Light scalar quarkonia from Laplace sum rule at NLO

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 $\mathcal{R}$ 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 $D⩽6-8$, 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 $t_c⩽(1\sim 1.5)$ GeV${}^2$. Our results for the different assignments of the scalar mesons are compiled in Tables 1 to 3

Comments: Talk given at QCD24 International conference (8-12 July 2024, Montpellier - France)