The ground states and the first radially excited states of D-wave vector $\rho$ and $\varphi$ 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 $\varphi$ 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 $2^3{D}_1$ $\varphi$ meson are consistent well with the experimental data of $\rho$($1700$) and $\varphi$($2170$). 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 $\varphi$ meson and $\rho$ meson families.