François-Xavier Josse-Michaux

arXiv2011

A Common Framework for Dark Matter, Leptogenesis and Neutrino Masses

We study a seesaw-type extension of the Standard Model in which the symmetry group is enlarged by a global U(1). We introduce adequate scalar and fermion representations which naturally explain the smallness of neutrino masses. With the addition of a viable scalar Dark Matter candidate, an original scenario of leptogenesis emerges. We solve the relevant set of Boltzmann equations and show how leptogenesis can be successfully implemented at the TeV scale. The constraints on the scalar mass spectrum are derived and the Dark Matter phenomenology is discussed.

hep-ph↗

arXiv2005

Finite dimensional quantizations of the (q,p) plane : new space and momentum inequalities

We present a N-dimensional quantization a la Berezin-Klauder or frame quantization of the complex plane based on overcomplete families of states (coherent states) generated by the N first harmonic oscillator eigenstates. The spectra of position and momentum operators are finite and eigenvalues are equal, up to a factor, to the zeros of Hermite polynomials. From numerical and theoretical studies of the large $N$ behavior of the product $λ\_m(N) λ\_M(N)$ of non null smallest positive and largest eigenvalues, we infer the inequality $δ\_N(Q) Δ\_N(Q) = σ\_N \overset{<}{\underset{N \to \infty}{\to}} 2 π$ (resp. $δ\_N(P) Δ\_N(P) = σ\_N \overset{<}{\underset{N \to \infty}{\to}} 2 π$) involving, in suitable units, the minimal ($δ\_N(Q)$) and maximal ($Δ\_N(Q)$) sizes of regions of space (resp. momentum) which are accessible to exploration within this finite-dimensional quantum framework. Interesting issues on the measurement process and connections with the finite Chern-Simons matrix model for the Quantum Hall effect are discussed.

quant-ph↗