Evidence for a vector charmonium-like state in $e^+e^- \to D^+_sD^*_{s2}(2573)^-+c.c.$

We report the measurement of $e^+e^- \to D^+_sD^*_{s2}(2573)^-+c.c.$ via initial-state radiation using a data sample of an integrated luminosity of 921.9 fb$^{-1}$ collected with the Belle detector at the $\Upsilon(4S)$ and nearby. We find evidence for an enhancement with a 3.4$\sigma$ significance in the invariant mass of $D^+_sD^*_{s2}(2573)^- +c.c.$ The measured mass and width are $(4619.8^{+8.9}_{-8.0}({\rm stat.})\pm2.3({\rm syst.}))~{\rm MeV}/c^{2}$ and $(47.0^{+31.3}_{-14.8}({\rm stat.})\pm4.6({\rm syst.}))~{\rm MeV}$, respectively. The mass, width, and quantum numbers of this enhancement are consistent with the charmonium-like state at 4626 MeV/$c^2$ recently reported by Belle in $e^+e^-\to D^+_sD_{s1}(2536)^-+c.c.$ The product of the $e^+e^-\to D^+_sD^*_{s2}(2573)^-+c.c.$ cross section and the branching fraction of $D^*_{s2}(2573)^-\to{\bar D}^0K^-$ is measured from $D^+_sD^*_{s2}(2573)^-$ threshold to 5.6 GeV.

Here, we search for Y states in another charmedantistrange and anticharmed-strange meson pair D + s D * s2 (2573) − in e + e − annihilations via initial-state radiation (ISR) [27]. The data set used in this analysis corresponds to an integrated luminosity of 921.9 fb −1 at center-of-mass (C.M.) energies of 10.52, 10.58, and 10.867 GeV collected with the Belle detector [28] at the KEKB asymmetric-energy e + e − collider [29,30].
We use phokhara [31] to generate signal Monte Carlo (MC) events. In the generator, considering that D + s and D * s2 (2573) − are produced from a vector state, the polar angle θ of the D + s in the D + s D * s2 (2573) − rest frame is distributed according to (1 + cos 2 θ) [32] for s , and e + e − → qq (q = u, d, s, c) at √ s = 10.52, 10.58, and 10.867 GeV with four times the luminosity of data are used to study possible backgrounds. The detector response is simulated with GEANT3 [34].
Next, we constrain the recoil mass of the γ ISR D + s K − to be the nominal mass of theD 0 meson [18] to improve the resolution of the ISR photon energy for events within theD 0 signal region (see below). As a result, the exclusive e + e − → D + s D * s2 (2573) − cross section can be measured according to the invariant mass spectrum of the D + s D * s2 (2573) − , which is equivalent to the mass of mesons recoiling against γ ISR .
Before calculation of the D + s candidate mass, a fit to a common vertex is performed for charged tracks in the D + s candidate. After the application of the above requirements, D + s signals are clearly observed. We define the D + s signal region as |M (D + s ) − m D + s | < 12 MeV/c 2 (∼2σ). Here and throughout the text, m i represents the nominal mass of particle i [18]. To improve the momentum resolution of the D + s meson candidate, a mass-constrained fit to the nominal D + s mass [18] is performed. The The D + s candidate with the smallest χ 2 from the D + s mass fit is kept. Besides the selected ISR photon and D + s , we require at least one additional K − candidate in the event and retain all the combinations (the fraction of events with multiple candidates is 4%). Figure 1 shows the recoil mass spectrum against the γ ISR D + s K − system after requiring the events be within the D * s2 (2573) − signal region (see below) in data, where the yellow histogram shows the normalized D * s2 (2573) − mass sidebands (see below). TheD 0 signal is wide and asymmetric due to the asymmetric resolution function of the ISR photon energy and higherorder ISR corrections. We perform a simultaneous likelihood fit to the M rec (γ ISR D + s K − ) distributions of all selected D * s2 (2573) − signal candidates and the normalized D * s2 (2573) − mass sidebands. TheD 0 signal component is modeled using a Gaussian function convolved with a Novosibirsk function [36] derived from the signal MC samples, while normalized D * s2 (2573) − mass sidebands are described by a second-order polynomial. The solid curve is the total fit; theD 0 signal yield is 224 ± 42. An asymmetric requirement of −200 < M rec (γ ISR D + s K − ) − mD0 < 400 MeV/c 2 is defined for theD 0 signal region. Hereinafter the mass constraint to the recoil mass of the γ ISR D + s K − system is applied for events in theD 0 signal region to improve the resolution of the mass.
The recoil mass spectrum against the γ ISR D + s system after requiring the events withinD 0 signal region is shown in Fig. 2. A D * s2 (2573) − signal is evident. The signal shape is described by a Breit-Wigner (BW) function convolved with a Gaussian function (all the parameters are fixed to those from a fit to the MC simulated distribution), and a second-order polynomial is used for the backgrounds. The fit yields 182 ± 47 D * s2 (2573) − signal events as shown in Fig. 2. We define the D * s2 (2573) − signal region as  The D + s D * s2 (2573) − invariant mass distribution is shown in Fig. 3 (top). There is an evident peak around 4620 MeV/c 2 , while no structure is seen in the normalized D * s2 (2573) − mass sidebands shown as the yellow histogram. In addition, no peaking background is found in the D + s D * s2 (2573) − mass distribution from generic MC samples. Therefore, we interpret the peak in the data as evidence for a charmonium-like state decaying into D + s D * s2 (2573) − , called Y (4620) hereafter. One possible background, which is not included in the D * s2 (2573) − mass sidebands, is from e + e − → D * + s (→ D + s γ)D * s2 (2573) − , where the photon from the D * + 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 endcaps [38] to ground events in the Y (4260) signal region is 1.7±1.5, which corresponds to an upper limit of 4.3 at 90% confidence level by using the frequentist approach [39] implemented in the POLE (Poissonian limit estimator) program [40].
We perform an unbinned maximum likelihood fit simultaneously to the M (D + s D * s2 (2573) − ) distributions of all selected D * s2 (2573) − signal candidates and the normalized D * s2 (2573) − mass sidebands. The following components are included in the fit to the M (D + s D * s2 (2573) − ) distribution: a resonance signal, a non-resonant contribution, and the D * s2 (2573) − mass sidebands. A D-wave BW function convolved with a Gaussian function (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 M (D + s D * s2 (2573) − ) and the differential ISR effective luminosity [41] is taken as the signal shape. Here the BW formula used has the form [42] BW where M is the mass of the resonance, Γ and Γ ee are the total width and partial width to e + e − , respectively, is the product branching fraction of the Y (4620) into the final state, and Φ 2 is the D-wave two-body decay phase-space form that increases smoothly from the mass threshold with √ s. The D-wave two-body phase space form (Φ 2 ( √ s)) is also taken into account for the non-resonant contribution. The D * s2 (2573) − mass sidebands are parameterized with a threshold function. The threshold function is where the parameters α, β 1 , and β 2 are free; x = M (D + s D * s2 (2573) − ) − x thr , and the threshold parameter x thr is fixed from generic MC simulations.
The fit results are shown in Fig. 3 (top), where the solid blue curve is the best fit, the blue dotted curve is the sum of the backgrounds, and the red dot-dashed curve is the result of the fit to the normalized D * s2 (2573) − mass sidebands. The yield of the Y (4620) signal is 66 +26 −20 . The statistical significance of the Y (4620) signal is 3.7σ, calculated from the difference of the logarithmic likelihoods [37], −2 ln(L 0 /L max ) = 19.6, 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 (∆ndf = 3). The significance including systematic uncertainties related with the parameterization of the mass resolution, non-resonant contribution, fitted range, signal-parameterization, and efficiency function is reduced to be 3.4σ. We take this value as the signal significance. The fitted mass and width for the Y (4620) are (4619.8 +8.9 −8.0 (stat.) ± 2.3(syst.)) MeV/c 2 and (47.0 +31.3 −14.8 (stat.) ± 4.6(syst.)) MeV, respectively.
The product of the e + e − → D + s D * s2 (2573) − dressed cross section (σ) [43] and the decay branching fraction B(D * s2 (2573) − →D 0 K − ) for each D + s D * s2 (2573) − mass bin from threshold to 5.6 GeV/c 2 in steps of 20 MeV/c 2 is computed as where N obs is the number of observed e + e − → D + s D * s2 (2573) − signal events after subtracting the normalized D * s2 (2573) − mass sidebands in data, Σ i (ε i × B i ) is the sum of the product of reconstruction efficiency and branching fraction for each D + s decay mode (i), and ∆L is effective luminosity in each D + s D * s2 (2573) − mass bin, respectively. The values used to calculate σ(e + e − → D + s D * s2 (2573) − ) × B(D * s2 (2573) − →D 0 K − ) are summarized in the supplemental material [45]. The resulting Fig. 4 with statistical uncertainties only. The sources of systematic uncertainties for the cross section measurement include detection-efficiency-related uncertainties, branching fractions of the intermediate states, the MC event generator, background subtraction, and MC statistics 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%), π 0 reconstruction efficiency (2.25%/π 0 ), and photon reconstruction efficiency (2.0%/photon). The above individual uncertainties from different D + s decay channels are added linearly, and weighted by the product of the detection efficiency and D + s branching fraction. These uncertainties are summed in quadrature to obtain the final uncertainty related to the reconstruction efficiency. For e + e − → D + s D * s2 (2573) − , the uncertainty from the θ dependence assumption is estimated to be 2.0% by comparing the difference in detection efficiency between a phase space distribution and the angular distribution of (1 + cos 2 θ). Uncertainties for the D + s decay branching fractions are taken from Ref. [18]; the final uncertainties on the D + s branching fractions are summed in quadrature over all the D + s decay modes weighted by the product of the efficiency and the D + s branching fraction. The phokhara generator calculates the ISR-photon radiator function with 0.1% accuracy [31]. The uncertainty attributed to the generator can be neglected.
The systematic uncertainty associated with the combinatorial background subtraction is due to an uncertainty in the scaling factor (1.7%) for the D * s2 (2573) − sideband estimation. We evaluate its effect on the signal yield for each bin and conservatively assign a maximum value, 3%. The statistical uncertainty in the determination of efficiency from signal MC sample is about 2.0%. The total luminosity is determined to 1.4% uncertainty 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 uncertainty. The following systematic uncertainties on the measured mass and width of the Y (4620), and the Γ ee × B(Y (4620 , where Γ 0 t is the width of the resonance, Φ 2 (M (D + s D * s2 (2573) − )) is the phase-space form for a D-wave two-body system, and Φ 2 (M Y (4620) ) is the value at the Y (4620) mass. The differences in the measured Y (4620) mass and width, and In summary, the product of the e + e − → D + s D * s2 (2573) − cross section and the decay branching fraction B(D * s2 (2573) − →D 0 K − ) is measured over the C.M. energy range from the D + s D * s2 (2573) − mass threshold to 5.6 GeV for the first time. We report evidence for a vector charmonium-like state decaying to D + s D * s2 (2573) − with a significance of 3.4σ. The measured mass and width are (4619.8 +8.9 −8.0 (stat.) ± 2.3(syst.)) MeV/c 2 and (47.0 +31.3 −14.8 (stat.) ± 4.6(syst.)) MeV, respectively, which are consistent with the mass of (4625.9 +6.2 −6.0 (stat.) ± 0.4(syst.)) MeV/c 2 and width of (49.8 +13.9 −11.5 (stat.) ± 4.0(syst.)) MeV of the Y (4626) observed in e + e − → D + s D s1 (2536) − [19], and also close to the corresponding parameters of the Y (4660) [18].
We measure Γ ee × B(Y (4620) → D + s D * s2 (2573) − ) × B(D * s2 (2573) − →D 0 K − ) to be (14.7 +5.9 −4.5 (stat.) ± 3.6(syst.)) eV. We thank the KEKB group for the excellent operation of the accelerator; the KEK cryogenics group for the efficient operation of the solenoid; and the KEK computer group, and the Pacific Northwest National Laboratory (PNNL) Environmental Molecular Sciences Laboratory (EMSL) computing group for strong computing support; and the National Institute of Informatics, and Science Information NETwork 5 (SINET5) for valuable network support. We acknowledge support from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan, the Japan Society for the Promotion of Science (JSPS), and the Tau-Lepton Physics Research Center of Nagoya University; the Australian Research Council including grants DP180102629, DP170102389, DP170102204, DP150103061, FT130100303; Austrian Science Fund (FWF); the National Natural Science Foundation of China under Con-