Non-Relativistic Approximation of the Dirac Equation for Slow Fermions in Static Metric Spacetimes

We analyse the non-relativistic approximation of the Dirac equation for slow fermions moving in spacetimes with a static metric, caused by the weak gravitational field of the Earth and a chameleon field, and derive the most general effective gravitational potential, induced by a static metric of spacetime. The derivation of the non-relativistic Hamilton operator of the Dirac equation is carried out by using a standard Foldy-Wouthuysen (SFW) transformation. We discuss the chameleon field as source of a torsion field and torsion-matter interactions.Comment: 8 page

Molecule model for kaonic nuclear cluster anti-KNN

We analyse the properties of the kaonic nuclear cluster (KNC) anti-KNN with the structure Nx(anti-KN)_(I = 0), having the quantum numbers I(J^P) = 1/2(0^-), and treated as a quasi-bound hadronic molecule state. We describe the properties of the hadronic molecule, or the KNC Nx(anti-KN)_(I = 0), in terms of vibrational degrees of freedom with oscillator wave functions and chiral dynamics. These wave functions, having the meaning of trial wave functions of variational calculations, are parameterised by the frequency of oscillations of the (anti-KN)_(I = 0) pair, which is fixed in terms of the binding energy of the strange baryon resonance Lambda(1405), treated as a quasi-bound (anti-KN)_(I = 0) state. The binding energies B_X and widths Gamma_X of the states X = (anti-KN)_(I = 0) and X = anti-KNN, respectively, are calculated in the heavy-baryon approximation by using chiral Lagrangians with meson-baryon derivative couplings invariant under chiral SU(3)xSU(3) symmetry at the tree-level approximation. The results are B_(anti-KNN) = 40.2 MeV and Gamma_(anti-KNN) = Gamma^(non-pionic)_(anti-KNN) + Gamma^(pionic)_(anti-KNN) ~ (85 - 106) MeV and, where Gamma^(non-pionic)_(anti-KNN) ~ 21 MeV and Gamma^(pionic)_(anti-KNN) ~ (64 - 86) MeV are the widths of non-pionic anti-KNN -> N Lambda^0, N Sigma and pionic anti-KNN -> N Sigma pi decay modes, calculated for B_(anti-KN) = 29 MeV and Gamma_(anti-KN) = (30 - 40) MeV, respectively.Comment: 16 pages, 3 figure