The ground states and the first radially excited states of D-wave vector $\rho$ and $\phi$ mesons

TL;DR

This paper uses QCD sum rules to predict the masses and decay constants of D-wave vector $ ho$ and $phi$ mesons, including ground and first radially excited states, aligning well with experimental data and clarifying the structure of the $Y(2040)$ state.

Contribution

It introduces two specific QCD sum rules for analyzing D-wave vector mesons and provides mass and decay constant predictions consistent with experimental observations.

Findings

Predicted masses match experimental data for $ ho(1700)$ and $phi(2170)$.

Supports assigning $Y(2040)$ as the $2^{3}D_{1}$ $ ho$ meson.

Provides decay constants for these mesons.

Abstract

In this article, we firstly derive two QCD sum rules QCDSR I and QCDSR II which are respectively used to extract observable quantities of the ground states and the first radially excited states of D-wave vector $\rho$ and $\phi$ mesons. In our calculations, we consider the contributions of vacuum condensates up to dimension-7 in the operator product expansion. The predicted masses for $1^{3}D_{1}$ $\rho$ meson and $2^{3}D_{1}$ $\phi$ meson are consistent well with the experimental data of $\rho$($1700$) and $\phi$($2170$). Besides, our analysis indicates that it is reliable to assign the recent reported $Y$($2040$) state as the $2^{3}D_{1}$ $\rho$ meson. Finally, we obtain the decay constants of these states with QCDSR I and QCDSR II. These predictions are helpful not only to reveal the structure of the newly observed $Y$($2040$) state but also to establish $\phi$ meson and $\rho$ meson families.