Comment on "Theory of collisions between an atom and a diatomic molecule in the body-fixed coordinate system"

It is shown that the phase factor i^(J+j+I) omitted in a theory of atom‐diatom monreactive scattering formulated by schatz and kupperman but included in the Choi, Poe, and Tang theory does not lead to errors in the analysis of te (H,H_2) system

Piecewise Certificates of Positivity for matrix polynomials

We show that any symmetric positive definite homogeneous matrix polynomial $M\in\R[x_1,...,x_n]^{m\times m}$ admits a piecewise semi-certificate, i.e. a collection of identites $M(x)=\sum_jf_{i,j}(x)U_{i,j}(x)^TU_{i,j}(x)$ where $U_{i,j}(x)$ is a matrix polynomial and $f_{i,j}(x)$ is a non negative polynomial on a semi-algebraic subset $S_i$, where $\R^n=\cup_{i=1}^r S_i$. This result generalizes to the setting of biforms. Some examples of certificates are given and among others, we study a variation around the Choi counterexample of a positive semi-definite biquadratic form which is not a sum of squares. As a byproduct we give a representation of the famous non negative sum of squares polynomial $x^4z^2+z^4y^2+y^4x^2-3 x^2y^2z^2$ as the determinant of a positive semi-definite quadratic matrix polynomial

Is X(3872) a possible candidate of hybrid meson

The associate productions of X(3872) and J/\psi in hadron collisions and flavor independence of hadrons in ee^+\to X(3872)+hadrons and the decays X(3872)\to \gamma+hadrons are discussed. It is pointed out X(3872)\to J/\psi+\sigma could be a significant decay channel.Comment: 13 page

Studies of charmed states in amplitude analyses at LHCb

Amplitude analysis is a powerful tool to study the properties of intermediate resonances produced in the decays of B mesons. At LHCb we have studied B+ decays to X(3872) K+, where X(3872) decays to J/psi pi+ pi-, to determine the quantum numbers of the X(3872), and B+ decays to proton anti-proton K+ to learn more about (charm anti-charm) to proton anti-proton transitions. We also exploit the spin of the J/psi to perform amplitude analyses of the decays B0_s to J/psi pi+ pi-, B0_s to J/psi K+ K-, B0 to J/psi pi+ pi-, and B0 to J/psi K+ K-. Our results use 1.0 inverse femtobarn of data taken in 2011 from 7 TeV proton-proton collisions, provided by the LHC.Comment: 9 pages, 3 figures, to appear in the proceedings of The 6th International Workshop on Charm Physics (CHARM 2013