Puzzle of the ${\Lambda }_c$ spectrum

Abstract

There is a puzzle in the ${\Lambda }_c^{+}$ family, i.e., one member with $J^P=3/2^{+}$ is missing in a $L=2$ multiplet which the heavy quark effective theory predicts, and $J^P$'s of ${\Lambda }_c(2765{)}^{+}$ and ${\Lambda }_c(2940{)}^{+}$ are unknown. Using a light diquark picture to calculate baryon masses, we study possible assignments of two ${\Lambda }_c$'s with unknown $J^P$ and the missing ${\Lambda }_c^{+}$ with $3/2^{+}$ for $L=2$, and we find the most probable possibility that the peak corresponding to ${\Lambda }_c(2880{)}^{+}$ actually includes a missing member with spin $3/2^{+}$ for $L=2$ and that quantum numbers of ${\Lambda }_c(2765{)}^{+}$ and ${\Lambda }_c(2940{)}^{+}$ are $2S(1/2^{+})$ and $2P(1/2^{-})$, respectively.

Comments: 3 pages, 3 tables