$2^{++}$ Light Tensor Hybrid Meson from QCD Laplace Sum Rules

TL;DR

This paper calculates the mass and coupling of the light tensor hybrid meson using QCD Laplace Sum Rules, including NLO corrections and condensate contributions, suggesting certain mesons may have hybrid components.

Contribution

It provides the first NLO analysis of the tensor hybrid meson mass and coupling, incorporating condensate effects up to dimension-six in QCD Laplace Sum Rules.

Findings

Mass of tensor hybrid meson: 2038 ± 190 MeV

Small coupling constant: 10.5 ± 2.9 MeV

Tensor hybrid topological charge computed for the first time

Abstract

We present an analysis of the light tensor ($J^{PC}=2^{++}$) hybrid meson mass and coupling from QCD Laplace Sum Rules where the next-to-leading order (NLO) perturbative (PT) corrections and the contributions of the non-perturbative (NP) condensates up to dimension-six ($D=6$) are included. NLO leading-logarithms corrections due to the condensates which contribute in the chiral limit are considered. We obtain the mass $M_{2^+}= (2038\pm 190)$ MeV and a relatively small coupling $f_{2^+}=(10.5\pm 2.9)$ MeV normalized as $f_\pi=93$ MeV. Our results suggest that the $f_2(1950)$ or/and the $f'_2(2010)$ may have a sizeable $\bar qqg$ hybrid component. We also compute the tensor hybrid topological charge (value of the two-point function at zero momentum) and find (for the first time) at NLO: $\Pi_{qg}(0)=(2.41\pm 0.43) \times 10^{-4}{\rm GeV}^6$ which could be checked from some lattice QCD or/and low energy theorems (LET).