4,541 research outputs found
Integration by parts identities in integer numbers of dimensions. A criterion for decoupling systems of differential equations
Integration by parts identities (IBPs) can be used to express large numbers
of apparently different d-dimensional Feynman Integrals in terms of a small
subset of so-called master integrals (MIs). Using the IBPs one can moreover
show that the MIs fulfil linear systems of coupled differential equations in
the external invariants. With the increase in number of loops and external
legs, one is left in general with an increasing number of MIs and consequently
also with an increasing number of coupled differential equations, which can
turn out to be very difficult to solve. In this paper we show how studying the
IBPs in fixed integer numbers of dimension d=n with one can
extract the information useful to determine a new basis of MIs, whose
differential equations decouple as and can therefore be more easily
solved as Laurent expansion in (d-n).Comment: 31 pages, minor typos corrected, references added, accepted for
publication in Nuclear Physics
Observation of Events with Isolated Charged Leptons and Large Missing Tra nsverse Momentum and of Events with Multi-Electrons at HERA
Striking events with isolated charged leptons, large missing transverse
momentum and large transverse momentum of the hadronic final state (PTX) have
been observed at the electron proton collider HERA. In the full HERA-I data
sample corresponding to an integrated luminosity of about 130 invpb, the H1
experiment observes 10 events with isolated electrons or muons and with PTX >25
GeV. Only 2.9 pm 0.4 events are expected from Standard Model (SM) processes.
Six of these events have PTX >40 GeV, while 1.1 pm 0.2 events are expected. The
ZEUS experiment observes good agreement with the SM. However, in a preliminary
search ZEUS has found two events with a similar event topology, but tau-leptons
instead of electrons or muons in the final state . Only 0.12 pm 0.02 events are
expected from SM processes.
Moreover, six events with two or more electrons forming an invariant mass
bigger than 100 GeV have been observed by the H1 experiment. Three events have
two electrons and three events have three electrons, while only 0.25 events are
expected in each case. The ZEUS measurement is in agreement with the SM
expectation.Comment: talk given at 38th Recontres de Moriond Electroweak Interactions and
Unified Theories, Les Arc (France) 200
A hierarchical Bayesian approach to record linkage and population size problems
We propose and illustrate a hierarchical Bayesian approach for matching
statistical records observed on different occasions. We show how this model can
be profitably adopted both in record linkage problems and in capture--recapture
setups, where the size of a finite population is the real object of interest.
There are at least two important differences between the proposed model-based
approach and the current practice in record linkage. First, the statistical
model is built up on the actually observed categorical variables and no
reduction (to 0--1 comparisons) of the available information takes place.
Second, the hierarchical structure of the model allows a two-way propagation of
the uncertainty between the parameter estimation step and the matching
procedure so that no plug-in estimates are used and the correct uncertainty is
accounted for both in estimating the population size and in performing the
record linkage. We illustrate and motivate our proposal through a real data
example and simulations.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS447 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Schouten identities for Feynman graph amplitudes; the Master Integrals for the two-loop massive sunrise graph
A new class of identities for Feynman graph amplitudes, dubbed Schouten
identities, valid at fixed integer value of the dimension d is proposed. The
identities are then used in the case of the two loop sunrise graph with
arbitrary masses for recovering the second order differential equation for the
scalar amplitude in d=2 dimensions, as well as a chained sets of equations for
all the coefficients of the expansions in (d-2). The shift from to
dimensions is then discussed.Comment: 30 pages, 1 figure, minor typos in the text corrected, results
unchanged. Version accepted for publication on Nuclear Physics
Flavour transitions of Dirac-Majorana neutrinos
From a phenomenological point of view, we study active-active and
active-sterile flavour-changing (and flavour-conserving) oscillations of
Dirac-Majorana neutrinos both in vacuum and in matter. The general expressions
for the transition probabilities in vacuum are reported. We then investigate
some interesting consequences following from particular simple forms of the
neutrino mass matrices, and for the envisaged scenarios we discuss in detail
neutrino propagation in matter. Special emphasis is given to the problem of
occurrence of resonant enhancement of active-active and active-sterile neutrino
oscillations in a medium. The peculiar novel features related to the
Dirac-Majorana nature of neutrinos are particularly pointed out.Comment: latex 2e, 19 pages, 1 figure; to be published in The European Journal
of Physics
An Elliptic Generalization of Multiple Polylogarithms
We introduce a class of functions which constitutes an obvious elliptic
generalization of multiple polylogarithms. A subset of these functions appears
naturally in the \epsilon-expansion of the imaginary part of the two-loop
massive sunrise graph. Building upon the well known properties of multiple
polylogarithms, we associate a concept of weight to these functions and show
that this weight can be lowered by the action of a suitable differential
operator. We then show how properties and relations among these functions can
be studied bottom-up starting from lower weights.Comment: 27 pages plus three appendices, v2: references added, typos
corrected, accepted for publication on NP
Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph
We consider the calculation of the master integrals of the three-loop massive
banana graph. In the case of equal internal masses, the graph is reduced to
three master integrals which satisfy an irreducible system of three coupled
linear differential equations. The solution of the system requires finding a matrix of homogeneous solutions. We show how the maximal cut can be
used to determine all entries of this matrix in terms of products of elliptic
integrals of first and second kind of suitable arguments. All independent
solutions are found by performing the integration which defines the maximal cut
on different contours. Once the homogeneous solution is known, the
inhomogeneous solution can be obtained by use of Euler's variation of
constants.Comment: 39 pages, 3 figures; Fixed a typo in eq. (6.16
Comparing parametric and semi-parametric approaches for bayesian cost-effectiveness analyses in health economics
We consider the problem of assessing new and existing technologies for their cost-effectiveness in the case where data on both costs and effects are available from a clinical trial, and we address it by means of the cost-effectiveness acceptability curve. The main difficulty in these analyses is that cost data usually exhibit highly skew and heavytailed distributions, so that it can be extremely difficult to produce realistic probabilistic models for the underlying population distribution, and in particular to model accurately the tail of the distribution, which is highly influential in estimating the population mean. Here, in order to integrate the uncertainty about the model into the analysis of cost data and into cost-effectiveness analyses, we consider an approach based on Bayesian model averaging: instead of choosing a single parametric model, we specify a set of plausible models for costs and estimate the mean cost with its posterior expectation, that can be obtained as a weighted mean of the posterior expectations under each model, with weights given by the posterior model probabilities. The results are compared with those obtained with a semi-parametric approach that does not require any assumption about the distribution of costs. 1 IntroductionHealthcare cost data, cost-effectiveness analysis, mixture models, Bayesian model averaging
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