Study of $\gamma \gamma \to \gamma \psi (2S)$ at Belle

Using $980{\mathrm{fb}}^{-1}$ of data at and around the $\mathrm{\Upsilon }(nS)$ ($n=1$, 2, 3, 4, 5) resonances collected with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider, the two-photon process $\gamma \gamma \to \gamma \psi (2S)$ is studied from the threshold to 4.2 GeV for the first time. Two structures are seen in the invariant mass distribution of $\gamma \psi (2S)$: one at $M_{R_1}=3922.4\pm 6.5\pm 2.0\mathrm{MeV}/c^2$ with a width of ${\mathrm{\Gamma }}_{R_1}=22\pm 17\pm 4\mathrm{MeV}$, and another at $M_{R_2}=4014.3\pm 4.0\pm 1.5\mathrm{MeV}/c^2$ with a width of ${\mathrm{\Gamma }}_{R_2}=4\pm 11\pm 6\mathrm{MeV}$; the signals are parametrized with the incoherent sum of two Breit-Wigner functions. The first structure is consistent with the $X(3915)$ or the ${\chi }_{c2}(3930)$, and the local statistical significance is determined to be $3.1\sigma$ with the systematic uncertainties included. The second matches none of the known charmonium or charmoniumlike states, and its global significance is determined to be $2.8\sigma$ including the look-elsewhere effect. The production rates are ${\mathrm{\Gamma }}_{\gamma \gamma }\mathcal{B}(R_1\to \gamma \psi (2S))=9.8\pm 3.6\pm 1.3\mathrm{eV}$ assuming $(J^{PC},|\lambda |)=(0^{++},0)$ or $2.0\pm 0.7\pm 0.2\mathrm{eV}$ with $(2^{++},2)$ for the first structure and ${\mathrm{\Gamma }}_{\gamma \gamma }\mathcal{B}(R_2\to \gamma \psi (2S))=6.2\pm 2.2\pm 0.8\mathrm{eV}$ with $(0^{++},0)$ or $1.2\pm 0.4\pm 0.2\mathrm{eV}$ with $(2^{++},2)$ for the second. Here, the first errors are statistical and the second systematic, and $\lambda$ is the helicity.

Figure 1

Invariant mass distributions of (a) ${\ell }^{+}{\ell }^{-}(l=e,\mu )$ for the $J/\psi$ signal and (b) ${\pi }^{+}{\pi }^{-}J/\psi$ for the $\psi (2S)$ signal in data. The curves show the best fit results. The red solid arrows show the signal regions and the green dashed arrows show the sideband regions.

Figure 2

The distributions of recoil mass square of $\gamma \psi (2S)$. The dots with error bars are data, the black blank histogram is the background estimated from the $\psi (2S)$ mass sidebands, the blue histogram is the ISR MC simulation and the green histogram is the signal MC simulation. The normalization of ISR MC simulation is according to the region $M_{\mathrm{rec}}^2(\gamma \psi (2S))<10(\mathrm{GeV}/c^2{)}^2$, and the one of the signal MC simulation is arbitrary. The arrow shows the position of $M_{\mathrm{rec}}^2(\gamma \psi (2S))=10(\mathrm{GeV}/c^2{)}^2$.

Figure 3

The distributions of transverse momenta of $\psi (2S)$ (top row) and $\gamma \psi (2S)$ (bottom row) in the c.m. system of $e^{+}{e}^{-}$ collision. In the left panel, the dots with error bars are from the signal region, the shaded histograms are the backgrounds estimated from the $\psi (2S)$ mass sidebands, the black blank histograms are signal MC simulation with arbitrary normalizations, and the blue blank histograms are ISR MC simulation. The normalization of the ISR MC simulation in (a) is according to data with $P_t^{*}(\psi (2S))<0.1\mathrm{GeV}/c^2$, and the one in (c) is according to the size of the ISR MC simulation sample. The right panel shows the Punzi FOMs in dots and efficiencies in diamonds versus (b) $P_t^{*}(\psi (2S))$ and (d) $P_t^{*}(\gamma \psi (2S))$. The arrows show the selections applied.

Figure 4

The invariant mass distributions of $\gamma \psi (2S)$ from (a) $e^{+}{e}^{-}$ mode and (b) ${\mu }^{+}{\mu }^{-}$ mode. The dots with error bars are data, and the shaded histograms are backgrounds estimated from the $\psi (2S)$ mass sidebands. The blank histograms are ISR events simulated and scaled to the size of the Belle data sample.

Figure 5

(a) The efficiencies at different $M_{\gamma \psi (2S)}$ from MC simulation, and (b) the two-photon luminosity function $L_{\gamma \gamma }(\sqrt{s})$. In (a), the blue dots are the efficiencies for $J^{PC}=0^{++}$, and the black (red) dots are the efficiencies for $2^{++}$ with helicity $|\lambda |=0$ ($|\lambda |=2$). The curves show the best fits with polynomial functions.

Figure 6

The $\gamma \psi (2S)$ invariant mass distribution and the fit result. The points with error bars show the data while the shaded histogram is the normalized background from the $\psi (2S)$ mass sidebands. The solid blue curve shows the best fit results. The red signal curves from the convolutions of BW and CB functions show the contributions from the two structures. The green blank histogram shows the component of ISR events of $e^{+}{e}^{-}\to \psi (2S)\to {\pi }^{+}{\pi }^{-}J/\psi$. The pink dashed line shows the possible additional background, modeled by a second-order polynomial.