Non-Relativistic Approximation of Dirac Equation for Slow Fermions Coupled to the Chameleon and Torsion Fields in the Gravitational Field of the Earth

We analyse a non-relativistic approximation of the Dirac equation for slow fermions, coupled to the chameleon field and torsion in the spacetime with the Schwarzschild metric, taken in the weak gravitational field of the Earth approximation. We follow the analysis of the Dirac equation in the curved spacetime with torsion, proposed by Kostelecky (Phys. Rev. D69, 105009 (2004)), and apply the Foldy--Wouthuysen transformations. We derive the effective low-energy gravitational potentials for slow fermions, coupled to the gravitational field of the Earth, the chameleon field and to torsion with minimal and non-minimal couplings.Comment: 12 page

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

Standard Electroweak Interactions in Gravitational Theory with Chameleon Field and Torsion

We propose a version of a gravitational theory with the torsion field, induced by the chameleon field. Following Hojman et al. Phys. Rev. D17, 3141 (1976) the results, obtained in Phys. Rev. D90, 045040 (2014), are generalised by extending the Einstein gravity to the Einstein-Cartan gravity with the torsion field as a gradient of the chameleon field through a modification of local gauge invariance of minimal coupling in the Weinberg-Salam electroweak model. The contributions of the chameleon (torsion) field to the observables of electromagnetic and weak processes are calculated. Since in our approach the chameleon-photon coupling constant beta_(gamma) is equal to the chameleon-matter coupling constant beta, i.e. beta_(gamma) = beta, the experimental constraints on beta, obtained in terrestrial laboratories by T. Jenke et al. (Phys. Rev. Lett. 112, 115105 (2014)) and by H. Lemmel et al. (Phys. Lett. B743, 310 (2015)), can be used for the analysis of astrophysical sources of chameleons, proposed by C. Burrage et al. (Phys. Rev. D79, 044028 (2009)), A.-Ch. Davis et al. (Phys. Rev. D80, 064016 (2009), and in references therein, where chameleons induce photons because of direct chameleon-photon transitions in the magnetic fields.Comment: 26 pages, 8 figure

On kaonic deuterium. Quantum field theoretic and relativistic covariant approach

We study kaonic deuterium, the bound K^-d state A_(K d). Within a quantum field theoretic and relativistic covariant approach we derive the energy level displacement of the ground state of kaonic deuterium in terms of the amplitude of K^-d scattering for arbitrary relative momenta. Near threshold our formula reduces to the well-known DGBT formula. The S-wave amplitude of K^-d scattering near threshold is defined by the resonances Lambda(1405), Sigma(1750) and a smooth elastic background, and the inelastic channels K^- d -> NY and K^- d -> NY pion, with Y = Sigma^(+/-), Sigma^0 and Lambda^0, where the final-state interactions play an important role. The Ericson-Weise formula for the S-wave scattering length of K^-d scattering is derived. The total width of the energy level of the ground state of kaonic deuterium is estimated using the theoretical predictions of the partial widths of the two-body decays A_(Kd) -> NY and experimental data on the rates of the NY-pair production in the reactions K^-d -> NY. We obtain Gamma_{1s} = (630 +/-100) eV. For the shift of the energy level of the ground state of kaonic deuterium we predict epsilon_(1s) = (353 +/-60)eV.Comment: 73 pages,10 figures, Latex, We have slightly corrected the contribution of the double scattering. The change of the S-wave scattering length of K^-d scattering does not go beyond the theoretical uncertainty, which is about 18