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

Comment on Choi, Y.-J., et al. Cellular Phone Use and Risk of Tumors:Systematic Review and Meta-Analysis. Int. J. Environ. Res. Public Health 2020, 17, 8079

We welcome the updated systematic review and meta-analysis of case-control studies of mobile phone use and cancer by Choi et al [...].</p

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

Inclusive decays of ηb\eta_{b} into SS- and PP-wave charmonium states

Inclusive S- and P-wave charmonium productions in the bottomonium ground state $\eta_b$ decay are calculated at the leading order in the strong coupling constant $\alpha_s$ and quarkonium internal relative velocity $v$ in the framework of the NRQCD factorization approach. We find the contribution of $\eta_b \to \chi_{c_J}+ g g$ followed by $\chi_{c_J} \to J/\psi+ \gamma$ is also very important to the inclusive $J/\psi$ production in the $\eta_b$ decays, which maybe helpful to the investigation of the color-octet mechanism in the inclusive $J/\psi$ production in the $\eta_b$ decays in the forthcoming LHCb and SuperB. As a complementary work, we also study the inclusive production of $\eta_c$, and $\chi_{cJ}$ in the $\eta_b$ decays, which may help us understand the X(3940) and X(3872) states.Comment: 7 pages, 2 figure