B+→K−π+π+B^+\to K^-\pi^+\pi^+: three-body final state interactions and KπK\pi isospin states

Final state interactions are considered to formulate the $B$ meson decay amplitude for the $K\pi\pi$ channel. The Faddeev decomposition of the Bethe-Salpeter equation is used in order to build a relativistic three-body model within the light-front framework. The S-wave scattering amplitude for the $K\pi$ system is considered in the $1/2$ and $3/2$ isospin channels with the set of inhomogeneous integral equations solved perturbatively. In comparison with previous results for the $D$ meson decay in the same channel, one has to consider the different partonic processes, which build the source amplitudes, and the larger absorption to other decay channels appears, that are important features to be addressed. As in the $D$ decay case, the convergence of the rescattering perturbative series is also achieved with two-loop contributions.Comment: 10 pages, 4 figure

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.

Color-suppression of non-planar diagrams in bosonic bound states

We study the suppression of non-planar diagrams in a scalar QCD model of a meson system in $3+1$ space-time dimensions due to the inclusion of the color degrees of freedom. As a prototype of the color-singlet meson, we consider a flavor-nonsinglet system consisting of a scalar-quark and a scalar-antiquark with equal masses exchanging a scalar-gluon of a different mass, which is investigated within the framework of the homogeneous Bethe-Salpeter equation. The equation is solved by using the Nakanishi representation for the manifestly covariant bound-state amplitude and its light-front projection. The resulting non-singular integral equation is solved numerically. The damping of the impact of the cross-ladder kernel on the binding energies are studied in detail. The color-suppression of the cross-ladder effects on the light-front wave function and the elastic electromagnetic form factor are also discussed. As our results show, the suppression appears significantly large for $N_c=3$, which supports the use of rainbow-ladder truncations in practical nonperturbative calculations within QCD.Comment: 12 pages, 7 figures. To appear in Physics Letters

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

Late time cosmological approach in mimetic f(R,T)f(R,T) gravity

In this paper, we investigate the late-time cosmic acceleration in mimetic $f(R,T)$ gravity with Lagrange multiplier and potential in a Universe containing, besides radiation and dark energy, a self-interacting (collisional) matter. We obtain through the modified Friedmann equations, the main equation that can describe the cosmological evolution and with several models from $Q(z)$ and the well known particular model $f(R, T)$, we perform an analysis of the late-time evolution. We examine the behavior of the Hubble parameter, the dark energy equation of state and the total effective equation of state and we compare in each case the resulting picture with the non-collisional matter (assumed as dust) and also with the collisional matter in mimetic $f(R, T)$ gravity. The results obtained are in good agreement with the observational data and show that in presence of the collisional matter the dark energy oscillations in mimetic f(R, T) gravity can be damped.Comment: 18 pages, 2 figure

Late time cosmological approach in mimetic f(R,T)f(R,T) gravity

In this paper, we investigate the late-time cosmic acceleration in mimetic $f(R,T)$ gravity with Lagrange multiplier and potential in a Universe containing, besides radiation and dark energy, a self-interacting (collisional) matter. We obtain through the modified Friedmann equations, the main equation that can describe the cosmological evolution and with several models from $Q(z)$ and the well known particular model $f(R, T)$, we perform an analysis of the late-time evolution. We examine the behavior of the Hubble parameter, the dark energy equation of state and the total effective equation of state and we compare in each case the resulting picture with the non-collisional matter (assumed as dust) and also with the collisional matter in mimetic $f(R, T)$ gravity. The results obtained are in good agreement with the observational data and show that in presence of the collisional matter the dark energy oscillations in mimetic f(R, T) gravity can be damped.Comment: 18 pages, 2 figure

Bound state structure and electromagnetic form factor beyond the ladder approximation

We investigate the response of the bound state structure of a two-boson system, within a Yukawa model with a scalar boson exchange, to the inclusion of the cross-ladder contribution to the ladder kernel of the Bethe-Salpeter equation. The equation is solved by means of the Nakanishi integral representation and light-front projection. The valence light-front wave function and the elastic electromagnetic form factor beyond the impulse approximation, with the inclusion of the two-body current, generated by the cross-ladder kernel, are computed. The valence wave function and electromagnetic form factor, considering both ladder and ladder plus cross-ladder kernels, are studied in detail. Their asymptotic forms are found to be quite independent of the inclusion of the cross-ladder kernel, for a given binding energy. The asymptotic decrease of form factor agrees with the counting rules. This analysis can be generalized to fermionic systems, with a wide application in the study of the meson structure.Comment: 19 pages, 6 figures, submitted to Phys. Lett.