Excited Heavy Baryons and Their Symmetries III: Phenomenology

Abstract

Phenomenological applications of an effective theory of low-lying excited states of charm and bottom isoscalar baryons are discussed at leading and next-to-leading order in the combined heavy quark and large $N_c$ expansion. The combined expansion is formulated in terms of the counting parameter $\lambda \sim 1/m_Q,1/N_c$; the combined expansion is in powers of ${\lambda }^{1/2}$. We work up to next-to-leading order. We obtain model-independent predictions for the excitation energies, the semileptonic form factors and electromagnetic decay rates. The spin-averaged mass of the doublet of the first orbitally excited sate of ${\Lambda }_b$ is predicted to be approximately $5920MeV$. It is shown that in the combined limit at leading and next-to-leading order there is only one independent form factor describing ${\Lambda }_b\to {\Lambda }_c\ell \bar{\nu }$; similarly, ${\Lambda }_b\to {\Lambda }_c^{\ast }\ell \bar{\nu }$ and ${\Lambda }_b\to {\Lambda }_{c1}\ell \bar{\nu }$ decays are described by a single independent form factor. These form factors are calculated at leading and next-to-leading order in the combined expansion. The electromagnetic decay rates of the first excited states of ${\Lambda }_c$ and ${\Lambda }_b$ are determined at leading and next-to leading order. The ratio of radiative decay rates $\Gamma ({\Lambda }_c^{\ast }\to {\Lambda }_c\gamma )/\Gamma ({\Lambda }_{b1}\to {\Lambda }_b\gamma )$ is predicted to be approximately 0.2, greatly different from the heavy quark effective theory value of unity.

Comments: 21 pages, 2 figures