Vector tetraquark state candidates: $Y(4260/4220)$, $Y(4360/4320)$, $Y(4390)$ and $Y(4660/4630)$

TL;DR

This study constructs specific currents to analyze vector tetraquark states using QCD sum rules, supporting certain experimental states as tetraquarks and disfavoring others as pure tetraquark states.

Contribution

It introduces a method to determine the nature of Y states as vector tetraquarks using operator product expansion and QCD sum rules with specific interpolating currents.

Findings

Supports Y(4660/4630) as $c\bar{c}s\bar{s}$ tetraquark

Supports Y(4360/4320) as $c\bar{c}q\bar{q}$ tetraquark

Disfavors Y(4260/4220) and Y(4390) as pure tetraquarks

Abstract

In this article, we construct the $C \otimes \gamma_\mu C$ and $C\gamma_5 \otimes \gamma_5\gamma_\mu C$ type currents to interpolate the vector tetraquark states, then carry out the operator product expansion up to the vacuum condensates of dimension-10 in a consistent way, and obtain four QCD sum rules. In calculations, we use the formula $\mu=\sqrt{M^2_{Y}-(2{\mathbb{M}}_c)^2}$ to determine the optimal energy scales of the QCD spectral densities, moreover, we take the experimental values of the masses of the $Y(4260/4220)$, $Y(4360/4320)$, $Y(4390)$ and $Y(4660/4630)$ as input parameters and fit the pole residues to reproduce the correlation functions at the QCD side. The numerical results support assigning the $Y(4660/4630)$ to be the $C \otimes \gamma_\mu C$ type vector tetraquark state $c\bar{c}s\bar{s}$, assigning the $Y(4360/4320)$ to be $C\gamma_5 \otimes \gamma_5\gamma_\mu C$ type vector tetraquark state $c\bar{c}q\bar{q}$, and disfavor assigning the $Y(4260/4220)$ and $Y(4390)$ to be the pure vector tetraquark states.