Light scalar quarkonia from Laplace sum rule at NLO

TL;DR

This paper uses advanced QCD Laplace sum rules with higher-order corrections to analyze light scalar quarkonia, providing insights into their masses and structure, and refining previous estimates with improved theoretical constraints.

Contribution

It presents a comprehensive NLO analysis of light scalar quarkonia using Laplace sum rules, including higher order perturbative corrections and stability criteria, to improve mass and structure predictions.

Findings

Scalar meson masses around 500-600 MeV are excluded.

QCD continuum threshold $t_c$ influences resonance mass estimates.

Higher order corrections refine scalar quarkonia spectral function analysis.

Abstract

We review our results on light scalar quarkonia ($\bar{q}q$ and four-quark states) from (inverse) QCD Laplace sum rules (LSR) and their ratios ${\cal R}$ within stability criteria and including higher order perturbative (PT) corrections up to the (estimated) ${\mathcal O}(\alpha_{s}^{5})$. As the Operator Product Expansion (OPE) usually converges for $D\leqslant 6-8$, we evaluated the QCD spectral functions at Lowest Order (LO) of PT QCD and up to the $D=6$ dimension vaccum condensates. We request that the optimal results obey the constraint: Pole (Resonance) contribution to the spectral integral is larger than the QCD continuum one which excludes an on-shell mass around $(500-600)$MeV obtained for values of the QCD continuum threshold $t_c\leqslant(1\sim 1.5)$ GeV$^2$. Our results for the different assignments of the scalar mesons are compiled in Tables 1 to 3