NLO Effects in QCD Sum-Rule Analyses of $f_{0}(500)$ as a Tetraquark state

TL;DR

This study investigates the impact of next-to-leading order corrections on QCD sum-rule estimates of the lightest tetraquark state, the $f_{0}(500)$, revealing that NLO effects influence mass predictions and support a four-quark structure consistent with other theoretical models.

Contribution

It provides the first detailed analysis of NLO effects on the QCD sum-rule mass estimates for the $f_{0}(500)$ tetraquark, including multiple resonance and width effects.

Findings

Mass prediction range: 0.52 to 0.77 GeV.

NLO corrections have limited impact on sum-rule ratios.

Results agree with Chiral Lagrangian studies.

Abstract

QCD sum-rule studies have been useful to understand and get an insight on the structure of exotic states, such as tetraquark systems. Moreover, the majority of these studies are performed only at leading-order (LO) within the light tetraquarks systems picture, overlooking the effects of higher order corrections, thus motivating our analysis. Our study focused on the effects of next-to-leading order (NLO) contributions to the mass estimates of the lightest tetraquark state ($J^{PC} = 0^{++}$), the so-called $\sigma$ or $f_{0}(500)$, using ratios of QCD Laplace sum-rules. A variety of different models were used, which included multiple resonances and width effects, resulting in a final mass prediction of $0.52\,\text{GeV}< m_{\sigma}< 0.77\,\text{GeV}$. Even though the ratios of sum-rules demonstrated some insensitivity under superficially large NLO contributions, they added the beneficial feature of canceling the dependence on the anomalous dimension. Our findings were in good agreement with patterns found in Chiral Lagrangian studies regarding the four-quark structure of the $\sigma$ state, including the relative coupling strengths within the multiple resonance analysis.