# The mass spectra and wave functions for the doubly heavy baryons with $J^P=1^+$ heavy diquark core

## TL;DR

This paper calculates the mass spectra and wave functions of doubly heavy baryons with a $J^P=1^+$ diquark core using relativistic Bethe-Salpeter equations, providing new insights into their structure and properties.

## Contribution

It introduces a novel approach to modeling doubly heavy baryons by explicitly considering the diquark core and its structure effects within the Bethe-Salpeter framework.

## Key findings

- Mass spectra for $(ccq)$, $(bcq)$, $(bbq)$ baryons are obtained.
- Wave functions for low-lying states are computed.
- Results are compared with other theoretical approaches.

## Abstract

The mass spectra and wave functions for the doubly heavy baryons are computed under the picture that the two heavy quarks inside a doubly heavy baryon, such as two $c$-quarks in $\Xi_{cc}$, combine into a heavy `diquark core' in color anti-triplet firstly, then the diquark core turns into a color-less doubly heavy baryon via combining the light $q$-quark inside the baryon. Namely both of the combinations, the two heavy quarks inside the baryon into a diquark core in color anti-triplet and the heavy diquark core with the light quark into the baryon, are depicted by relativistic Bethe-Salpeter equations (BSEs) with an accordingly QCD inspired kernel respectively, although in the paper only the heavy diquark cores with the quantum numbers $J^P=1^+$ are considered. Since the `second combination' is of the heavy diquark core and the light quark, so the structure effect of the diquark core to the relevant kernel of the BSE is specially considered in terms of the diquark-core wave functions. The mass spectra and wave functions for the `low-laying' doubly heavy baryons in the flavors $(ccq)$, $(bcq)$ and $(bbq)$ and in the quantum numbers $J^P=\frac{1}{2}^+$, $J^P=\frac{3}{2}^+$, achieved by solving the equations under the so-called instantaneous approximation, are presented properly and some comparisons with the others' results under different approaches in the literature are made.