Branching fraction measurements of ${\chi }_{c0}$ and ${\chi }_{c2}$ to ${\pi }^0{\pi }^0$ and $\eta \eta$

Using a sample of $1.06\times {10}^8$ ${\psi }^{\prime }$ decays collected by the BESIII detector, ${\chi }_{c0}$ and ${\chi }_{c2}$ decays into ${\pi }^0{\pi }^0$ and $\eta \eta$ are studied. The branching fraction results are $\mathrm{Br}({\chi }_{c0}\to {\pi }^0{\pi }^0)=(3.23\pm 0.03\pm 0.23\pm 0.14)\times {10}^{-3}$, $\mathrm{Br}({\chi }_{c2}\to {\pi }^0{\pi }^0)=(8.8\pm 0.2\pm 0.6\pm 0.4)\times {10}^{-4}$, $\mathrm{Br}({\chi }_{c0}\to \eta \eta )=(3.44\pm 0.10\pm 0.24\pm 0.2)\times {10}^{-3}$, and $\mathrm{Br}({\chi }_{c2}\to \eta \eta )=(6.5\pm 0.4\pm 0.5\pm 0.3)\times {10}^{-4}$, where the uncertainties are statistical, systematic due to this measurement, and systematic due to the branching fractions of ${\psi }^{\prime }\to \gamma {\chi }_{cJ}$. The results provide information on the decay mechanism of ${\chi }_c$ states into pseudoscalars.

Figure 1

Comparisons between data and Monte Carlo simulation of ${\psi }^{\prime }\to \gamma {\chi }_{cJ}$, ${\chi }_{cJ}\to {\pi }^0{\pi }^0$ for selection criteria used. (a) Photon multiplicity distribution. (b) The $\gamma \gamma$ invariant mass distribution for ${\pi }^0$ candidates. (c) The distribution of $p_{t\gamma }^2$. (d) The ${\chi }_{{\pi }^0{\pi }^0}$ distribution. Dots with error bars are data in the ${\chi }_{c0}$ region. The histogram is the Monte Carlo simulation for ${\psi }^{\prime }\to \gamma {\chi }_{c0}$, ${\chi }_{c0}\to {\pi }^0{\pi }^0$ plus the normalized background estimated from inclusive ${\psi }^{\prime }$ Monte Carlo samples.

Figure 2

Comparisons between data and Monte Carlo simulation for ${\psi }^{\prime }\to \gamma {\chi }_{cJ}$, ${\chi }_{cJ}\to \eta \eta$ for the selection criteria used. (a) Photon multiplicity distribution. (b) The $\gamma \gamma$ invariant mass distribution for $\eta$ candidates. (c) The distribution of $p_{t\gamma }^2$. (d) The ${\chi }_{\eta \eta }$ distribution. Dots with error bars are data in the ${\chi }_{c0}$ region. The histogram is the Monte Carlo simulation for ${\psi }^{\prime }\to \gamma {\chi }_{c0}$, ${\chi }_{c0}\to \eta \eta$ plus the normalized background estimated from inclusive ${\psi }^{\prime }$ Monte Carlo samples.

Figure 3

Radiative photon energy distributions of (a) selected ${\chi }_c\to {\pi }^0{\pi }^0$ events, and (b) selected ${\chi }_c\to \eta \eta$ events. Dots with error bars are data. The open histogram is the normalized background estimated from the inclusive ${\psi }^{\prime }$ Monte Carlo sample and from the continuum. The shaded histogram is the normalized contribution from the continuum.

Figure 4

(a) The distribution of the number of charged tracks for events satisfying selection criteria. (b) The distribution of the total energy in the EMC divided by the center of mass energy, $E_{\mathrm{EMC}}/E_{\mathrm{cm}}$, for events satisfying selection criteria. All requirements are applied to events with one to three charged tracks except the EMC requirements. Dots are data, the light shaded histogram is the sum of normalized continuum and ${\psi }^{\prime }\to \mathrm{\text{hadrons}}$ simulated events, and the dark shaded histogram is from continuum data.

Figure 5

The radiative photon energy spectrum of selected ${\chi }_c\to {\pi }^0{\pi }^0$ events. Dots with error bars are data. The solid curve is the result of a fit described in the text. The dotted curves are the ${\chi }_{cJ}$ signals. The dashed curve is the background polynomial.

Figure 6

The radiative photon energy spectrum of selected ${\chi }_c\to \eta \eta$ events. Dots with error bars are data. The solid curve is the result of a fit described in the text. The dotted curves are the ${\chi }_{cJ}$ signals. The dashed curve is the background polynomial.