Mass spectra of radially and orbitally excited states of mesons

Meson mass spectra, evaluated in the framework of the relativistic model of quasi-independent quarks, are presented. Mass values are obtained with the help of numerical calculations based on the Dirac equation and by phenomenological mass formulae. The Dirac equation involves the potential, which is sum of the vector quasi-Coulombic potential and the scalar linear rising confinement potential. The phenomenological mass formulae are applied to excited meson states consisting of u-, d-quarks and antiquarks with isotopical spin I=1. A comparison of the evaluated mass spectra with existing data is performed. Problems of identification of some meson states in vector and scalar channels are discussed.Comment: 4 pages, Talk given at 12th Lomonosov Conference on Elementary Particle Physics, Moscow, August 25-31, 200

On continuous choice of retractions onto nonconvex subsets

For a Banach space $B$ and for a class \A of its bounded closed retracts, endowed with the Hausdorff metric, we prove that retractions on elements A \in \A can be chosen to depend continuously on $A$, whenever nonconvexity of each A \in \A is less than \f{1}{2}. The key geometric argument is that the set of all uniform retractions onto an \a-paraconvex set (in the spirit of E. Michael) is \frac{\a}{1-\a}-paraconvex subset in the space of continuous mappings of $B$ into itself. For a Hilbert space $H$ the estimate \frac{\a}{1-\a} can be improved to \frac{\a (1+\a^{2})}{1-\a^{2}} and the constant \f{1}{2} can be reduced to the root of the equation \a+ \a^{2}+a^{3}=1

Triple and quartic interactions of Higgs bosons in the two-Higgs-doublet model with CP violation

We consider the two-Higgs-doublet model with explicit CP-violation, where the effective Higgs potential is not CP-invariant at the tree-level. Three neutral Higgs bosons of the model are the mixtures of CP-even and CP-odd bosons which exist in the CP-conserving limit of the theory. The mass spectrum and tree-level couplings of the neutral Higgs bosons to gauge bosons and fermions are significantly dependent on the parameters of the Higgs boson mixing matrix. We calculate the Higgs-gauge boson, Higgs-fermion, triple and quartic Higgs self-interactions in the MSSM with explicit CP-violation in the Higgs sector and CP-violating Yukawa interactions of the third generation scalar quarks. In some regions of the MSSM parameter space substantial changes of the self-interaction vertices take place, leading to significant suppression or enhancement of the multiple Higgs boson production cross sections.Comment: 29 pages, 4 figures. Minor changes in section 3, misprints in (47) corrected. Version accepted by EPJ