# Analyzing doubly heavy tetra- and penta-quark states by variational method

## TL;DR

This paper uses a variational method within a non-relativistic quark model to analyze the spectra of doubly-heavy pentaquarks and tetraquarks, providing possible assignments for recently observed LHCb pentaquarks and proposing experimental detection channels.

## Contribution

It introduces a model-independent variational approach to classify doubly-heavy pentaquarks and tetraquarks, offering new insights into their structure and decay properties.

## Key findings

- $P_c(4312)^+$ may be the ground state with $J^P=1/2^-$ or $3/2^-$
- $P_c(4440)^+$ and $P_c(4457)^+$ are likely excited states with $J^P=1/2^-$
- Several channels for experimental observation are proposed.

## Abstract

Motivated by the very recent observations of hidden charm pentaquarks $P_c(4312)^+$, $P_c(4440)^+$ and $P_c(4457)^+$ of the LHCb Collaboration, we systematically study the spectra of the doubly-heavy (with or without charm/bottom numbers) pentaquarks and tetraquarks in non-relativistic constituent quark model. The model independent variational method is employed to solve the Schr\"odinger equation, where the test functions adopted are symmetric for the light quarks. In our study, the $P_c(4312)^+$ may be assigned as the ground state with spin-parity $\frac{1}{2}^-$ or $\frac{3}{2}^-$, while the $P_c(4440)^+$ and $P_c(4457)^+$ may be assigned as the excited states with $\frac{1}{2}^-$, which might all belong to the sextet with $s_{c\bar{c}}=1$ and $s_\ell=\frac{3}{2}$. It is notable that our working framework is quite similar to that of Hydrogen molecule, but with different potential structure. We also classify these pentaquarks and tetraquarks in light of the heavy quark symmetry and their decay properties are analyzed. Several promising channels for the observation of doubly-heavy pentaquarks and doubly-heavy tetraquarks in experiment are proposed.