Experimental study of ${\chi }_b(2\mathrm{P})\to \pi \pi {\chi }_b(1\mathrm{P})$

We have searched for the di-pion transition ${\chi }_b(2\mathrm{P})\to \pi \pi {\chi }_b(1\mathrm{P})$ in the CLEO III sample of ${\rm Y}(3\mathrm{S})$ decays in the exclusive decay chain: ${\rm Y}(3\mathrm{S})\to \gamma {\chi }_b(2\mathrm{P})$, ${\chi }_b(2\mathrm{P})\to \pi \pi {\chi }_b(1\mathrm{P})$, ${\chi }_b(1\mathrm{P})\to \gamma {\rm Y}(1\mathrm{S})$, ${\rm Y}(1\mathrm{S})\to {\ell }^{+}{\ell }^{-}$. Our studies include both ${\pi }^{+}{\pi }^{-}$ and ${\pi }^0{\pi }^0$, each analyzed both in fully-reconstructed events and in events with one pion undetected. We show that the null hypothesis is not substantiated. Under reasonable assumptions, we find the partial decay width to be $\Gamma ({\chi }_b(2\mathrm{P})\to \pi \pi {\chi }_b(1\mathrm{P}))=(0.83\pm 0.22\pm 0.08\pm 0.19)\mathrm{keV}$, with the uncertainties being statistical, internal CLEO systematics, and common systematics from outside sources.

Figure 1

The decay process under study and the main background process, denoted in the text as “$\pi \pi \gamma \gamma$.” Note that these have the same ${\gamma }_2$, so that the energy of this photon is not a distinguishing observable.

Figure 2

Definition of the three regions in the charged two-pion analysis in the $E_1\mathrm{\text{vs}}{M}_{\mathrm{rec}}$ plane. The outline of the figure defines the sideband region, which does not include the two smaller regions, namely, the solid rectangle in which the $\pi \pi \gamma \gamma$ process dominates and the dashed rectangle in which the signal dominates. On the left (a) we show Monte Carlo events from both the $1\to 1$ and $2\to 2$ transitions, with the production ratio of 2.3:1, as described in the text. In the middle (b) we similarly show Monte Carlo events from the $\pi \pi \gamma \gamma$ process. The data for this two-pion analysis is shown on the right in (c).

Figure 3

Definition of the three regions in the charged one-pion analysis in the $E_1\mathrm{\text{vs}}{M}_{\mathrm{miss}}$ plane. In both cases the outline of the figure is the large sideband region. On the top (a) we show the smaller “signal” region and the “$\pi \pi \gamma \gamma$” region, and the Monte Carlo events from both the $1\to 1$ and $2\to 2$ transitions. On the bottom (b) we similarly show both of these regions and the Monte Carlo events from the “$\pi \pi \gamma \gamma$” process.

Figure 4

The data events falling into our three defined regions for the charged one-pion analysis, shaded according to their ${\chi }_{\gamma \gamma }^2$ value. The darkest boxes are for events with ${\chi }_{\gamma \gamma }^2$ values between 0 and 1 and the lightest for those with ${\chi }_{\gamma \gamma }^2$ values between 3 and 4. Most of the events in the small signal region (the smaller rectangle) show low values for ${\chi }_{\gamma \gamma }^2$, indicating excellent fits of the photon energy sum to that expected for signal events.