where θ̄ = θQCD + θQFD which violates CP. From the experimental bound on the neutron electric dipole moment , |θ̄| is required to be less than 10. This is “the strong CP problem”. The axion solution of the strong CP problem is to introduce a dynamical field axion (a) so that θ̄ is settled very near 0. In this case, one can study the following Lagrangian below the electroweak scale, after integrati...

We show the relation between Appell's remark on the central projection in the dynamic of a particle and T.-Y. Thomas and Nijenhuis studies of the polynomial first integrals of the geodesic flow on a space of constant curvature. Among the consequences: the space of leading terms of a quadratic first integral of an equation¨q = f (q), q ∈ IR n , is isomorphic to the space of quadrilin-ear forms o...

In this article we consider four particular cases of Synthetic Aperture Radar imaging with moving objects. In each case, we analyze the forward operator F and the normal operator F ∗F , which appear in the mathematical expression for the recovered reflectivity function (i.e. the image). In general, by applying the backprojection operator F ∗ to the scattered waveform (i.e. the data), artifacts ...

Effective Lagrangians with dimension-six operators are widely used to analyse Higgs and other electroweak data. We show how to build a basis of operators such that each operator is linked to a coupling which is well measured or will be in the future. We choose a set of couplings such that the correspondence is one-to-one. The usual arbitrary coefficients in front of operators can be constrained...

Gravitational analogues of the nonlinear electrodynamics of Born and of Born and Infeld are introduced and applied to the black hole problem. This work is mainly devoted to the 2-dimensional case in which the relevant lagrangians are nonpolynomial in the scalar curvature.

We derive a tree-level heavy quark effective Lagrangian keeping particle-antiparticle mixed sectors allowing for heavy quark-antiquark pair annihilation and creation. However, when removing the unwanted degrees of freedom from the effective Lagrangian one has to be careful in using the classical equations of motion obeyed by the effective fields in order to get a convergent expansion on the rec...

The production cross section for pseudo-scalar Higgs bosons at hadron colliders is computed at next-to-next-to-leading order (NNLO) in QCD. The pseudo-scalar Higgs is assumed to couple only to top quarks. The NNLO effects are evaluated using an effective Lagrangian where the top quarks are integrated out. The NNLO corrections are similar in size to those found for scalar Higgs boson production.

The lower bound is the same as before, due to the fact that Tr(n) is Kr+1-free. Define the adjacency matrix A = A(G) = (aij) for a graph G of order n. Let V = {v1, · · · , vn}. Then A is a n-by-n 0 − 1 matrix such that aij = 1 if and only if vivj ∈ E. Thus A is symmetric. We will be interested in a quadratic form ⟨Ax,x⟩ where x denotes a vector of length n. This is often called the Lagrangian o...

We investigate the spectrum of the lightest states of N = 1 Super Yang-Mills. We first study the spectrum using the recently extended Veneziano Yankielowicz theory containing also the glueball states besides the gluinoball ones. Using a simple Kähler term we show that within the effective Lagrangian approach one can accommodate either the possibility in which the glueballs are heavier or lighte...

An Hamiltonian formulation with complex fluxes and currents is proposed. This formulation is derived from a recent Lagrangian formulation with complex electrical quantities. The complexification process avoids the usual separation into real and imaginary parts and notably simplifies modeling issues. Simple modifications of the magnetic energy underlying standard (α, β) models yield new (α, β) m...