7,794 research outputs found
-Torsion Points In Finite Abelian Groups And Combinatorial Identities
The main aim of this article is to compute all the moments of the number of
-torsion elements in some type of nite abelian groups. The averages
involved in these moments are those de ned for the Cohen-Lenstra heuristics for
class groups and their adaptation for Tate-Shafarevich groups. In particular,
we prove that the heuristic model for Tate-Shafarevich groups is compatible
with the recent conjecture of Poonen and Rains about the moments of the orders
of -Selmer groups of elliptic curves. For our purpose, we are led to de ne
certain polynomials indexed by integer partitions and to study them in a
combinatorial way. Moreover, from our probabilistic model, we derive
combinatorial identities, some of which appearing to be new, the others being
related to the theory of symmetric functions. In some sense, our method
therefore gives for these identities a somehow natural algebraic context.Comment: 24 page
A Dark Sector for , and a Diphoton Resonance
We revisit a set of dark sector models, motivated by anomalies observed in
decays and the muon anomalous magnetic moment, in the light of a recently
reported diphoton excess around 750GeV. Interpreting the excess as a scalar
resonance associated with the symmetry breaking sector of a dark gauge group,
we show that a diphoton cross section of few fb can be accomodated, together
with anomalies in and within a minimal dark sector model. The
resulting prominent collider signatures are in the form of wide resonant
signals into top and muon pair final states below TeV. The model
further predicts a dark matter candidate, yet with a significantly
underabundant relic density, unless produced by an appropriate non-thermal
mechanism.Comment: 7 pages, 3 figure
Probing New Physics with Isotope Shift Spectroscopy
We investigate the potential to probe physics beyond the Standard Model with
isotope shift measurements of optical atomic clock transitions. We first derive
the reach for generic new physics above the GeV scale at the effective field
theory level, as well as estimate the limits on possible new spin-independent
forces mediated by sub-GeV states coupled to electrons and neutrons. We also
study the weak force and show that isotope shifts could provide strong
constraints on the couplings to valence quarks, which complement
precision observables at LEP and atomic parity violation experiments. Finally,
motivated by recent experimental hints of a new 750 GeV resonance in diphotons,
we also consider the potential to probe its parity-preserving couplings to
electrons, quarks and gluons with this method. In particular, combining the
diphoton signal with indirect constraints from and isotope shifts in
Ytterbium allows to probe the resonance coupling to electrons with
unprecedented precision.Comment: 6 pages, 2 figures, 2 table
Regulators of rank one quadratic twists
We investigate the regulators of elliptic curves with rank 1 in some families
of quadratic twists of a fixed elliptic curve. In particular, we formulate some
conjectures on the average size of these regulators. We also describe an
efficient algorithm to compute explicitly some of the invariants of an odd
quadratic twist of an elliptic curve (regulator, order of the Tate-Shafarevich
group, etc.) and we discuss the numerical data that we obtain and compare it
with our predictions.Comment: 28 pages with 32 figure
A Dark Matter Relic From Muon Anomalies
We show that the recently reported anomalies in
transitions, as well as the long-standing discrepancy, can be
addressed simultaneously by a new massive abelian gauge boson with loop-induced
coupling to muons. Such a scenario typically leads to a stable dark matter
candidate with a thermal relic density close to the observed value. Dark matter
in our model couples dominantly to leptons, hence signals in direct detection
experiments lie well below the current sensitivity. The LHC, in combination
with indirect detection searches, can test this scenario through distinctive
signatures with muon pairs and missing energy.Comment: 10 pages, 7 figures, 1 tabl
The Dark Side of Electroweak Naturalness Beyond the MSSM
Weak scale supersymmetry (SUSY) remains a prime explanation for the radiative
stability of the Higgs field. A natural account of the Higgs boson mass,
however, strongly favors extensions of the Minimal Supersymmetric Standard
Model (MSSM). A plausible option is to introduce a new supersymmetric sector
coupled to the MSSM Higgs fields, whose associated states resolve the little
hierarchy problem between the third generation squark masses and the weak
scale. SUSY also accomodates a weakly interacting cold dark matter (DM)
candidate in the form of a stable neutralino. In minimal realizations, the
thus-far null results of direct DM searches, along with the DM relic abundance
constraint, introduce a level of fine-tuning as severe as the one due to the
SUSY little hierarchy problem. We analyse the generic implications of new SUSY
sectors parametrically heavier than the minimal SUSY spectrum, devised to
increase the Higgs boson mass, on this little neutralino DM problem. We focus
on the SUSY operator of smallest scaling dimension in an effective field theory
description, which modifies the Higgs and DM sectors in a correlated manner.
Within this framework, we show that recent null results from the LUX experiment
imply a tree-level fine-tuning for gaugino DM which is parametrically at least
a few times larger than that of the MSSM. Higgsino DM whose relic abundance is
generated through a thermal freeze-out mechanism remains also severely
fine-tuned, unless the DM lies below the weak boson pair-production threshold.
As in the MSSM, well-tempered gaugino-Higgsino DM is strongly disfavored by
present direct detection results.Comment: 41 pages, 8 figures, references adde
An experimental study of particle sedimentation using ultrasonic speckle velocimetry
Ultrasonic speckle velocimetry (USV) is a non-invasive technique that allows the measurement of fluid velocity in flow and also that of powders under sedimentation. To improve the USV method, we studied the sedimentation of polymethyl methacrylate and silica particles in water. Then, we built a sedimentation cell and characterized the diameter distribution of the particles. Subsequently, we carried out a specific study to optimize the USV procedure, the signal processing and data analysis. Space and temporal resolution and USV dynamics are also discussed with regard to the optimization conditions. We found that USV is a useful technique to measure velocities between 10−5 and 1 m s−1, using appropriate ultrasonic transducers. The space resolution is fixed by the length and the percentage of overlapping of the analyzed speckle windows and varies between 48 and 536 μm for the different studied particle families. Furthermore, we found that a 0.1 ns temporal resolution
could be obtained after a zero padding signal processing. In the context of our sedimentation experiments, we showed that the velocities measured by USV are in close agreement with those measured by particle image velocimetry and theory
On the measurement of B(E2, 0+ -> 2+) using intermediate-energy Coulomb excitation
Coulomb excitation is a standard method used to extract quadrupole excitation
strengths of even-even nuclei. In typical analyses the reaction is assumed to
be one-step, Coulomb only, and is treated within a semi-classical model. In
this work, fully-quantal coupled-channel calculations are performed for three
test cases in order to determine the importance of multi-step effects, nuclear
contributions, feeding from other states and corrections to the semi-classical
approximation. We study the excitation of 30S, 58Ni and 78Kr on 197Au at ~ 50
AMeV. We find that nuclear effects may contribute more than 10% and that
feeding contributions can be larger than 15%. These corrections do not alter
significantly the published B(E2) values, however an additional theoretical
error of up to 13% should be added to the experimental uncertainty if the
semi-classical model is used. This theoretical error is reduced to less than 7%
when performing a quantal coupled-channel analysis.Comment: 9 pages, accepted for publication in J. Phys. G: Nucl. Phy
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