${\Lambda }_c$ 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 ${\Lambda }_c\to {\Lambda }^{\ast }{l}^{+}{\nu }_l\to \Sigma \pi l^{+}{\nu }_l$ and ${\Lambda }_c\to {\Lambda }^{\ast }{l}^{+}{\nu }_l\to N\bar{K}{l}^{+}{\nu }_l$ 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.

Comments: 44 pages, 24 figures, submitted to Physical Review D