Next-to-leading order (NLO) perturbative effects in QCD sum-rule analyses of light tetraquark systems: Acase study in the scalar-isoscalar channel

QCD sum-rule mass predictions for tetraquark states provide insights on the interpretations and internal structure of experimentally-observed exotic mesons. However, the overwhelming majority of tetraquark QCD sum-rule analyses have been performed at leading order (LO), which raises questions about the underlying theoretical uncertainties from higher-loop corrections. The impact of next-to-leading order (NLO) perturbative effects are systematically examined in scalar (J(PC) = 0(++)) isoscalar light-quark tetraquark systems where comprehensive LO sum-rule analyses have been performed and NLO perturbative corrections to the correlators have previously been calculated. Using the scalar-isoscalar state as a detailed case study to illustrate the differences between LO and NLO analyses, it is shown that NLO effects in individual Laplace sum-rules are numerically significant and have an important role in improving the reliability of the sum-rule analyses by widening the Borel window. However, ratios of sum-rules are found to be less sensitive to NLO effects with the additional advantage of cancelling the anomalous dimension that emerges from the NLO corrections. NLO mass predictions based on these sum-rule ratios are thus remarkably robust despite the slow perturbative convergence of the underlying correlator. The mass predictions 0.52 GeV< m(sigma) < 0.77 GeV for the lightest scalar-isoscalar sigma state are in good agreement with the four-quark interpretation of the f(0)(500), and the relative coupling strengths of the f(0)(980) and f(0)(500) to the tetraquark current agree with the pattern found in chiral Lagrangian analyses. Effects of the sigma resonance width are studied for different models, including resonance shapes inspired by chiral Lagrangians. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

The perturbative effects of leading order and next-to-leading order in tetraquark QCD sum-rule analyses are studied. The results show that the next-to-leading order effects have a significant impact on individual Laplace sum-rules and improve the reliability of the analyses by widening the Borel window. However, the ratios of sum-rules are less sensitive to the next-to-leading order effects and can cancel the anomalous dimension.