Estimating the mass of the hidden charm $1^+(1^{+})$ tetraquark state via QCD sum rules

TL;DR

This paper estimates the masses of hidden charm and bottom tetraquark states using QCD sum rules, supporting their identification with observed exotic resonances like Zc(3900) and Zb(10610).

Contribution

It provides the first detailed QCD sum rule calculation of the $1^+$ hidden charm tetraquark mass, including contributions up to dimension eight in the OPE.

Findings

Mass of hidden charm tetraquark: 3912 MeV with uncertainties.

Mass of hidden bottom tetraquark: 10561 MeV with uncertainties.

Results support tetraquark interpretation of Zc(3900) and Zb(10610).

Abstract

By using QCD sum rules, the mass of the hidden charm tetraquark $[cu][\bar{c}\bar{d}]$ state with $I^{G} (J^{P}) = 1^+ (1^{+})$ (HCTV) is estimated, which presumably will turn out to be the newly observed charmonium-like resonance $Z_c^+(3900)$. In the calculation, contributions up to dimension eight in the operator product expansion(OPE) are taken into account. We find $m_{1^+}^c = (3912^{+306}_{-153}) \, \text{MeV}$, which is consistent, within the errors, with the experimental observation of $Z_c^+(3900)$. Extending to the b-quark sector, $m_{1^+}^b = (10561^{+395}_{-163}) \,\text{MeV}$ is obtained. The calculational result strongly supports the tetraquark picture for the "exotic" states of $Z_c^+(3900)$ and $Z_b^+(10610)$.