Helicity amplitude and branching fraction measurement of $χ_{cJ} \rightarrow Λ\barΛ $

TL;DR

This work conducts a partial wave analysis of ψ(3686) → γχ_{cJ} → γΛΛ̄ (J=0,1,2) using $ (2712.4 \pm 14.3) \times 10^{6} $ ψ(3686) events collected by BESIII to extract helicity amplitudes, angular distributions, and branching fractions for χ_{cJ} → ΛΛ̄. The analysis employs a helicity-based amplitude framework within a covariant, gauge-consistent approach, incorporating mass resolution and detector effects via TF-PWA. The study reports the first measurement of the χ_{c2} helicity-amplitude ratio $R_{χ_{c2}}=0.575\pm0.048\pm0.018$ with a phase $ΔΦ_{χ_{c2}}=0.37\pm0.15\pm0.05$ rad, along with angular parameters $α_{χ_{c2}}= -0.211\pm0.100\pm0.050$ and $β_{χ_{c2}}= -0.039\pm0.089\pm0.033$, and a χ_{c0} width of $Γ_{χ_{c0}}=12.31\pm0.26\pm0.12$ MeV. The branching fractions are measured as $\mathcal{B}(χ_{c0}\toΛΛ̄)=(3.662\pm0.048\pm0.111)\times10^{-4}$, $\mathcal{B}(χ_{c1}\toΛΛ̄)=(1.182\pm0.026\pm0.042)\times10^{-4}$, and $\mathcal{B}(χ_{c2}\toΛΛ̄)=(1.704\pm0.035\pm0.057)\times10^{-4}$, significantly improving precision over PDG values. These results test helicity selection rules and illuminate nonperturbative QCD dynamics in charmonium decays, with implications for baryon production mechanisms in radiative charmonium transitions.

Abstract

Utilizing $2712.4 \pm 14.3$ million $ψ(3686)$ events accumulated by the BESIII experiment, we perform a partial wave analysis of $ψ(3686)\rightarrowγχ_{cJ}\rightarrowγΛ\barΛ$ decay ($J=0,1,2$). The ratio of the helicity amplitudes with same (++) and opposite (+-) helicity for $χ_{c2}\rightarrowΛ\barΛ$ decay is determined for the first time to be $R_{χ_{c2}}=0.575 \pm 0.048 \pm 0.018 $, with a relative phase angle $ΔΦ_{χ_{c2}} = 0.37 \pm 0.15 \pm 0.05 $~rad. The parameters of the angular distribution of $χ_{c2}$ are determined to be $α_{χ_{c2}} = -0.211 \pm 0.100 \pm 0.050 $ and $β_{χ_{c2}} = -0.039 \pm 0.089 \pm 0.033 $, based on the distribution $dN / d\cosθ= 1 + α_{χ_{c2}} \cos^2θ+ β_{χ_{c2}} \cos^4θ$. The width of $χ_{c0}$ is determined to be $12.31 \pm 0.26 \pm 0.12 $~MeV. Additionally, the branching fractions for $χ_{cJ} \rightarrow Λ\barΛ$ are measured to be $(3.662 \pm 0.048 \pm 0.111) \times 10^{-4}$, $(1.182 \pm 0.026 \pm 0.042) \times 10^{-4}$, and $(1.704 \pm 0.035 \pm 0.057) \times 10^{-4}$ for $χ_{c0}$, $χ_{c1}$ and $χ_{c2}$, respectively, where the first uncertainty is statistical and the second systematic.

Figures (4)

• Figure 1: Invariant mass distribution of $\Lambda$ and $\bar{\Lambda}$ reconstructed by $p\pi^-$ and $\bar{p}\pi^+$ respectively. The two vertical dashed lines represent the mass window [1.108,1.123] GeV/$c^2$.
• Figure 2: Invariant mass distributions of $\Lambda\bar{\Lambda}$, $\gamma\Lambda$ and $\gamma\bar{\Lambda}$ for the selected events. The signal MC is normalized to the data by area normalization, excluding the background component. The three peaks in the left panel correspond to the $\chi_{c0}$, $\chi_{c1}$, and $\chi_{c2}$ signals, respectively. The dip around 1.2 GeV/$c^2$ in the middle and right panels is caused by the $\Sigma^0$ and $\bar{\Sigma}^0$ veto requirements.
• Figure 3: Definition of helicity angles for each sequential decays in $e^+e^-\to\psi(3686)\to\gamma\chi_{cJ},~\chi_{cJ}\to\Lambda\bar{\Lambda},~\Lambda\to p\pi^-$ and $\bar{\Lambda}\to\bar{p}\pi^+$.
• Figure 4: Nominal fit results. (a), (b), (c) are the invariant mass distribution for $\Lambda\bar{\Lambda}$, $\gamma\Lambda$ and $\gamma\bar{\Lambda}$, respectively. (d), (e) are the helicity angle distribution of $\chi_{cJ}$ ($\phi_{0}$,cos$\theta_{0}$), (f), (g) are the helicity angle distribution for $\Lambda$ ($\phi_{1}$,cos$\theta_{1}$), and (h), (i) are the helicity angle distribution for the proton ($\phi_{3}$,cos$\theta_{3}$). The helicity angle distribution for anti-proton are similar. In all figures, the black dots with error bars are data, the brown histograms are the total fit results, and the color histograms are the line shapes for each of the components, defined in the legend in figure (a). The gray histograms are the background contributions. Figure (a) uses 100 bins, while the other figures use 60 bins. The $p$-value shown in each figure is calculated assuming a $\chi^2$ distribution with $n_{\rm bin}$ degrees of freedom, where $n_{\rm bin}$ is the number of bins in each projection. This value serves only to assess the consistency between data and model in each projection, and is not used in the parameter estimation.