$\Lambda_c$ Semileptonic Decays in a Quark Model

Abstract

Hadronic form factors for semileptonic decay of the $\Lambda_c$ are calculated in a nonrelativistic quark model. The full quark model wave functions are employed to numerically calculate the form factors to all relevant orders in ($1/m_c$, $1/m_s$). The form factors obtained satisfy relationships expected from the heavy quark effective theory (HQET). The differential decay rates and branching fractions are calculated for transitions to the ground state and a number of excited states of $\Lambda$. The branching fraction of the semileptonic decay width to the total width of $\Lambda_c$ has been calculated and compared with other theoretical estimates and experimental results. The branching fractions for $\Lambda_c\to\Lambda^{*} l^{+}\nu_l\to\Sigma\pi l^{+}\nu_l$ and $\Lambda_c\to\Lambda^{*} l^{+}\nu_l\to N\bar{K} l^{+}\nu_l$ are also calculated. Apart from decays to the ground state $\Lambda$(1115), it is found that decays through the $\Lambda(1405)$ provide a significant portion of the branching fraction $\Lambda_c\to X_s l\nu_l$. A new estimate for $f=B(\Lambda_c^{+}\to\Lambda l^{+}\nu_l)/B(\Lambda_c^{+}\to X_s l^{+}\nu_l)$ is obtained.