Scrutinizing the Light Scalar Quarkonia from LSR at Higher Orders

TL;DR

This paper refines the determination of light scalar quarkonia masses and couplings using QCD Laplace Sum Rules with higher-order perturbative corrections, challenging previous mass estimates and clarifying scalar meson assignments.

Contribution

It introduces improved mass and coupling calculations for light scalar mesons incorporating higher-order PT corrections up to ${ m O}(ar{ ext{alpha}}_s^5)$ and establishes rigorous constraints on resonance and continuum contributions.

Findings

Higher-order PT corrections enhance analysis accuracy.

Scalar meson masses below 600 MeV are disfavored under the sum rule constraints.

Small SU3 breaking effects observed in mass splittings.

Abstract

We scrutinize, improve some determinations of the masses and couplings of light scalar quarkonia ($\bar qq$ and four-quark states) and present new results for the $\pi^+\pi^-,K^+K^-,\dots$ molecules using QCD Laplace Sum Rule (LSR) truncated at the $D=6$ dimension vacuum condensates. We pay a special attention on the higher order perturbative (PT) corrections up to the (estimated) ${\cal O}(\alpha_s^5)$ which improve the quality of the analysis. We request that the optimal results obey the rigorous constraint: {\it Resonance $\geq$ QCD continuum contributions ($R_{P/C}\geq 1$)} in the LSR which excludes a Breit-Wigner / on-shell (not to be confused with a complex pole) scalar meson mass around (500-600) MeV obtained for values [$t_c\leq (1\sim 1.5)$ GeV$^2$] of the QCD continuum threshold. Mass-splittings due to $SU3$ breakings are small. We discuss the different assignements of the observed scalar mesons below 2 GeV in the Conclusions where the $I=0$ states are compared with the scalar gluonia. The results are compiled in Table 3 to 6.