Search for the electromagnetic Dalitz decays $χ_{cJ}\to e^{+}e^{-}φ$

TL;DR

This study searches for the electromagnetic Dalitz decays $\chi_{cJ}\to e^+e^-\phi$ (J=0,1,2) using a large $\psi(3686)$ data sample collected at BESIII via radiative $\psi(3686)\to \gamma\chi_{cJ}$. The analysis employs a detailed event selection with a 4C kinematic fit, φ reconstruction from $K^+K^-$, sideband techniques for background estimation, and signal MC driven by a $q^2$-dependent amplitude and a monopole transition form factor $|F(q^2)|=1/(1-q^2/\Lambda^2)$. No significant signals are observed, and upper limits at 90% C.L. are set: $\mathcal{B}(\chi_{c0}\to e^+e^-\phi)<2.4\times10^{-7}$, $\mathcal{B}(\chi_{c1}\to e^+e^-\phi)<6.7\times10^{-7}$, and $\mathcal{B}(\chi_{c2}\to e^+e^-\phi)<4.1\times10^{-7}$, representing the first constraints on EM Dalitz transitions for these P-wave charmonium states. The work constrains the time-like transition form factor and offers a valuable benchmark for future high-luminosity facilities to probe non-perturbative QCD in charmonium.

Abstract

Using a data sample of $(2.712 \pm 0.014)\times10^{9}$ $ψ(3686)$ events collected at $\sqrt{s}=3.686$ GeV by the BESIII detector, we search for the rare electromagnetic Dalitz decays $χ_{cJ}\to e^+e^-φ~(J=0,\,1,\,2)$ via the radiative transitions $ψ(3686)\toγχ_{cJ}$. No statistically significant $χ_{cJ}\to e^+e^-φ$ signals are observed. The upper limits on the branching fractions of $χ_{cJ}\to e^+e^-φ~(J=0,\,1,\,2)$, excluding the $φ$ resonance to $e^+e^-$ final states, are set to be $2.4\times10^{-7},~6.7\times10^{-7}$ and $4.1\times10^{-7}$ at 90\% confidence level, respectively. This is the first search for the electromagnetic Dalitz transition of P-wave charmonium $χ_{cJ}$ states to a light vector meson.

Figures (5)

• Figure 1: Feynman diagrams of (a) $\chi_{cJ}\to\gamma\phi$ and (b) $\chi_{cJ}\to e^+e^-\phi$ decays.
• Figure 2: The distributions of $M_{e^+e^-K^+K^-}$ versus $M_{K^+K^-}$ of the accepted candidate events for (a) $\chi_{c0}$, (b) $\chi_{c1}$, and (c) $\chi_{c2}$ decays into $e^+e^-\phi$ in data, where the red/green/blue boxes are the signal regions and the magenta boxes are the sideband regions. The sideband regions of non-$\phi$ components are indicated as (1), those of non-$\chi_{cJ}$ components as (2), and of neither $\phi$ nor $\chi_{cJ}$ components as (3).
• Figure 3: The distribution of $M_{e^+e^-K^+K^-}$. The areas within the red, green, and blue dashed lines represent the $\chi_{c0}$, $\chi_{c1}$, and $\chi_{c2}$ decays into $e^+e^-\phi$, respectively.
• Figure 4: The distribution of $M_{e^+e^-}$.
• Figure 5: The profile likelihoods of the branching fractions of (a) $\chi_{c0}$, (b) $\chi_{c1}$, and (c) $\chi_{c2}$ decays into $e^+e^-\phi$. The red arrows show the upper limits on individual branching fractions at 90% C.L..