A Structure at 2175 MeV in $e^+ e^- \to \phi f_0(980)$ Observed via Initial-State Radiation

We study the initial-state-radiation processes $e^+ e^- \to K^+ K^-\pi^+\pi^-\gamma$ and $e^+ e^- \to K^+ K^-\pi^0\pi^0\gamma$ using an integrated luminosity of 232 fb$^{-1}$ collected at the $\Upsilon(4S)$ mass with the BaBar detector at SLAC. Even though these reactions are dominated by intermediate states with excited kaons, we are able to study for the first time the cross section for $e^+ e^- \to \phi(1020) f_{0}(980)$ as a function of center-of-mass energy. We observe a structure near threshold consistent with a $1^{--}$ resonance with mass $m = 2.175 \pm 0.010\pm 0.015 GeV/c^2$ and width $\Gamma = 58\pm 16\pm 20 MeV$. We observe no Y(4260) signal and set a limit of $BR_{Y\to\phi\pi^+\pi^-}\cdot\Gamma^{Y}_{ee}<0.4$ eV (90% confidence level), which excludes some models.

81 Yale University, New Haven, Connecticut 06511, USA (Dated: November 28, 2021) We study the initial-state-radiation processes e + e − → K + K − π + π − γ and e + e − → K + K − π 0 π 0 γ using an integrated luminosity of 232 fb −1 collected at the Υ (4S) mass with the BABAR detector at SLAC. Even though these reactions are dominated by intermediate states with excited kaons, we are able to study for the first time the cross section for e + e − → φ(1020)f0(980) as a function of center-of-mass energy. We observe a structure near threshold consistent with a 1 −− resonance with mass m = 2.175 ± 0.010 ± 0.015 GeV/c 2 and width Γ = 58 ± 16 ± 20 MeV. We observe no Y (4260) signal and set a limit of B Y →φπ + π − · Γ Y ee < 0.4 eV (90% confidence level), which excludes some models.
PACS numbers: 13.66.Bc,14.40.Cs,13.25.Gv,13.25.Jx,13.20.Jf The nature of the Y (4260) resonance, which BABAR recently discovered [1] through its production via initial state radiation (ISR) in e + e − annihilations and its decay into J/ψπ + π − , remains unclear. It is well above threshold for the D ( * ) D ( * ) decays expected for a wide charmonium state, but no peak is observed in the total cross section e + e − → hadrons in this mass region. Some models [2] predict a large branching fraction for Y (4260) into φππ. Moreover, the rich spectroscopy of the J/ψππ final state motivates a thorough investigation of the analogous φππ state.
In this paper we update our previous analysis with ISR of e + e − → K + K − π + π − [3]. We include more data and relax the selection criteria, resulting in a fivefold increase in the number of selected events. We obtain an improved e + e − → K + K − π + π − cross section measurement over a wide range of effective e + e − center-of-mass (C.M.) energies, and perform the first studies of the φπ + π − , f 0 (980)K + K − and φf 0 intermediate states. We also present the first measurements of the e + e − → K + K − π 0 π 0 cross section and its φf 0 component.
We use data corresponding to an integrated luminosity of 232 fb −1 recorded by the BABAR detector [4] on and off the Υ (4S) resonance. Charged-particle tracking is provided by a five-layer silicon vertex tracker (SVT) and a 40-layer drift chamber (DCH) in a 1.5 T axial magnetic field. Photon and electron energies are measured in a CsI(Tl) electromagnetic calorimeter (EMC). Charged particles are identified by specific ionization in the SVT and DCH, and an internally reflecting ringimaging Cherenkov detector (DIRC).
We use a simulation package developed for radiative processes that generates hadronic final states following Ref. [5], multiple soft photons from the initial-state using a structure-function technique [6,7], and photons from the final-state particles using PHOTOS [8]. We generate K + K − ππ final states both according to phase space and with a model that includes the φ(1020) → K + K − and f 0 (980) → ππ channels. We pass the events through a detector simulation [9], and reconstruct them in the same way as we do the data. We generate a number of backgrounds with this package, including the ISR processes e + e − → π + π − π + π − γ, π + π − π 0 π 0 γ, φηγ, φπ 0 γ and π + π − π 0 γ, and we also study e + e − → qq events generated by JETSET [10], e + e − → τ + τ − by KORALB [11], and Υ (4S) decays using our own generator [12].
The initial selection of events with a high-energy photon recoiling against a set of charged particles and photons is described in Refs. [3,13]. Here we accept all charged tracks that extrapolate to the interaction region, and photon candidates with an EMC energy greater than 30 MeV. The reconstructed vertex of the set of charged tracks is used as the point of origin for all photons.
For each four-track event with one or two identified K ± , we perform a set of three-constraint kinematic fits (see Ref. [13]). We assume the photon with the highest C.M. energy to be from ISR, and the fits use its direction, along with the four-momenta and covariance matrices of the initial e + e − and the reconstructed tracks. A fit using the π + π − π + π − hypothesis returns a χ 2 4π . If the event contains an identified K + and K − , we fit to the K + K − π + π − hypothesis and require χ 2 KKπ + π − < 30. For events with one identified kaon, we perform fits with each of the two oppositely charged tracks given the kaon hypothesis, and the combination with the lowest χ 2 KKπ + π − is retained if it is lower than 30 and χ 2 4π > χ 2 KKπ + π − . For the events with two tracks, both identified as charged kaons, and five or more photon candidates, all non-ISR photons are paired, and combinations lying within 35 MeV/c 2 of the π 0 mass are considered π 0 candidates. We perform a six-constraint fit to each set of two non-overlapping π 0 candidates plus the ISR photon and the K + and K − tracks, and the combination with the lowest χ 2 KKπ 0 π 0 is retained if χ 2 KKπ 0 π 0 < 50. To suppress ISR K + K − π 0 and K + K − η events, in which photons from an energetic π 0 or η combine with soft background clusters to form two π 0 candidates, we reject events with large differences between the two photon energies in both π 0 candidates. The fitted three-momenta for each charged track and photon are used in further kinematical calculations.
We consider three types of backgrounds. The first, which peaks at low values of χ 2 , is due to non-ISR events, and is dominated by e + e − → qq events with a hard π 0 producing a fake ISR photon. To evaluate this background, we use simulated mass and χ 2 distribu-tions normalized to data events in which the ISR photon combines with another cluster to form a π 0 candidate. The second type of background, due to ISR e + e − → π + π − ππ events with misidentified π ± , also contributes at low χ 2 values. We derive reliable estimates of their contributions from the known cross sections [3]. The third type of background comprises all remaining background sources and is estimated from the control regions 30 < χ 2 KKπ + π − < 60 and 50 < χ 2 KKπ 0 π 0 < 100, as detailed in Refs. [3,13]. We subtract these backgrounds, about 8-10% (15-20%) total contribution, from the se- We measure the track-finding efficiency from the data, and measure the kaon identification efficiency from a clean sample of ISR e + e − → φ→ K + K − events to a precision of 2.0%, a fourfold improvement over our previous result [3]. The π 0 reconstruction efficiency is determined from ISR e + e − → ωπ 0 γ → π + π − π 0 π 0 γ events and the method described in Ref. [13]. The above procedures allow us to correct the efficiency obtained from the MC simulation. In Fig. 1 we show the cross sections for the two processes, calculated by dividing the backgroundsubtracted yield in each bin by the efficiency and the ISR luminosity [3]. The errors are statistical only. The e + e − → K + K − π + π − cross section ( Fig. 1a) is consistent with both the direct measurement by DM1 [14] and our previous measurement [3], but is far more precise. In addition to the sharp J/ψ peak, wider structures are visible near 1.8 GeV, 2.2 GeV and possibly 2.4 GeV. The e + e − → K + K − π 0 π 0 cross section ( Fig. 1b) shows the same general features, including a J/ψ peak and a steep drop around 2.2 GeV. The total systematic uncertainty in the K + K − π + π − (π 0 π 0 ) cross section ranges from 7% (10%) at threshold to 9% (15%) at high E C.M. . As seen previously [3], there is a rich substructure in the e + e − → K + K − π + π − process, dominated by the K * 0 (892)Kπ intermediate state, but with large signals from the K 1 (1270), K * 0 2 (1430) and K 1 (1400) resonances. The e + e − → K + K − π 0 π 0 process is also dominated by the K * ± (892)K ∓ π 0 intermediate state. Understanding these contributions via a partial wave analysis is outside the scope of this paper.
Here we concentrate on events with an intermediate φ(1020) and/or f 0 (980) state. Figure 2 shows scatter plots of m(π + π − ) or m(π 0 π 0 ) versus m(K + K − ) for the selected events (including backgrounds) in the data. A φ → K + K − band is visible in both cases, as well as a concentration of events indicating correlated production of φ and f 0 . A horizontal ρ(770) band is visible for the charged mode only, and is due to K 1 → Kρ decays. Most of the K * intermediate states are outside the bounds of these plots. Selecting φ events with |m(K + K − )− 1020 MeV/c 2 | < 10 MeV/c 2 , and subtracting events with 10 < |m(K + K − )− 1020 MeV/c 2 | < 20 MeV/c 2 (see Figs. 3a,c) and MC simulated backgrounds, we obtain the φ-associated m(ππ) distributions shown in  1: The a) e + e − → K + K − π + π − and b) e + e − → K + K − π 0 π 0 cross sections as a function of e + e − C.M. energy. The direct measurements by DM1 [14] are shown for comparison as open circles. Only statistical errors are shown.
We now consider the quasi-two-body intermediate state φf 0 (980). In each 25 MeV/c 2 (40 MeV/c 2 ) bin of m(K + K − ππ) we select K + K − π + π − (K + K − π 0 π 0 ) events with m(π + π − ) (m(π 0 π 0 )) in the 0.85-1.1 GeV/c 2 region and fit their m(K + K − ) distribution to extract the number of events with a true φ. These are shown in Fig. 5 with about 700 events for the K + K − π + π − channel and about 120 events for the K + K − π 0 π 0 channel; there is a contribution of about 10% from e + e − → φππ events where the pion pair is not produced through the f 0 (980). Both distributions show the sharp rise from threshold as expected for a pair of relatively narrow resonances, and a slow, smooth decrease at high E C.M. , with signals for J/ψ and ψ(2S) in Fig. 5a. Both also show a resonancelike structure at about 2.15 GeV/c 2 . There are no known meson resonances with I=0 near this mass.
Dividing by the efficiency, ISR luminosity, B φ→K + K − = 0.491 [15], and B f0→π + π − (π 0 π 0 ) = 2/3(1/3), we obtain the two consistent measurements of the e + e − → φf 0 cross section shown in Fig. 6 (including about 10% φππ contribution). We use the following function of s = E 2 C.M. : The number of a) e + e − → φf0 → K + K − π + π − and b) e + e − → φf0 → K + K − π 0 π 0 events vs. invariant mass extracted as described in the text. Some bins have been combined for clarity, as indicated by the horizontal error bars. and relative phase of the non-resonant amplitude to the standard Breit-Wigner amplitude. The factor P (s) gives a good approximation of the two-body phase space factor for particles with similar masses; both the φ(1020) and f 0 (980) have small but finite widths, and our selection cut of m(ππ) > 0.85 GeV/c 2 defines an effective minimum mass, m 0 = 1.8 GeV/c 2 . The form of A nr is determined from a simulation that takes the φ and f 0 (980) lineshapes into account. A very sharp exponential cutoff (parameter a 1 ) is needed to describe the simulation well, but does not affect the spectrum well above threshold. There is no theoretical prediction for the form at high s, other than that, in the absence of resonances, it should fall smoothly with increasing s. A second order polynominal  (980) cross section, with about 10% of the φππ contribution, obtained via ISR in the K + K − π + π − (circles) and K + K − π 0 π 0 (squares) final states. The curves represent results of the fits described in the text.
(parameters a 2 and a 3 ) describes the simulation, so we fit Eq. 2 to the data, floating N nr , a 1 , a 2 and a 3 . The result without a resonant component is shown as the dashed curve in Fig. 6. The χ 2 0 = 80.5/(56 − 5) has confidence level P (χ 2 0 ) = 0.0053, and the fitted parameter values are close to those from the simulation; it is unlikely that a simple, smooth threshold curve can accomodate the data.
The first error is statistical and the second is systematic. Monte Carlo simulations show that the probability of such a signal arising by chance is less than 10 −3 . The modestly negative value of ψ x provides constructive interference below the resonance peak and destructive interference above it, in accord with the data. Variations in the resonance parameters are used to estimate the systematic errors. The fit of the mass spectra in Fig. 5a,b with Eq. 1 with normalization to the number of events under the Breit-Wigner curve gives 170 ± 63 and 31 ± 15 events for π + π − and π 0 π 0 respectively. Note that the observed structure is close to the ΛΛ production threshold at 2.23 GeV/c 2 and the opening of this channel may also contribute to the φf 0 cross section. We perform a number of systematic checks. Treating selected K + K − K + K − and π + π − ππ events as signal, we observe no structure. Selecting K * (892)Kπ events, which have little kinematic overlap with φf 0 (980), we see no structure. Excluding the dominant K * (892)Kπ intermediate states and selecting events with m(π + π − ) in the range 0.6-0.85 GeV/c 2 for the charged mode we observe structure at 2.15 GeV/c 2 with a similar yield. Because of the many overlapping intermediate states we cannot perform a quantitative measurement. This will be the subject of future investigation. Events with no f 0 (980) candidate do not exhibit a structure in the K + K − π 0 π 0 mode. We conclude that the new structure decays to φf 0 (980) with a relatively large branching fraction. We estimate where we fit the product Γ x σ 0 to reduce correlations, and the conversion constant C = 0.389 mb (GeV/c 2 ) 2 .
In summary, we present the most precise measurements of the cross sections for e + e − → K + K − π + π − and e + e − → K + K − π 0 π 0 from threshold to 4.5 GeV.
In the φππ channels we observe the J/ψ and ψ(2S) but not the Y (4260). In the φf 0 channel, we observe a new resonance-like structure, which might be interpreted as an ss analogue of the Y (4260), or as an ssss state that decays predominantly to φf 0 (980).
We are grateful for the excellent luminosity and machine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the computing organizations that support BABAR. The collaborating institutions wish to thank SLAC for its support and kind hospitality. This work is supported by DOE and NSF (USA), NSERC (Canada), IHEP (China), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MIST (Russia), MEC (Spain), and PPARC (United Kingdom). Individuals have received support from the Marie Curie EIF (European Union) and the A. P. Sloan Foundation.