Study of the reaction $e^{+}{e}^{-}\to \psi (2S){\pi }^{+}{\pi }^{-}$ via initial-state radiation at BaBar

We study the process $e^{+}{e}^{-}\to \psi (2S){\pi }^{+}{\pi }^{-}$ with initial-state-radiation events produced at the PEP-II asymmetric-energy collider. The data were recorded with the BABAR detector at center-of-mass energies at and near the $\mathrm{\Upsilon }(\mathrm{nS})$ ($n=2,3,4$) resonances and correspond to an integrated luminosity of $520{\mathrm{fb}}^{-1}$. We investigate the $\psi (2S){\pi }^{+}{\pi }^{-}$ mass distribution from 3.95 to $5.95\mathrm{GeV}/c^2$, and measure the center-of-mass energy dependence of the associated $e^{+}{e}^{-}\to \psi (2S){\pi }^{+}{\pi }^{-}$ cross section. The mass distribution exhibits evidence of two resonant structures. A fit to the $\psi (2S){\pi }^{+}{\pi }^{-}$ mass distribution corresponding to the decay mode $\psi (2S)\to J/\psi {\pi }^{+}{\pi }^{-}$ yields a mass value of $4340\pm 16(\text{stat})\pm 9(\text{syst})\mathrm{MeV}/c^2$ and a width of $94\pm 32(\text{stat})\pm 13(\text{syst})\mathrm{MeV}$ for the first resonance, and for the second a mass value of $4669\pm 21(\text{stat})\pm 3(\text{syst})\mathrm{MeV}/c^2$ and a width of $104\pm 48(\text{stat})\pm 10(\text{syst})\mathrm{MeV}$. In addition, we show the ${\pi }^{+}{\pi }^{-}$ mass distributions for these resonant regions.

Figure 1

(a) The $\psi (2S){\pi }^{+}{\pi }^{-}$ invariant mass distribution from the kinematic threshold to $5.95\mathrm{GeV}/c^2$ for $\psi (2S)\to J/\psi {\pi }^{+}{\pi }^{-}$; the points with error bars represent the data in the $\psi (2S)$ signal region, and the shaded histogram is the background estimated from the $\psi (2S)$ sideband regions. The solid curve shows the result of the fit described in the text. The dashed (dotted) curves indicate the individual resonant contributions for constructive (destructive) interference. (b) The corresponding distributions for $\psi (2S)\to l^{+}{l}^{-}$. (c) The combined $\psi (2S){\pi }^{+}{\pi }^{-}$ invariant mass distribution for $\psi (2S)\to J/\psi {\pi }^{+}{\pi }^{-}$ and $\psi (2S)\to l^{+}{l}^{-}$. The solid curve shows the result of the fit. The dashed curve represents the background, while the dotted curves indicate the individual resonant contributions. Only one solution is found in this case.

Figure 2

(a) The comparison between the observed $\psi (2S){\pi }^{+}{\pi }^{-}$ [$\psi (2S)\to J/\psi {\pi }^{+}{\pi }^{-}$] invariant mass spectrum from BABAR (dots) and that from Belle [6] (hatched histogram). (b) The combined BABAR and Belle $\psi (2S){\pi }^{+}{\pi }^{-}$ [$\psi (2S)\to J/\psi {\pi }^{+}{\pi }^{-}$] invariant mass spectrum.

Figure 3

The cross section for the reaction $e^{+}{e}^{-}\to \psi (2S){\pi }^{+}{\pi }^{-}$ as a function of c.m. energy obtained by using Eq. (3) (points with error bars); the curve shows the c.m. energy dependence which results from the fit to the data of Fig. 1.

Figure 4

The ${\pi }^{+}{\pi }^{-}$ invariant mass spectrum for the $\psi (2S)\to J/\psi {\pi }^{+}{\pi }^{-}$ channel in the $\psi (2S){\pi }^{+}{\pi }^{-}$ mass region (a) $4.0–4.5\mathrm{GeV}/c^2$, and (b) $4.5–4.9\mathrm{GeV}/c^2$. The histogram represents a MC distribution corresponding to the decay according to phase space of (a) one resonance with a mass of $4.360\mathrm{GeV}/c^2$ and width 70 MeV, and (b) one resonance with a mass of $4.660\mathrm{GeV}/c^2$ and width 50 MeV. Each histogram is normalized to the corresponding data sample.