AUTHOR=Dong Rui-Rui , Su Niu , Chen Hua-Xing , Cui Er-Liang 

TITLE=QCD sum rule study on the fully strange tetraquark states of JPC = 2++

JOURNAL=Frontiers in Physics

VOLUME=11

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1184103

DOI=10.3389/fphy.2023.1184103

ISSN=2296-424X

ABSTRACT=<p>We apply the QCD sum rule method to systematically study the fully strange tetraquark states with the quantum number <italic>J</italic><sup><italic>PC</italic></sup> = 2<sup>++</sup>. We construct both the diquark–antidiquark and mesonic–mesonic currents and calculate both their diagonal and off-diagonal correlation functions. Based on the obtained results, we further construct three mixing currents that are nearly non-correlated. We use one mixing current to extract the mass of the lowest-lying state to be <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>2.0</mml:mn><mml:msubsup><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow><mml:mo>−</mml:mo><mml:mn>0.15</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>0.16</mml:mn></mml:mrow></mml:msubsup></mml:math></inline-formula> GeV, which can be used to explain <italic>f</italic><sub>2</sub>(2010) as a fully strange tetraquark state of <italic>J</italic><sup><italic>PC</italic></sup> = 2<sup>++</sup>. This state was observed by BESIII in the <italic>ϕϕ</italic> channel, and we propose to confirm it in the <italic>η</italic><sup>(</sup>′<sup>)</sup><italic>η</italic><sup>(</sup>′<sup>)</sup> channel.</p>