Spin Symmetry Without Heavy Quarks: Hyperon Form Factors In The Large $N_c$ Limit

Abstract

In the large $N_c$ limit, all hyperon decays involving the same quark diagram $Q\to Q'$ are described by a single weak form factor $\eta_{QQ'}(w)$. No assumption on the mass of $Q$ or $Q'$ is necessary, making our results applicable to both $b\to c$ and $c\to s$ transitions. This same form factor describes both $\Lambda_Q\to\Lambda_{Q'}$ and $\Sigma^{(*)}_Q\to\Sigma^{(*)}_{Q'}$ transitions. The (non-)commutativity between the heavy quark and the large $N_c$ limits is briefly discussed under the definite example of $\Lambda_b\to\Lambda_c$ decay.