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

Abstract

We calculate the form factor $M(q^2)$ for the Dalitz decay $J/\psi \to {\gamma }^{\ast }(q^2){\eta }_{(N_f=1)}$ with ${\eta }_{(N_f)}$ being the SU($N_f$) flavor singlet pseudoscalar meson. The difference among the partial widths $\Gamma (J/\psi \to \gamma {\eta }_{(N_f)})$ 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 $M(q^2)=M(0)/(1-q^2/{\Lambda }^2)$. Combined with the known experimental results of the Dalitz decays $J/\psi \to P{e}^{+}{e}^{-}$, the pseudoscalar mass $m_P$ dependence of the pole parameter $\Lambda$ is approximated by $\Lambda (m_P^2)={\Lambda }_1(1-m_P^2/{\Lambda }_2^2)$ with ${\Lambda }_1=2.64(4)\mathrm{GeV}$ and ${\Lambda }_2=2.97(33)\mathrm{GeV}$. These results provide inputs for future theoretical and experimental studies on the Dalitz decays $J/\psi \to P{e}^{+}{e}^{-}$.

Comments: 9 pages, 5 figures