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In this article, we firstly derive two QCD sum rules QCDSR I and QCDSR IIwhich are respectively used to extract observable quantities of the groundstates and the first radially excited states of D-wave vector $\rho$ and $\phi$mesons. In our calculations, we consider the contributions of vacuumcondensates up to dimension-7 in the operator product expansion. The predictedmasses for $1^{3}D_{1}$ $\rho$ meson and $2^{3}D_{1}$ $\phi$ meson areconsistent well with the experimental data of $\rho$($1700$) and$\phi$($2170$). Besides, our analysis indicates that it is reliable to assignthe 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 QCDSRII. These predictions are helpful not only to reveal the structure of the newlyobserved $Y$($2040$) state but also to establish $\phi$ meson and $\rho$ mesonfamilies.

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