Comment on "Tetraquarks as diquark-antidiquark bound systems"

The author argues that the calculated masses of heavy tetraquarks obtained by solution of the spin-independent homogeneous Lippmann-Schwinger integral equation in a diquark-antidiquark picture reported by M. Monemzadeh et al., Phys. Lett. B {\bf741}, 124 (2015), are incorrect. We have reexamined all of the published results and we believe that not only the reported tetraquark masses for states with zero total angular momentum are incorrect, the reported masses for states with non-zero total angular momentum are quite misleading, because these states cannot be predicted by a spin-independent formalism

Three-Nucleon Bound State in a Spin-Isospin Dependent Three Dimensional Approach

A spin-isospin dependent Three-Dimensional approach based on momentum vectors for formulation of the three-nucleon bound state is presented in this paper. The three-nucleon Faddeev equations with two-nucleon interactions are formulated as a function of vector Jacobi momenta, specifically the magnitudes of the momenta and the angle between them with the inclusion of the spin-isospin quantum numbers, without employing a partial wave decomposition. As an application the spin-isospin dependent Faddeev integral equations are solved with Bonn-B potential. Our result for the Triton binding energy with the value of -8.152 MeV is in good agreement with the achievements of the other partial wave based methods.Comment: 24 pages, 1 figure, 7 tables. Major changes; version to appear in Physical Review

Calculation of Relativistic Nucleon-Nucleon Potentials in Three-Dimensions

In this paper, we have applied a three-dimensional approach for calculation of the relativistic nucleon-nucleon potential. The quadratic operator relation between the non-relativistic and the relativistic nucleon-nucleon interactions is formulated as a function of relative two-nucleon momentum vectors, which leads to a three-dimensional integral equation. The integral equation is solved by the iteration method, and the matrix elements of the relativistic potential are calculated from non-relativistic ones. Spin-independent Malfliet-Tjon potential is employed in the numerical calculations, and the numerical tests indicate that the two-nucleon observables calculated by the relativistic potential are preserved with high accuracy

Toward the Application of Three-Dimensional Approach to Few-body Atomic Bound States

The first step toward the application of an effective non partial wave (PW) numerical approach to few-body atomic bound states has been taken. The two-body transition amplitude which appears in the kernel of three-dimensional Faddeev-Yakubovsky integral equations is calculated as function of two-body Jacobi momentum vectors, i.e. as a function of the magnitude of initial and final momentum vectors and the angle between them. For numerical calculation the realistic interatomic interactions HFDHE2, HFD-B, LM2M2 and TTY are used. The angular and momentum dependence of the fully off-shell transition amplitude is studied at negative energies. It has been numerically shown that, similar to the nuclear case, the transition amplitude exhibits a characteristic angular behavior in the vicinity of 4He dimer pole.Comment: 8 pages, 6 figures, 4 tables. Oral contribution to the 19th International IUPAP Conference on Few-Body Problems In Physics, 31 Aug-5 Sep 2009, Bonn, German

Solution of Two-Body Bound State Problems with Confining Potentials

The homogeneous Lippmann-Schwinger integral equation is solved in momentum space by using confining potentials. Since the confining potentials are unbounded at large distances, they lead to a singularity at small momentum. In order to remove the singularity of the kernel of the integral equation, a regularized form of the potentials is used. As an application of the method, the mass spectra of heavy quarkonia, mesons consisting from heavy quark and antiquark $(\Upsilon(b\bar{b}), \psi(c\bar{c}))$, are calculated for linear and quadratic confining potentials. The results are in good agreement with configuration space and experimental results.Comment: 6 pages, 5 table

Four-Body Bound State Formulation in Three-Dimensional Approach (Without Angular Momentum Decomposition)

The four-body bound state with two-body forces is formulated by the Three-Dimensional approach, which greatly simplifies the numerical calculations of few-body systems without performing the Partial Wave components. We have obtained the Yakubovsky equations directly as three dimensional integral equations.Comment: Talk given at the Third Asia-Pacific Conference on Few-Body Problems in Physics. Nakhon Ratchasima, Thailand. July 200

Bound State Calculations of the Three-Dimensional Yakubovsky Equations with the inclusion of Three-Body Forces

The four-body Yakubovsky equations in a Three-Dimensional approach with the inclusion of the three-body forces is proposed. The four-body bound state with two- and three-body interactions is formulated in Three-Dimensional approach for identical particles as function of vector Jacobi momenta, specifically the magnitudes of the momenta and the angles between them. The modified three dimensional Yakubovsky integral equations is successfully solved with the scalar two-meson exchange three-body force where the Malfliet-Tjon-type two-body force is implemented. The three-body force effects on the energy eigenvalue and the four-body wave function, as well as accuracy of our numerical calculations are presented.The four-body Yakubovsky equations in a Three-Dimensional approach with the inclusion of the three-body forces is proposed. The four-body bound state with two- and three-body interactions is formulated in Three-Dimensional approach for identical particles as function of vector Jacobi momenta, specifically the magnitudes of the momenta and the angles between them. The modified three dimensional Yakubovsky integral equations is successfully solved with the scalar two-meson exchange three-body force where the Malfliet-Tjon-type two-body force is implemented. The three-body force effects on the energy eigenvalue and the four-body wave function, as well as accuracy of our numerical calculations are presented.Comment: 23 pages, 2 eps figures, 5 tables. Major changes; version to appear in European Physical Journal

R-Matrix Calculations for Few-Quark Bound States

The R--matrix method is implemented to study the heavy charm and bottom diquark, triquark, tetraquark and pentaquarks in configuration space, as the bound states of quark--antiquark, diquark--quark, diquark--antidiquark and diquark--antitriquark systems, respectively. The mass spectrum and the size of these systems are calculated for different partial wave channels. The calculated masses are compared with recent theoretical results obtained by other methods in momentum and configuration spaces and also by available experimental data