Masses of the tensor mesons with $J^{P}=2^{-}$

TL;DR

This paper calculates the masses of tensor mesons with quantum numbers $J^{P}=2^{-}$ using sum rule methods, providing predictions for various heavy and light meson systems.

Contribution

It introduces a comprehensive sum rule analysis for tensor mesons with $J^{P}=2^{-}$ across multiple quark configurations, extending previous studies.

Findings

Masses of $2^{--}$ tensor charmonium and bottomonium are approximately 3.97 GeV and 10.13 GeV.

Mass predictions for various $ar qq$, $ar qs$, $ar ss$, $ar qc$, $ar sc$, $ar qb$, $ar sb$, and $ar cb$ systems.

The analysis confirms the mass spectrum of tensor mesons with $J^{P}=2^{-}$ across different quark contents.

Abstract

We calculate the two-point correlation function using the interpolating current with $J^{PC}=2^{-}$. After performing the Borel sum rule analysis, the extracted masses of the $2^{--}$ tensor charmonium and bottomonium are $3.97\pm0.25$ GeV and $10.13\pm0.34$ GeV respectively. For comparison, we also perform the moment sum rule analysis for the charmonium and bottomonium systems. We extend the same analysis to study the $\bar qq, \bar qs, \bar ss, \bar qc, \bar sc, \bar qb, \bar sb$ and $\bar cb$ systems. Their masses are $1.78\pm 0.12, 1.85\pm 0.14, 2.00\pm 0.16, 2.86\pm 0.14, 3.01\pm 0.21, 5.66\pm0.33, 6.40\pm 0.25$, and $7.08\pm 0.34$ GeV respectively.