We evaluate static properties and semileptonic decays for the ground state of doubly heavy Ξ, Ξ ′ , Ξ * and Ω, Ω ′ , Ω * baryons. Working in the framework of a nonrelativistic quark model, we solve the three-body problem by means of a variational ansazt made possible by heavy quark spin symmetry constraints. To check the dependence of our results on the inter-quark interaction we use five different quark-quark potentials that include a confining term plus Coulomb and hyperfine terms coming from one-gluon exchange. Our results for static properties (masses, charge and mass radii, magnetic moments. . . ) are, with a few exceptions for the magnetic moments, in good agreement with a previous Faddeev calculation. Our much simpler wave functions are used to evaluate semileptonic decays of doubly heavy Ξ, Ξ ′ (J = 1/2) and Ω, Ω ′ (J = 1/2) baryons. Our results for the decay widths are in good agreement with calculations done within a relativistic quark model in the quark-diquark approximation.

The use of Heavy Quark Symmetry to study bottom and charmed baryons leads to important simplifications of the non-relativistic three body problem, which turns out to be easily solved by a simple variational ansatz. Our simple scheme reproduces previous results (baryon masses, charge and mass radii, · · ·) obtained by solving the Faddeev equations with simple non-relativistic quark-quark potentials, adjusted to the light and heavy-light meson spectra. Wave functions, parameterized in a simple manner, are also given and thus they can be easily used to compute further observables. Our method has been also used to find the predictions for strangeness-less baryons of the SU(2) chirally inspired quark-quark interactions. We find that the one pion exchange term of the chirally inspired interactions leads to relative changes of the Λ b and Λc binding energies as large as 90%.

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Two-particle two-hole contributions to electroweak response functions are computed in a fully relativistic Fermi gas, assuming that the electroweak current matrix elements are independent of the kinematics. We analyze the genuine kinematical and relativistic effects before including a realistic mesonexchange current operator. This allows one to study the mathematical properties of the nontrivial sevendimensional integrals appearing in the calculation and to design an optimal numerical procedure to reduce the computation time. This is required for practical applications to charged-current neutrino scattering experiments, in which an additional integral over the neutrino flux is performed. Finally, we examine the viability of this model to compute the electroweak two-particle-two-hole response functions.

We qualitatively corroborate the results of W. Roberts and M. Pervin in Int. J. Mod. Phys. A 24, 2401 according to which hyperfine mixing greatly affects the decay widths of b → c semileptonic decays involving doubly heavy bc baryons. However, our predictions for the decay widths of the unmixed states differ from those reported in the work of Roberts and Pervin by a factor of 2, and this discrepancy translates to the mixed case. We further show that the predictions of heavy quark spin symmetry, might be used in the future to experimentally extract information on the admixtures in the actual physical bc baryons, in a model independent manner.