Solving the three-body bound-state Bethe-Salpeter equation in Minkowski space

The scalar three-body Bethe-Salpeter equation, with zero-range interaction, is solved in Minkowski space by direct integration of the four-dimensional integral equation. The singularities appearing in the propagators are treated properly by standard analytical and numerical methods, without relying on any ansatz or assumption. The results for the binding energies and transverse amplitudes are compared with the results computed in Euclidean space. A fair agreement between the calculations is found.Comment: 10 pages, 2 figures, version accepted for publication in Phys. Lett.

Non-centro-symmetric superconductors Li2Pd3B and Li2(Pd0.8Pt0.2)3B: amplitude and phase fluctuations analysis of the experimental magnetization data

We report on magnetization data obtained as a function of temperature and magnetic field in Li2 (Pd0.8Pt0.2)3B and Li2Pd3B non-centro-symmetric superconductors. Reversible magnetization curves were plotted as M1/2 vs. T. This allows study of the asymptotic behavior of the averaged order parameter amplitude (gap) near the superconducting transition. Results of the analysis show, as expected, a mean field superconducting transition for Li2Pd3B. On contrary, a large deviation from the mean field behavior is revealed for Li2(Pd0.8Pt0.2)3B. This is interpreted as due to the strength of the non s-wave spin-triplet pairing in this Pt-containing compound which produces nodes in the order parameter and consequently, phase fluctuations. The diamagnetic signal above Tc(H) in Li2Pd3B is well explained by superconducting Gaussian fluctuations, which agrees with the observed mean field transition. For Li2(Pd0.8Pt0.2)3B the diamagnetic signal above Tc(H) is much higher than the expected Gaussian values and appears to be well explained by three dimensional critical fluctuations of the lowest-Landau-level type, which somehow agrees with the scenario of a phase mediated transition.Comment: 7 pages (1 column) 3 figure

Three-body bound states with zero-range interaction in the Bethe-Salpeter approach

The Bethe-Salpeter equation for three bosons with zero-range interaction is solved for the first time. For comparison the light-front equation is also solved. The input is the two-body scattering length and the outputs are the three-body binding energies, Bethe-Salpeter amplitudes and light-front wave functions. Three different regimes are analyzed: ({\it i}) For weak enough two-body interaction the three-body system is unbound. ({\it ii}) For stronger two-body interaction a three-body bound state appears. It provides an interesting example of a deeply bound Borromean system. ({\it iii}) For even stronger two-body interaction this state becomes unphysical with a negative mass squared. However, another physical (excited) state appears, found previously in light-front calculations. The Bethe-Salpeter approach implicitly incorporates three-body forces of relativistic origin, which are attractive and increase the binding energy.Comment: 13 pages, 7 figure