# Heavy quark spin multiplet structure of $P_c$-like pentaquark as P-wave hadronic molecular state

## TL;DR

This paper investigates the spin multiplet structure of P-wave pentaquarks as hadronic molecules, classifies HQS multiplets using a light-cloud spin basis, and predicts bound states with specific degeneracy patterns for future experimental verification.

## Contribution

It introduces a light-cloud spin basis to classify heavy quark spin multiplets and constructs a potential model to identify bound states in P-wave pentaquark systems.

## Key findings

- HQS multiplets classified into singlets, doublets, triplets
- Bound states exhibit degeneracy patterns in the heavy quark limit
- Finite mass effects lift degeneracy among multiplets

## Abstract

We study the heavy quark spin (HQS) multiplet structure of P-wave $Q\bar{Q}qqq$-type pentaquarks treated as molecules of a heavy meson and a heavy baryon. We define the light-cloud spin (LCS) basis decomposing the meson-baryon spin wavefunction into the LCS and HQS parts. Introducing the LCS basis, we find HQS multiplets classified by the LCS; five HQS singlets, two HQS doublets, and three HQS triplets. We construct the one-pion exchange potential respecting the heavy quark spin and chiral symmetries to demonstrate which HQS multiplets are realized as a bound state. By solving the coupled channel Schr\"odinger equations, we study the heavy meson-baryon systems with $I=1/2$ and $J^P=(1/2^+, 3/2^+, 5/2^+, 7/2^+)$. The bound states which have same LCS structure are degenerate at the heavy quark limit, and the degeneracy is resolved for finite mass. This HQS multiplet structure will be measured in the future experiments.