Hyperfine Mixing and the Semileptonic Decays of Double-Heavy Baryons in a Quark Model

The semileptonic decays of the lowest-lying double-heavy baryons is treated in a quark model. For the $\Xi_{bb}$, hyperfine mixing in the spin wave function leaves the total rate for decay into the lowest lying daughter baryons essentially unchanged, but changes the relative rates into the $\Xi_{bc}$ and $\Xi_{bc}^\prime$. The same pattern is obtained in the decays of the $\Omega_{bb}$. For the $\Xi_{bc}$, this mixing leads to factor of about 17 suppression in the decay rate to the $\Xi_{cc}^*$, and a factor of two suppression in the total decay rate. For the $\Omega_{bc}$, the decay to the $\Omega_{cc}^*$ is suppressed by a factor of more than 30 from the unmixed case, and the total decay rate is decreased to about 40% of the decay rate obtained when mixing is ignored.Comment: 7 page

Semileptonic Decays of Heavy Omega Baryons in a Quark Model

The semileptonic decays of $\Omega_c$ and $\Omega_b$ are treated in the framework of a constituent quark model developed in a previous paper on the semileptonic decays of heavy $\Lambda$ baryons. Analytic results for the form factors for the decays to ground states and a number of excited states are evaluated. For $\Omega_b$ to $\Omega_c$ the form factors obtained are shown to satisfy the relations predicted at leading order in the heavy-quark effective theory at the non-recoil point. A modified fit of nonrelativistic and semirelativistic Hamiltonians generates configuration-mixed baryon wave functions from the known masses and the measured \lcle rate, with wave functions expanded in both harmonic oscillator and Sturmian bases. Decay rates of \ob to pairs of ground and excited \omc states related by heavy-quark symmetry calculated using these configuration-mixed wave functions are in the ratios expected from heavy-quark effective theory, to a good approximation. Our predictions for the semileptonic elastic branching fraction of $\Omega_Q$ vary minimally within the models we use. We obtain an average value of (84$\pm$ 2%) for the fraction of $\Omega_c\to \Xi^{(*)}$ decays to ground states, and 91% for the fraction of $\Omega_c\to \Omega^{(*)}$ decays to the ground state $\Omega$. The elastic fraction of \ob \to \omc ranges from about 50% calculated with the two harmonic-oscillator models, to about 67% calculated with the two Sturmian models.Comment: 52 pages, 8 figure

Quantum Monte Carlo calculations of electroweak transition matrix elements in A = 6,7 nuclei

Green's function Monte Carlo calculations of magnetic dipole, electric quadrupole, Fermi, and Gamow-Teller transition matrix elements are reported for A=6,7 nuclei. The matrix elements are extrapolated from mixed estimates that bracket the relevant electroweak operator between variational Monte Carlo and GFMC propagated wave functions. Because they are off-diagonal terms, two mixed estimates are required for each transition, with a VMC initial (final) state paired with a GFMC final (initial) state. The realistic Argonne v18 two-nucleon and Illinois-2 three-nucleon interactions are used to generate the nuclear states. In most cases we find good agreement with experimental data.Comment: v2: minor corrections to text and figure

Heavy Baryons in a Quark Model

A quark model is applied to the spectrum of baryons containing heavy quarks. The model gives masses for the known heavy baryons that are in agreement with experiment, but for the doubly-charmed baryon Cascade_{cc}, the model prediction is too heavy. Mixing between the Cascade_Q and Cascade_Q^\prime states is examined and is found to be small for the lowest lying states. In contrast with this, mixing between the Cascade_{bc} and Cascade_{bc}^\prime states is found to be large, and the implication of this mixing for properties of these states is briefly discussed. We also examine heavy-quark spin-symmetry multiplets, and find that many states in the model can be placed in such multiplets. We compare our predictions with those of a number of other authors.Comment: Version published in International Journal of Modern Physics

The Role of Δ(1232)\Delta(1232) in Two-pion Exchange Three-nucleon Potential

In this paper we have studied the two-pion exchange three-nucleon potential $(2\pi E-3NP)$ using an approximate $SU(2) \times SU(2)$ chiral symmetry of the strong interaction. The off-shell pion-nucleon scattering amplitudes obtained from the Weinberg Lagangian are supplemented with contributions from the well-known $\sigma$-term and the $\Delta(1232)$ exchange. It is the role of the $\Delta$-resonance in $2\pi E-3NP$, which we have investigated in detail in the framework of the Lagrangian field theory. The $\Delta$-contribution is quite appreciable and, more significantly, it is dependent on a parameter Z which is arbitrary but has the empirical bounds $|Z| \leq 1/2$. We find that the $\Delta$-contribution to the important parameters of the $2\pi E-3NP$ depends on the choice of a value for Z, although the correction to the binding energy of triton is not expected to be very sensitive to the variation of Z within its bounds.Comment: 14 pages, LaTe

Semileptonic Decays of Heavy Lambda Baryons in a Quark Model

The semileptonic decays of Lambda_c and Lambda_b are treated in the framework of a constituent quark model. Both nonrelativistic and semirelativistic Hamiltonians are used to obtain the baryon wave functions from a fit to the spectra, and the wave functions are expanded in both the harmonic oscillator and Sturmian bases. The latter basis leads to form factors in which the kinematic dependence on q^2 is in the form of multipoles, and the resulting form factors fall faster as a function of q^2 in the available kinematic ranges. As a result, decay rates obtained in the two models using the Sturmian basis are significantly smaller than those obtained using the harmonic oscillator basis. In the case of the Lambda_c, decay rates calculated using the Sturmian basis are closer to the experimentally reported rates. However, we find a semileptonic branching fraction for the Lambda_c to decay to excited Lambda* states of 11% to 19%, in contradiction with what is assumed in available experimental analyses. Our prediction for the Lambda_b semileptonic decays is that decays to the ground state Lambda_c provide a little less than 70% of the total semileptonic decay rate. For the decays Lambda_b to Lambda_c, the analytic form factors we obtain satisfy the relations expected from heavy-quark effective theory at the non-recoil point, at leading and next-to-leading orders in the heavy-quark expansion. In addition, some features of the heavy-quark limit are shown to naturally persist as the mass of the heavy quark in the daughter baryon is decreased.Comment: 51 pages, 8 figures, submitted to Physical Review

Light cone QCD sum rules study of the semileptonic heavy ΞQ\Xi_{Q} and ΞQ′\Xi'_{Q} transitions to Ξ\Xi and Σ\Sigma baryons

The semileptonic decays of heavy spin--1/2, $\Xi_{b(c)}$ and $\Xi'_{b(c)}$ baryons to the light spin-- 1/2, $\Xi$ and $\Sigma$ baryons are investigated in the framework of the light cone QCD sum rules. In particular, using the most general form of the interpolating currents for the heavy baryons as well as the distribution amplitudes of the $\Xi$ and $\Sigma$ baryons, we calculate all form factors entering the matrix elements of the corresponding effective Hamiltonians in full QCD. Having calculated the responsible form factors, we evaluate the decay rates and branching fractions of the related transitions.Comment: 30 Pages, 5 Figures and 18 Table