaningful. However, this doesn't have
to be the case as we show explicitly at the example of the Georgi-Machacek
model. This model comes with an appealing custodial symmetry to explain the
smallness of the parameter. However, the model cannot be renormalised
on-shell without breaking the custodial symmetry. Moreover, we find that it can
often happen that the radiative corrections are so large that any consideration
based on a perturbative expansion appears to be meaningless: counter-terms to
quartic couplings can become much larger than and/or two-loop mass
corrections can become larger than the one-loop ones. Therefore, conditions are
necessary to single out parameter regions which cannot be treated
perturbatively. We propose and discuss different sets of such perturbativity
conditions and show their impact on the parameter space of the Georgi-Machacek
model. Moreover, the proposed conditions are general enough that they can be
applied to other models as well. We also point out that the vacuum stability
constraints in the Georgi-Machacek model, which have so far only been applied
at the tree level, receive crucial radiative corrections. We show that large
regions of the parameter space which feature a stable electroweak vacuum at the
loop level would have been - wrongly - ruled out by the tree-level conditions.Comment: 64 pages, 20 figure
Estimation of Distribution Overlap of Urn Models
A classical problem in statistics is estimating the expected coverage of a
sample, which has had applications in gene expression, microbial ecology,
optimization, and even numismatics. Here we consider a related extension of
this problem to random samples of two discrete distributions. Specifically, we
estimate what we call the dissimilarity probability of a sample, i.e., the
probability of a draw from one distribution not being observed in k draws from
another distribution. We show our estimator of dissimilarity to be a
U-statistic and a uniformly minimum variance unbiased estimator of
dissimilarity over the largest appropriate range of k. Furthermore, despite the
non-Markovian nature of our estimator when applied sequentially over k, we show
it converges uniformly in probability to the dissimilarity parameter, and we
present criteria when it is approximately normally distributed and admits a
consistent jackknife estimator of its variance. As proof of concept, we analyze
V35 16S rRNA data to discern between various microbial environments. Other
potential applications concern any situation where dissimilarity of two
discrete distributions may be of interest. For instance, in SELEX experiments,
each urn could represent a random RNA pool and each draw a possible solution to
a particular binding site problem over that pool. The dissimilarity of these
pools is then related to the probability of finding binding site solutions in
one pool that are absent in the other.Comment: 27 pages, 4 figure
Bounds for Non-Locality Distillation Protocols
Non-locality can be quantified by the violation of a Bell inequality. Since
this violation may be amplified by local operations an alternative measure has
been proposed - distillable non-locality. The alternative measure is difficult
to calculate exactly due to the double exponential growth of the parameter
space. In this article we give a way to bound the distillable non-locality of a
resource by the solutions to a related optimization problem. Our upper bounds
are exponentially easier to compute than the exact value and are shown to be
meaningful in general and tight in some cases.Comment: 8 pages, 3 figures; small changes in introduction and application
section due to the exact verification of distillation bounds using a symbolic
computation package (Maple 14); added journal re
Renormalization of spin-orbit coupling in quantum dots due to Zeeman interaction
We derive analitycally a partial diagonalization of the Hamiltonian
representing a quantum dot including spin-orbit interaction and Zeeman energy
on an equal footing. It is shown that the interplay between these two terms
results in a renormalization of the spin-orbit intensity. The relation between
this feature and experimental observations on conductance fluctuations is
discussed, finding a good agreement between the model predictions and the
experimental behavior.Comment: 4 pages, no figures. To appear in Phys. Rev. B (Brief Report) (2004
- …