The Rotating Mass Matrix, the Strong CP Problem and Higgs Decay

We investigate a recent solution to the strong CP problem, obtaining a theta-angle of order unity, and show that a smooth trajectory of the massive eigenvector of a rank-one rotating mass matrix is consistent with the experimental data for both fermion masses and mixing angles (except for the masses of the lightest quarks). Using this trajectory we study Higgs decay and find suppression of $\Gamma(H\to c\bar{c})$ compared to the standard model predictions for a range of Higgs masses. We also give limits for flavour violating decays, including a relatively large branching ratio for the $\tau^-\mu^+$ mode.Comment: 15 pages, 6 figures; improvements to introduction and preliminarie

Sums of hermitian squares and the BMV conjecture

Recently Lieb and Seiringer showed that the Bessis-Moussa-Villani conjecture from quantum physics can be restated in the following purely algebraic way: The sum of all words in two positive semidefinite matrices where the number of each of the two letters is fixed is always a matrix with nonnegative trace. We show that this statement holds if the words are of length at most 13. This has previously been known only up to length 7. In our proof, we establish a connection to sums of hermitian squares of polynomials in noncommuting variables and to semidefinite programming. As a by-product we obtain an example of a real polynomial in two noncommuting variables having nonnegative trace on all symmetric matrices of the same size, yet not being a sum of hermitian squares and commutators.Comment: 21 pages; minor changes; a companion Mathematica notebook is now available in the source fil

Nontrivial eigenvalues of the Liouvillian of an open quantum system

We present methods of finding complex eigenvalues of the Liouvillian of an open quantum system. The goal is to find eigenvalues that cannot be predicted from the eigenvalues of the corresponding Hamiltonian. Our model is a T-type quantum dot with an infinitely long lead. We suggest the existence of the non-trivial eigenvalues of the Liouvillian in two ways: one way is to show that the original problem reduces to the problem of a two-particle Hamiltonian with a two-body interaction and the other way is to show that diagram expansion of the Green's function has correlation between the bra state and the ket state. We also introduce the integral equations equivalent to the original eigenvalue problem.Comment: 5 pages, 2 figures, proceeding

Existence of the σ\sigma-meson below 1 GeV and f0(1500)f_0(1500) glueball

On the basis of a simultaneous description of the isoscalar s-wave channel of the $\pi\pi$ scattering (from the threshold up to 1.9 GeV) and of the $\pi\pi\to K\bar{K}$ process (from the threshold to $\sim$ 1.4 GeV) in the model-independent approach, a confirmation of the $\sigma$-meson at $\sim$ 665 MeV and an indication for the glueball nature of the $f_0(1500)$ state are obtained. It is shown that the large $\pi\pi$-background, usually obtained, combines, in reality, the influence of the left-hand branch-point and the contribution of a very wide resonance at $\sim$ 665 MeV. The coupling constants of the observed states with the $\pi\pi$ and $K\bar{K}$ systems and lengths of the $\pi\pi$ and $K\bar{K}$ scattering are obtained.Comment: 13 pages, 3 figures, LaTex; submitted to Physics Letters