# Analysis of the axialvector $B_c$-like tetraquark states with the QCD sum rules

## TL;DR

This paper uses QCD sum rules with an energy scale formula to predict masses of axialvector $B_c$-like tetraquark states, providing insights into their structure and distinguishing features from conventional mesons.

## Contribution

It introduces a method to select ideal energy scales in QCD sum rules for doubly heavy tetraquark states, improving mass predictions and understanding of their structure.

## Key findings

- Predicted masses of $Z_{\bar{b}c}(1^{+-})$ and $Z_{\bar{b}c}(1^{++})$ are around 7.30 GeV.
- Mass predictions lie between 2P and 3P $B_c$ states, consistent with diquark-antidiquark models.
- The approach clarifies the nature of $B_c$-like tetraquark states in QCD.

## Abstract

In this article, we construct the diquark-antidiquark type current operators to study the axialvector $B_c$-like tetraquark states with the QCD sum rules. In calculations, we take the energy scale formula as a powerful constraint to choose the ideal energy scales of the QCD spectral densities and add detailed discussions to illustrate why we take the energy scale formula to improve the QCD sum rules for the doubly heavy tetraquark states. The predicted masses $M_{Z_{\bar{b}c}(1^{+-})}=7.30\pm0.08\,\rm{GeV}$ and $M_{Z_{\bar{b}c}(1^{++})}=7.31\pm0.08\,\rm{GeV}$ lie between the conventional $2\rm{P}$ and $3\rm{P}$ $B_c$ states with $J^P=1^+$ from the potential quark models, which is a typical feature of the diquark-antidiquark type $B_c$-like tetraquark states.