Puzzle of the $\Lambda_c$ spectrum

TL;DR

This paper investigates the spectrum of $\Lambda_c$ baryons, proposing possible quantum number assignments and suggesting that the observed $\Lambda_c(2880)^+$ peak may include a missing $J^P=3/2^+$ state, resolving a theoretical puzzle.

Contribution

The study applies a light diquark model to assign quantum numbers to $\Lambda_c$ states, identifying a potential missing $3/2^+$ state and clarifying the nature of observed resonances.

Findings

Proposes $\Lambda_c(2880)^+$ includes a missing $3/2^+$ state.

Assigns $\Lambda_c(2765)^+$ as $2S(1/2^+)$.

Identifies $\Lambda_c(2940)^+$ as $2P(1/2^-)$.

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.