The Mass and Decay Properties of the $1^{-+}$ Light Hybrid Meson

TL;DR

This paper calculates the mass and decay properties of the $1^{-+}$ light hybrid meson using QCD sum rules, suggesting the $ ext{pi}_1(2015)$ is more likely a hybrid state and analyzing decay patterns.

Contribution

It provides a comprehensive QCD sum rule analysis including higher dimension condensates and decay pattern predictions for the $1^{-+}$ light hybrid meson.

Findings

Mass range 1.72--2.60 GeV disfavors $ ext{pi}_1(1400)$ and $ ext{pi}_1(1600)$ as pure hybrids.

$ ext{pi}_1(2015)$ is more likely to have hybrid constituents.

Large partial decay width for $b_1 ext{pi}$ mode, small for $ ho ext{pi}$ mode.

Abstract

We calculate the complete form of the dimension-8 condensate contributions in the two-point correlator of the ($1^{-+}$,$0^{++}$) light hybrid current considering the operator mixing under renormalization. We find the inclusion these higher power corrections as well as the update of $\langle g^3G^3\rangle$ increase the QCD sum rule mass prediction for the $1^{-+}$ light hybrid. The obtained conservative mass range 1.72--2.60 GeV does not favor the $\pi_1(1400)$ and the $\pi_1(1600)$ to be pure hybrid states and suggests the $\pi_1(2015)$ observed by E852 is more likely to have much of a hybrid constituent. We also study the $b_1\pi$ and $\rho\pi$ decay patterns of the $1^{-+}$ light hybrid with light-cone QCD sum rules. We obtain a relatively large partial decay width of the $b_1\pi$ mode, which is consistent with the predictions from the flux tube models and lattice QCD. More interestingly, using the tensor interpolating current we find the partial decay width of the $\rho\pi$ mode is small due to the absence of the leading twist contribution in the light-cone expansion of the correlation function.