Understanding light scalar meson by color-magnetic wavefunction in QCD sum rule

TL;DR

This paper investigates light scalar mesons as tetraquark states using a color-magnetic wavefunction approach within QCD sum rules, leading to improved agreement with experimental data and insights into their structure.

Contribution

It introduces a dynamic method to determine interpolating currents from the color-magnetic wavefunction, enhancing the understanding of scalar mesons in QCD sum rules.

Findings

Better agreement with experimental masses of sigma(600) and kappa(800)

Larger pole contributions indicate more stable states

Consistent results with instanton effects included

Abstract

In this paper, we study the $0^{+}$ nonet mesons as tetraquark states with interpolating currents induced from the color-magnetic wavefunction. This wavefunction is the eigenfunction of effective color-magnetic Hamiltonian with the lowest eigenvalue, meaning that the state depicted by this wavefunction is the most stable one and is most probable to be observed in experiments. Our approach can be recognized as determining interpolating currents dynamically. We perform an OPE calculation up to dimension eight condensates and find that the best QCD sum rule is achived when the current induced from the color-magnetic wavefunction is a proper mixture of the tensor and pseudoscalar diquark-antidiquark bound states. Compared with previous results, to sigma(600) and kappa(800), our results appear better, due to larger pole contribution. The direct instanton contribution are also considered, which yields a consistent result with previous OPE results. Finally, we also discuss the eta' problem as a possible six-quark state.