Observation of a vector charmoniumlike state

Using a data sample of 921 . 9 fb − 1 collected with the Belle detector, we study the process of e þ e − → D þ s D s 1 ð 2536 Þ − þ c : c : via initial-state radiation. We report the first observation of a vector charmoniumlike state decaying to D þ s D s 1 ð 2536 Þ − þ c : c : with a significance of 5 . 9 σ , including systematic uncertainties. The measured mass and width are ð 4625 . 9 þ 6 . 2 − 6 . 0 ð stat Þ(cid:2) 0 . 4 ð syst ÞÞ MeV =c 2 and ð 49 . 8 þ 13 . 9 − 11 . 5 ð stat Þ(cid:2) 4 . 0 ð syst ÞÞ MeV, respectively. The product of the e þ e − → D þ s D s 1 ð 2536 Þ − þ c : c : cross section and the branching fraction of D s 1 ð 2536 Þ − → ¯ D (cid:3) 0 K − is measured from the D s ¯ D s 1 ð 2536 Þ threshold to 5.59 GeV.

Using a data sample of 921.9 fb −1 collected with the Belle detector, we study the process of e þ e − → D þ s D s1 ð2536Þ − þ c:c: via initial-state radiation. We report the first observation of a vector charmoniumlike state decaying to D þ s D s1 ð2536Þ − þ c:c: with a significance of 5.9σ, including systematic uncertainties. The measured mass and width are ð4625.9 þ6.2 −6.0 ðstatÞAE0.4ðsystÞÞ MeV=c 2 and ð49.8 þ13.9 −11.5 ðstatÞAE4.0ðsystÞÞ MeV, respectively. The product of the e þ e − → D þ s D s1 ð2536Þ − þ c:c: cross section and the branching fraction of D s1 ð2536Þ − →D Ã0 K − is measured from the D sDs1 ð2536Þ threshold to 5.59 GeV. DOI: 10.1103/PhysRevD.100.111103 In the past decade, measurements of the exclusive cross sections for e þ e − annihilation into charmed or charmedstrange meson pairs above the open-charm threshold have attracted much attention [1][2][3][4][5][6][7][8][9][10]. These open-charm final states are dominantly produced from the Okubo-Zweig-Iizuka (OZI)-allowed strong decays of excited vector charmonium states (ψ states). A comprehensive study of the exclusive e þ e − cross sections to various open-charm final states could help one to understand the couplings of these ψ states, and extract their resonant parameters.
Many additional Y states with J PC ¼ 1 −− with masses above the open-charm threshold have been discovered in the last 14 years [11][12][13][14][15][16][17][18][19]. It has been noticed that the Y states above the open-charm threshold do not appear explicitly as peaks either in the total hadronic cross section or in the exclusive e þ e − cross sections to open-charm final states [20] [the only vector charmoniumlike states which reveal themselves as peaks at threshold are the Yð4630Þ and Yð4220Þ observed in the Λ þ cΛ − c and π þ D 0 D Ã− final states, respectively [21,22]]. In e þ e − → Y → π þ π − J=ψ and π þ π − ψð2SÞ [Y ¼ Yð4260Þ, Yð4660Þ] processes, events in π þ π − mass spectra tend to accumulate at the f 0 ð980Þ nominal mass, which has an ss component. Thus, it is natural to search for Y states with a ðcsÞðcsÞ quark component. As mentioned in Ref. [23], bound states of D sDs mesons, e.g., D sDs1 ð2536Þ, can appear as a result of f 0 ð980Þ exchange. Unfortunately, open-charmed-strange production associated with these Y states has not yet been observed.
In this Letter, we perform a measurement of the exclusive cross section for e þ e − → D þ S Þ as a function of center-of-mass (C.M.) energy from the D þ s D s1 ð2536Þ − mass threshold to 5.59 GeV via initial-state radiation (ISR) [24]. In this process, a charmoniumlike state decaying to D þ s D s1 ð2536Þ − is observed for the first time. The data used in this analysis correspond to 921.9 fb −1 of integrated luminosity at C.M. energies of 10.52, 10.58, and 10.867 GeV collected by the Belle detector [25] at the KEKB asymmetric-energy e þ e − collider [26,27].
We use PHOKHARA [28] to generate signal Monte Carlo (MC) events, determine the detector efficiency, and optimize selection criteria for signal events. Generic MC samples of We fully reconstruct the ISR photon γ ISR , D þ s , and K − =K 0 S , but do not reconstruct theD Ã0 =D Ã− . Since thē D Ã0 =D Ã− decays are not reconstructed, the detection efficiency for the e þ e − →D þ s D s1 ð2536Þ − ð→D Ã0 K − =D Ã− K 0 S Þ process is greatly improved. For the measurement of the e þ e − → D þ s D s1 ð2536Þ − cross section, we determine the invariant mass spectrum of D þ s D s1 ð2536Þ − (MðD þ s D s1 ð2536Þ − Þ), which is equivalent to the mass recoiling against γ ISR (M rec ðγ ISR Þ). Here, M rec ðγ ISR Þ is , where P C:M: . and P γ ISR are the four-momenta of the initial e þ e − system and the ISR photon, respectively. However, the energy resolution of γ ISR is very poor due to its high energy. We constrain the recoil mass of the γ ISR D þ s K − =γ ISR D þ s K 0 S to the nominal mass of theD Ã0 =D Ã− meson [29] to improve the resolution for the ISR photon for events within theD Ã0 =D Ã− signal region. Before applying the mass constraint, the mass resolution of the MðD þ s D s1 ð2536Þ − Þ system is about 180 MeV=c 2 . As a result of the constraint, the mass resolution is significantly improved, to about 5 MeV=c 2 .
The most energetic ISR photon is required to have energy greater than 3 GeV in the e þ e − C.M. frame. Pairs of photons are combined to form π 0 candidates. The energies of the photons from π 0 are required to be greater than 50 MeV in the calorimeter barrel and 100 MeV in the calorimeter end caps [31] in the laboratory frame. The η candidates are reconstructed via γγ and π þ π − π 0 decay modes. Photon candidates from η → γγ are required to have energies greater than 100 MeV in the laboratory frame. The reconstructed η candidates are then combined with π þ π − pairs to form η 0 candidates. The mass windows applied for π 0 , η → γγ, η → π þ π − π 0 , and η 0 candidates are AE12, AE20, AE10, and AE10 MeV=c 2 , which are within approximately 2.5σ of the corresponding meson nominal masses [29]. After applying the mass window requirements, mass-constrained fits are applied to the π 0 , η, and η 0 candidates to improve their momentum resolutions.
Before calculation of the D þ s candidate mass, a fit to a common vertex is performed for charged tracks in the D þ s candidate. After the application of the above requirements, D þ s signals are clearly observed. We define the D þ s signal region as jMðD þ s Þ − m D þ s j < 12 MeV=c 2 (∼2.0σ). Here and throughout the text, m i represents the nominal mass of particle i [29]. To improve the momentum resolution of the D þ s meson candidate, a mass-constrained fit to the D þ s nominal mass [29] is performed. The D þ s mass sideband regions are defined as 1912.34 < MðD þ s Þ < 1936.34 MeV=c 2 and 2000.34 < MðD þ s Þ < 2024.34 MeV=c 2 , which are twice as wide as the signal region. The D þ s candidates from the sidebands are also constrained to the central mass values in the defined D þ s sideband regions. The D þ s candidate with the smallest χ 2 from the D þ s mass fit is kept. Besides the selected ISR photon and D þ s , we require at least one additional K − or K 0 S candidate in the event, and retain all the combinations (the fraction of events with multiple candidates is 1.7%). Figure 1(a) shows the sum of the recoil mass spectra against the γ ISR D þ s K − and γ ISR D þ s K 0 S systems after requiring the events be within the D s1 ð2536Þ − signal region (see below) in data. Due to the poor recoil mass resolution, thē D Ã0 =D Ã− signal is very wide. TheD Ã0 =D Ã− signal component is modeled using a Gaussian function convolved with a Novosibirsk function [32] derived from the signal MC samples, while the combinatorial backgrounds are described by a second-order polynomial. The solid curve is the total fit; theD Ã0 =D Ã− signal yield is 275 AE 32. We define an Hereinafter theD Ã0 =D Ã− mass constraint is applied for events in theD Ã0 =D Ã− signal region to improve mass resolution.
The recoil mass spectrum against the γ ISR D þ s system after requiring the events withinD Ã0 =D Ã− signal region is shown in Fig. 1(b). A clear D s1 ð2536Þ − signal is observed. The signal shape is described by a double Gaussian function (all the parameters are fixed to those from a fit to the MC simulated distribution), and a threshold function is used for the backgrounds. The threshold function is where M rec is the recoil mass of the γ ISR D þ s ; the parameters α, β 1 , and β 2 are free; the threshold parameter x thr is fixed from generic MC simulations. The fit yields 254 AE 36 D s1 ð2536Þ − signal events as shown in Fig. 1(b) [33]. We define the D s1 ð2536Þ − signal region as jM rec ðγ ISR D þ s Þ − m D s1 ð2536Þ − j < 8 MeV=c 2 (∼2.5σ), and sideband regions as shown by blue dashed lines, which are three times as wide as the signal region. To estimate the signal significance of the D s1 ð2536Þ − , we compute ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi −2 lnðL 0 =L max Þ p [34], where L 0 and L max are the maximized likelihoods without and with the D s1 ð2536Þ − signal, respectively. The statistical significance of the D s1 ð2536Þ − signal is 8σ.
The D þ s D s1 ð2536Þ − invariant mass distribution is shown in Fig. 2(a). There is a significant peak around 4626 MeV=c 2 , while no structure is seen in the normalized D s1 ð2536Þ − mass sidebands shown as the yellow histogram. In addition, no peaking background is found in the D þ s D s1 ð2536Þ − mass distribution from generic MC samples. We therefore interpret the peak in the data as evidence for an exotic charmoniumlike state [35] decaying into D þ s D s1 ð2536Þ − , called Yð4626Þ hereafter. One possible background, which is not included in the D s1 ð2536Þ − mass sidebands, is from e þ e − → D Ãþ s ð→ D þ s γÞD s1 ð2536Þ − , where the photon from the D Ãþ s remains undetected. To estimate such a background contribution, we measure this process with the data following the same procedure as used for the signal process. We require an extra photon with E γ > 50 MeV in the barrel or E γ > 100 MeV in the end caps to combine with the D þ s to form the D Ãþ s candidate. The mass and vertex fits are applied to the D Ãþ s candidates to improve their momentum resolution. In events with multiple candidates, the best candidate is chosen using the lowest χ 2 value from the mass-constrained fit. The sameD Ã0 =D Ã− signal region requirement on M rec ðγ ISR D Ãþ s K − =K 0 S Þ and thē D Ã0 =D Ã− mass constraint are applied as before in e þ e − → D þ s D s1 ð2536Þ − . In the recoil mass spectrum of the γ ISR D Ãþ s an excess of 28 AE 13 D s1 ð2536Þ − signal events with a statistical significance of 2.4σ is observed in the D s1 ð2536Þ − signal region.
After requiring the D þ s K − =K 0 S mass to be within the D s1 ð2536Þ − signal region, the D Ãþ s D s1 ð2536Þ − invariant mass distribution is shown in Fig. 2(b). Note that the process e þ e − → D þ s D s1 ð2536Þ − is a source of backgrounds for the e þ e − → D Ãþ s D s1 ð2536Þ − when the D þ s candidates are combined with low energy photons to form D Ãþ s candidates. From Fig. 2(b), no obvious structure is observed. The normalized contribution from e þ e − → D Ãþ s D s1 ð2536Þ − to e þ e − → D þ s D s1 ð2536Þ − is the cyan shaded histogram which is shown in Fig. 2(a), and which is normalized to correspond to N obs D Ãþ − is the yield of e þ e − → D Ãþ s D s1 ð2536Þ − signal events in each MðD Ãþ s D s1 ð2536Þ − Þ bin in data after subtracting the normalized D s1 ð2536Þ − sidebands and the e þ e − → D þ s D s1 ð2536Þ − background contribution, and ε D þ s D s1 ð2536Þ − and ε D Ãþ s D s1 ð2536Þ − are the reconstruction efficiencies for e þ e − → D þ s D s1 ð2536Þ − and e þ e − → D Ãþ s D s1 ð2536Þ − , respectively, where the ratio of efficiencies is (1.00 AE 0.02). The yield of D Ãþ s D s1 ð2536Þ − after background subtraction for the entire region in Fig. 2(b) is (11.6 AE 3.6). A similar method is applied to estimate the background contribution from e þ e − → D þ s D s1 ð2536Þ − to e þ e − → D Ãþ s D s1 ð2536Þ − . We perform an unbinned likelihood fit simultaneously to the MðD þ s D s1 ð2536Þ − Þ distributions of all selected D s1 ð2536Þ − signal candidates, the normalized D s1 ð2536Þ − mass sidebands, and the e þ e − → D Ãþ s D s1 ð2536Þ − contribution. The yields in the normalized D s1 ð2536Þ − mass sidebands and the e þ e − → D Ãþ s D s1 ð2536Þ − contribution are fixed in the fit. The following components are included in the fit to the MðD þ s D s1 ð2536Þ − Þ distribution: a resonance signal, a nonresonant contribution, the D s1 ð2536Þ − mass sidebands, and an e þ e − → D Ãþ s D s1 ð2536Þ − contribution. A Breit-Wigner (BW) function convolved with a Gaussian function (with its width fixed at 5.0 MeV=c 2 according to the MC simulation), multiplied by an efficiency function that has a linear dependence on MðD þ s D s1 ð2536Þ − Þ and the differential ISR effective luminosity [36], is taken as the signal shape. Here the BW formula used has the form [37] BWð ffiffi ffi where M is the mass of the resonance, Γ and Γ ee are the total width and partial width to e þ e − , B f ¼ BðYð4626Þ → D þ s D s1 ð2536Þ − Þ × BðD s1 ð2536Þ − →D Ã0 K − Þ is the product branching fraction of the Yð4626Þ into the final state, and Φ 2 is the two-body decay phase space factor that increases smoothly from the mass threshold with ffiffi ffi s p , respectively. A two-body phase space form is also taken into account for the nonresonant contribution. The D s1 ð2536Þ − mass sidebands and the e þ e − → D Ãþ s D s1 ð2536Þ − contribution are parametrized with threshold functions.
The fit results are shown in Fig. 2(a), where the solid blue curve is the best fit, the blue dotted curve is the sum of the backgrounds, the red dot-dashed curve is the fitted result to the normalized D s1 ð2536Þ − mass sidebands, and the violet dot-dashed curve is for the e þ e − → D Ãþ s D s1 ð2536Þ − contribution. The yield of the Yð4626Þ signal is 89 þ17 −16 . The statistical significance of the Yð4626Þ signal is 6.5σ, calculated from the difference of the logarithmic likelihoods [34], −2 lnðL 0 =L max Þ ¼ 50.4, where L 0 and L max are the maximized likelihoods without and with a signal component, respectively, taking into account the difference in the number of degrees of freedom (Δndf ¼ 3). The parametrization of the nonresonant contribution is the dominant systematic uncertainty for the estimate of the signal significance. Changing the twobody phase space form to a threshold function parametrized by ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi M − x thr p or a two-body phase space form plus a threshold function, the Yð4626Þ signal significance is reduced to 5.9σ. We take this value as the signal significance with systematic uncertainties included. The fitted mass and width for the Yð4626Þ are ð4625.9 þ6.2 −6.0 ðstatÞAE 0.4ðsystÞÞ MeV=c 2 and ð49.8 þ13.9 −11.5 ðstatÞ AE 4.0ðsystÞÞ MeV, respectively. The value of Γ ee × BðYð4626Þ → D þ s D s1 ð2536Þ − Þ × BðD s1 ð2536Þ − →D Ã0 K − Þ is obtained to be ð14.3 þ2.8 −2.6 ðstatÞ AE 1.5ðsystÞÞ eV. The systematic uncertainties are discussed below.
The e þ e − → D þ s D s1 ð2536Þ − cross section is extracted from the recoil mass spectrum against the γ ISR D þ s system. The product of the e þ e − → D þ s D s1 ð2536Þ − dressed cross section (σ) [38] and the decay branching fraction BðD s1 ð2536Þ − →D Ã0 K − Þ for each D þ s D s1 ð2536Þ − mass bin from threshold to 5.59 GeV=c 2 in steps of 20 MeV=c 2 is computed as where N D s1 ð2536Þ − fit is the yield of fitted D s1 ð2536Þ − signal events after subtracting the e þ e − → D Ãþ s D s1 ð2536Þ − background contribution in data, dL is the effective luminosity [36], Σ i ðεD are the sums of the product of the reconstruction efficiency and branching fraction for each D þ s decay mode .06 taken from Ref. [29]. The values used to calculate σðe þ e − → D þ s D s1 ð2536Þ − Þ× BðD s1 ð2536Þ − →D Ã0 K − Þ are summarized in Supplemental Material [33]. In the fit to the recoil mass spectrum of γ ISR D þ s combinations in each D þ s D s1 ð2536Þ − mass bin, the D s1 ð2536Þ − signal shape is fixed to that from the overall fit, as shown by the blue solid curve in Fig. 1, and a threshold function is used for the backgrounds. The resulting σðe þ e − → D þ s D s1 ð2536Þ − Þ × BðD s1 ð2536Þ − → D Ã0 K − Þ value as a function of MðD þ s D s1 ð2536Þ − Þ is shown in Fig. 3 with the statistical and systematic uncertainties discussed below summed in quadrature.
The sources of systematic uncertainties for the cross section measurement include detection-efficiency-related uncertainties, branching fractions of the intermediate states, fit uncertainty, resonance parameters, the MC event generator, e þ e − → D Ãþ s D s1 ð2536Þ − background contribution, mass resolution as well as the integrated luminosity. The detection-efficiency-related uncertainties include those for tracking efficiency (0.35%/track), particle identification efficiency (1.1%/kaon and 0.9%/pion), K 0 S selection efficiency (1.4%) [40], π 0 reconstruction efficiency (2.25%/π 0 ) and photon reconstruction efficiency (2.0%/photon). The above individual uncertainties from different D þ s decay channels are added linearly, weighted by the product of the detection efficiency and D þ s partial decay width. These uncertainties are summed in quadrature to obtain the final uncertainty related to the reconstruction efficiency.
Uncertainties for D þ s decay branching fractions and R are taken from Ref. [29]; the final uncertainties on the D þ s partial decay widths are summed in quadrature over the eight D þ s decay modes weighted by the product of the efficiency and the D þ s partial decay width. Systematic uncertainties associated with the fitting procedure are estimated by changing the order of the background polynomial and the range of the fit. The deviations from nominal fit results are taken as systematic uncertainties.
Changing the values of mass and width of D s1 ð2536Þ − by 1σ [29] in each MðD þ s D s1 ð2536Þ − Þ bin has no effect on the fits. Thus, the uncertainty from the resonance parameters can be neglected. The PHOKHARA generator calculates the ISR-photon radiator function with 0.1% accuracy [28]. The uncertainty attributed to the generator can also be neglected.
By fitting the D s1 ð2536Þ − mass spectrum in each MðD Ãþ s D s1 ð2536Þ − Þ bin for e þ e − → D Ãþ s D s1 ð2536Þ − , we find the signal yields are less than 1. In addition, the D s1 ð2536Þ − signal from the e þ e − → D Ãþ s D s1 ð2536Þ − contribution has a much poorer mass resolution according to MC simulation. Therefore, the systematic uncertainty associated with the e þ e − → D Ãþ s D s1 ð2536Þ − contribution is neglected. The MC simulation is known to reproduce the resolution of mass peaks within 10% over a large number of different systems. The systematic uncertainty in the mass resolution is estimated by comparing the yields when the mass resolution is changed by 10%. The total luminosity is determined to 1.4% precision using wide-angle Bhabha scattering events. All the uncertainties are summarized in Table I. Assuming all the sources are independent, we sum them in quadrature to obtain the total systematic uncertainties.
The following systematic uncertainties on the measured mass and width for the Yð4626Þ, and the Γ ee × BðYð4626Þ → D þ s D s1 ð2536Þ − Þ × BðD s1 ð2536Þ − →D Ã0 K − Þ are considered. The resultant systematic uncertainties attributed to the mass resolution in the width and Γ ee × BðYð4626Þ → D þ s D s1 ð2536Þ − Þ × BðD s1 ð2536Þ − →D Ã0 K − Þ are 0.3 MeV and 0.1 eV. By changing the nonresonant background shape to a threshold function or to the sum of a two-body phase space form and a threshold function, the differences of 0.3 MeV=c 2 and 3.9 MeV in the measured mass and width, and 1.3 eV for the Γ ee × BðYð4626Þ → D þ s D s1 ð2536Þ − Þ × BðD s1 ð2536Þ − →D Ã0 K − Þ, respectively, are taken as systematic uncertainties. The uncertainty in the efficiency correction from detection efficiency, branching fractions of the intermediate states, and integrated luminosity is 4.9%. Changing the efficiency function by 4.9% gives a 0.1 MeV=c 2 change on the mass, 0.2 MeV on the width, and 0.7 eV on the product Γ ee × BðYð4626Þ → D þ s D s1 ð2536Þ − Þ × BðD s1 ð2536Þ − →D Ã0 K − Þ. Finally, the total systematic uncertainties on the Yð4626Þ mass, width, and Γ ee ×BðYð4626Þ→D þ s D s1 ð2536Þ − Þ×BðD s1 ð2536Þ − → D Ã0 K − Þ are 0.4 MeV=c 2 , 4.0 MeV, and 1.5 eV, respectively.
In summary, the product of the e þ e − →D þ s D s1 ð2536Þ − cross section and the decay branching fraction BðD s1 ð2536Þ − →D Ã0 K − Þ is measured over the C.M. energy range from the D þ s D s1 ð2536Þ − mass threshold to 5.59 GeV for the first time. We observe the first vector charmoniumlike state decaying to a charmedantistrange and anticharmed-strange meson pair D þ s D s1 ð2536Þ − with a signal significance of 5.9σ with systematic uncertainties included. The measured mass and width are ð4625.9 þ6.2 −6.0 ðstatÞ AE 0.4ðsystÞÞ MeV=c 2 and ð49.8 þ13.9 −11.5 ðstatÞ AE 4.0ðsystÞÞ MeV, respectively, which are consistent with the Yð4660Þ mass of ð4643AE9Þ MeV=c 2 and width of ð72 AE 11Þ MeV [29] within uncertainties. The Γ ee ×BðYð4626Þ→D þ s D s1 ð2536Þ − Þ×BðD s1 ð2536Þ − → D Ã0 K − Þ is obtained to be ð14.3 þ2.8 −2.6 ðstatÞ AE 1.5ðsystÞÞ eV.