383 research outputs found
Irredundant Triangular Decomposition
Triangular decomposition is a classic, widely used and well-developed way to
represent algebraic varieties with many applications. In particular, there
exist sharp degree bounds for a single triangular set in terms of intrinsic
data of the variety it represents, and powerful randomized algorithms for
computing triangular decompositions using Hensel lifting in the
zero-dimensional case and for irreducible varieties. However, in the general
case, most of the algorithms computing triangular decompositions produce
embedded components, which makes it impossible to directly apply the intrinsic
degree bounds. This, in turn, is an obstacle for efficiently applying Hensel
lifting due to the higher degrees of the output polynomials and the lower
probability of success. In this paper, we give an algorithm to compute an
irredundant triangular decomposition of an arbitrary algebraic set defined
by a set of polynomials in C[x_1, x_2, ..., x_n]. Using this irredundant
triangular decomposition, we were able to give intrinsic degree bounds for the
polynomials appearing in the triangular sets and apply Hensel lifting
techniques. Our decomposition algorithm is randomized, and we analyze the
probability of success
Permutable entire functions satisfying algebraic differential equations
It is shown that if two transcendental entire functions permute, and if one
of them satisfies an algebraic differential equation, then so does the other
one.Comment: 5 page
Fuchs versus Painlev\'e
We briefly recall the Fuchs-Painlev\'e elliptic representation of Painlev\'e
VI. We then show that the polynomiality of the expressions of the correlation
functions (and form factors) in terms of the complete elliptic integral of the
first and second kind,
and , is a straight consequence of the fact that the differential
operators corresponding to the entries of Toeplitz-like determinants, are
equivalent to the second order operator which has as solution (or,
for off-diagonal correlations to the direct sum of and ). We show
that this can be generalized, mutatis mutandis, to the anisotropic Ising model.
The singled-out second order linear differential operator being replaced
by an isomonodromic system of two third-order linear partial differential
operators associated with , the Jacobi's form of the complete elliptic
integral of the third kind (or equivalently two second order linear partial
differential operators associated with Appell functions, where one of these
operators can be seen as a deformation of ). We finally explore the
generalizations, to the anisotropic Ising models, of the links we made, in two
previous papers, between Painlev\'e non-linear ODE's, Fuchsian linear ODE's and
elliptic curves. In particular the elliptic representation of Painlev\'e VI has
to be generalized to an ``Appellian'' representation of Garnier systems.Comment: Dedicated to the : Special issue on Symmetries and Integrability of
Difference Equations, SIDE VII meeting held in Melbourne during July 200
The differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann type hierarchy revisited
A differential-algebraic approach to studying the Lax type integrability of
the generalized Riemann type hydrodynamic hierarchy is revisited, its new Lax
type representation and Poisson structures constructed in exact form. The
related bi-Hamiltonian integrability and compatible Poissonian structures of
the generalized Riemann type hierarchy are also discussed.Comment: 18 page
Viable Supersymmetry and Leptogenesis with Anomaly Mediation
The seesaw mechanism that explains the small neutrino masses comes naturally
with supersymmetric (SUSY) grand unification and leptogenesis. However, the
framework suffers from the SUSY flavor and CP problems, and has a severe
cosmological gravitino problem. We propose anomaly mediation as a simple
solution to all these problems, which is viable once supplemented by the
D-terms for U(1)_Y and U(1)_{B-L}. Even though the right-handed neutrino mass
explicitly breaks U(1)_{B-L} and hence reintroduces the flavor problem, we show
that it lacks the logarithmic enhancement and poses no threat to the framework.
The thermal leptogenesis is then made easily consistent with the gravitino
constraint.Comment: 5 pages, one figure, uses Revtex4; Discussion on the upper bound on
the LSP mass added. The version published in PR
Enhancing lepton flavour violation in the supersymmetric inverse seesaw beyond the dipole contribution
In minimal supersymmetric models the -penguin usually provides
sub-dominant contributions to charged lepton flavour violating observables. In
this study, we consider the supersymmetric inverse seesaw in which the
non-minimal particle content allows for dominant contributions of the
-penguin to several lepton flavour violating observables. In particular, and
due to the low-scale (TeV) seesaw, the penguin contribution to, for instance,
\Br(\mu \to 3e) and conversion in nuclei, allows to render some of
these observables within future sensitivity reach. Moreover, we show that in
this framework, the -penguin exhibits the same non-decoupling behaviour
which had previously been identified in flavour violating Higgs decays in the
Minimal Supersymmetric Standard Model.Comment: 29 pages, 9 figures, 4 tables; v2: minor corrections, version to
appear in JHE
On the Regularity Property of Differential Polynomials Modulo Regular Differential Chains
International audienceThis paper provides an algorithm which computes the normal form of a rational differential fraction modulo a regular differential chain if, and only if, this normal form exists. A regularity test for polynomials modulo regular chains is revisited in the nondifferential setting and lifted to differential algebra. A new characterization of regular chains is provided
Differential-Algebraic Integrability Analysis of the Generalized Riemann Type and Korteweg-de Vries Hydrodynamical Equations
A differential-algebraic approach to studying the Lax type integrability of
the generalized Riemann type hydrodynamic equations at N = 3; 4 is devised. The
approach is also applied to studying the Lax type integrability of the well
known Korteweg-de Vries dynamical system.Comment: 11 page
Muon to electron conversion in the Littlest Higgs model with T-parity
Little Higgs models provide a natural explanation of the little hierarchy
between the electroweak scale and a few TeV scale, where new physics is
expected. Under the same inspiring naturalness arguments, this work completes a
previous study on lepton flavor-changing processes in the Littlest Higgs model
with T-parity exploring the channel that will eventually turn out to be the
most sensitive, \mu-e conversion in nuclei. All one-loop contributions are
carefully taken into account, results for the most relevant nuclei are provided
and a discussion of the influence of the quark mixing is included. The results
for the Ti nucleus are in good agreement with earlier work by Blanke et al.,
where a degenerate mirror quark sector was assumed. The conclusion is that,
although this particular model reduces the tension with electroweak precision
tests, if the restrictions on the parameter space derived from lepton flavor
violation are taken seriously, the degree of fine tuning necessary to meet
these constraints also disfavors this model.Comment: 26 pages, 7 figures, 4 tables; discussion improved, results
unchanged, one reference added, version to appear in JHE
Muon Physics: A Pillar of the Standard Model
Since its discovery in the 1930s, the muon has played an important role in
our quest to understand the sub-atomic theory of matter. The muon was the first
second-generation standard-model particle to be discovered, and its decay has
provided information on the (Vector -Axial Vector) structure of the weak
interaction, the strength of the weak interaction, G_F, and the conservation of
lepton number (flavor) in muon decay. The muon's anomalous magnetic moment has
played an important role in restricting theories of physics beyond the standard
standard model, where at present there is a 3.4 standard-deviation difference
between the experiment and standard-model theory. Its capture on the atomic
nucleus has provided valuable information on the modification of the weak
current by the strong interaction which is complementary to that obtained from
nuclear beta decay.Comment: 8 pages, 9 figures. Invited paper for the Journal of Physical Society
in Japan (JPSJ), Special Topics Issue "Frontiers of Elementary Particle
Physics, The Standard Model and beyond
- …