Form factor for Dalitz decays from $J\mathrm{/}\psi$ to light pseudoscalars

We calculate the form factor $M(q^2)$ for the Dalitz decay $J\mathrm{/}\psi \to {\gamma }^{\ast }(q^2){\eta }_{(N_f=1)}$ with ${\eta }_{(N_f)}$ being the SU($N_f$) flavor singlet pseudoscalar meson. The difference among the partial widths $\mathrm{\Gamma }(J\mathrm{/}\psi \to \gamma {\eta }_{(N_f)})$ at different $N_f$ can be attributed in part to the ${\mathbf{U}}_A(1)$ anomaly that induces a $N_f$ scaling. $M(q^2)$'s in $N_f=1,2$ are both well described by the single pole model $M(q^2)=M(0)\mathrm{/}(1-q^2\mathrm{/}{\mathrm{\Lambda }}^2)$. Combined with the known experimental results of the Dalitz decays $J\mathrm{/}\psi \to P{e}^{+}{e}^{-}$, the pseudoscalar mass $m_P$ dependence of the pole parameter $\mathrm{\Lambda }$ is approximated by $\mathrm{\Lambda }(m_P^2)={\mathrm{\Lambda }}_1(1-m_P^2\mathrm{/}{\mathrm{\Lambda }}_2^2)$ with ${\mathrm{\Lambda }}_1=2.64(4)\mathrm{G}\mathrm{e}\mathrm{V}$ and ${\mathrm{\Lambda }}_2=2.97(33)\mathrm{G}\mathrm{e}\mathrm{V}$. These results provide inputs for future theoretical and experimental studies on the Dalitz decays $J\mathrm{/}\psi \to P{e}^{+}{e}^{-}$.