An Improved Limit for Gamma_ee of X(3872) and Gamma_ee Measurement of psi(3686)

Using the data sets taken at center-of-mass energies above 4 GeV by the BESIII detector at the BEPCII storage ring, we search for the reaction e+e- ->gamma_ISR X(3872) ->gamma_ISR pi+pi-J/psi via the Initial State Radiation technique. The production of a resonance with quantum numbers J^PC = 1^++ such as the X(3872) via single photon e+e- annihilation is forbidden, but is allowed by a next-to-leading order box diagram. We do not observe a significant signal of X(3872), and therefore give an upper limit for the electronic width times the branching fraction Gamma_ee^X(3872)Br(X(3872) ->pi+pi-J\psi)<0.13 eV at the 90% confidence level. This measurement improves upon existing limits by a factor of 46. Using the same final state, we also measure the electronic width of the psi(3686) to be Gamma_ee^psi(3686) = 2231 +- 18 +- 99 eV.


Abstract
Using the data sets taken at center-of-mass energies above 4 GeV by the BESIII detector at the BEPCII storage ring, we search for the reaction e + e − → γ ISR X(3872) → γ ISR π + π − J/ψ via the Initial State Radiation technique. The production of a resonance with quantum numbers J P C = 1 ++ such as the X(3872) via single photon e + e − annihilation is forbidden, but is allowed by a next-to-leading order box diagram. We do not observe a significant signal of X(3872), and therefore give an upper limit for the electronic width times the branching fraction Γ X(3872) ee B(X(3872) → π + π − J/ψ) < 0.13 eV at the 90% confidence level. This measurement improves upon existing limits by a factor of 46. Using the same final state, we also measure the electronic width of the ψ(3686) to be Γ ψ(3686) ee = 2213 ± 18 stat ± 99 sys eV .

Introduction
The X(3872) resonance was observed in 2003 by 2 Belle [1] in the decay channel π + π − J/ψ. The existence of this state was later confirmed by several 4 other experiments [2,3,4,5,6]. The observation of the decay channel X(3872) → γJ/ψ implies that 6 the state has even C-parity [5,7,8]. The quantum numbers were finally determined to be J P C = 1 ++ 8 [5,9]. However, the intrinsic nature of the resonance is still unknown and has led to many con- 10 jectures. It is a good candidate for a tetraquark state but also for a meson molecule as its mass 12 is close to the D 0D * 0 threshold [10]. The recent observation of the decay Y (4260) → γX(3872) by 14 BESIII [6] implies that the X(3872) could be a meson molecule, as suggested by a model dependent 16 calculation [11]. On the other hand, the large decay rate of X(3872) → γψ(3686) observed by BaBar 18 and LHCb, compared to X(3872) → γJ/ψ hints at a tetraquark state explanation [8,12,13]. One 20 of the interesting quantities, which may help to reveal the structure of the X(3872) is its electronic width Γ ee . A recent order-of-magnitude calculation using a Vector Meson Dominance model pre- 24 dicts Γ X(3872) ee ≈ 0.03 eV [14], without any prior assumption regarding the nature of the X(3872). 26 For comparison, calculations for the Γ ee of the ordinary 1 ++ charmonium state χ c1 have been carried 28 out [15] and the electronic width is found to be in the range between 0.044 eV and 0.46 eV. This was 30 also confirmed in a more recent calculation [14].
The current upper limit for Γ X(3872) ee is at the 32 O(10 2 ) eV level [16], which is three orders of magnitude larger than the theoretical prediction. The 34 aim of this work is to obtain a significantly improved experimental value for the electronic width 36 of X(3872) that may be contrasted with predictions of Γ ee within various theoretical models mak-  The production of a 1 ++ resonance has never 42 been observed in e + e − annihilation so far. Such a process may occur via a two-photon box dia-44 gram as depicted in Fig. 1. In order to search for a possible signal we analyze data taken by the 46 BESIII detector at center-of-mass (c.m.) energies above 3.872 GeV, using the Initial State Radia-48 tion (ISR) technique. The ISR photon reduces the available c.m. energy, such that the X(3872) can 50 be produced resonantly via the two-photon process. In the process e + e − → γ ISR X(3872) we search 52 for the X(3872) in its decay to π + π − J/ψ with J/ψ → + − ( = µ and e). The π + π − J/ψ mass 54 spectrum is expected to be dominated by the well known process e + e − → γ ISR ψ(3686). 56

BESIII Detector, Data and Monte Carlo
BESIII is a general purpose detector, covering 58 93% of the solid angle. It is operating at the e + e − double-ring collider BEPCII. A detailed description 60 of the facilities is given in Ref. [18]. BESIII consists of four main components: (a) The helium-based   Table 1. The total integrated luminosity is L tot = 2.94 fb −1 . We simulate the e + e − → X(3872)γ ISR 90 signal process using evtgen [21,22], which invokes the vectorisr generator model [23] for the 92 ISR process and the common ρJ/ψ model for the decay X(3872) → π + π − J/ψ. The Monte Carlo 94 (MC) simulation of the e + e − → γ ISR ψ(3686) process was performed using the phokhara genera-96 tor [24]. For the background study we simulate the e + e − → ηJ/ψ process with evtgen and the 98 e + e − → γ ISR π + π − π + π − process with phokhara. reaction e + e − → γX(3872) recently observed by BESIII [6], where the photon comes from a radia-132 tive transition of the Y (4260), represents an irreducible background to our signal process. To avoid 134 this background, the ISR photon is required to be emitted at small polar angles | cos θ ISR | > 0.95, al-136 most colinear to the beam direction. Since the ISR photon cannot be detected in this region of the de-138 tector, its energy and polar angle are calculated from the missing momentum of the event (untagged 140 ISR photon). As the photon from the radiative decay channel is predominantly emitted at large po-142 lar angles, an optimal signal to background ratio is obtained in this way. An MC simulation study 144 shows that the Y (4260) → γX(3872) background can be neglected in the region of small polar an-146 gles of the ISR photon. To improve the resolution of the π + π − J/ψ mass spectrum and to further re-148 move background, a two-constraint (2C) kinematic fit under the hypothesis of the γ ISR π + π − + − final 150 state is performed. The two constraints are the J/ψ mass for the lepton pair and the mass of the missing 152 ISR photon, which is zero. We accept events with χ 2 2C < 15. arbitrary normalization. The background channels of e + e − → π + π − π + π − γ ISR and e + e − → η J/ψ 168 with η → γπ + π − are found to be negligible in an MC simulation study. The background channel 170 e + e − → ηJ/ψ with η → π + π − π 0 is displayed as the orange dashed-dotted line in Fig. 2.

172
Unbinned maximum likelihood fits are performed to extract the yields of ψ(3686) and  Table 1.

Calculation of Γ ee 186
The measured radiative event yield N A of the process e + e − → γ ISR A can be expressed as a func- where s is the squared c.m. energy, W (s, x) de-    Using Eq. (1), the electronic width times the branching fraction B(A → π + π − J/ψ) can then be 214 obtained via the relation (3) which is used to determine the electronic widths 216 of X(3872) and ψ(3686). As no significant signal is found in the case of X(3872), we calcu- e + e − → γ ISR ψ(3686), respectively. We apply an additional relative correction factor of 2%, which 226 stems from a data-MC difference found in the χ 2 Since no X(3872) signal is observed, we set We obtain γ up tot = Γ X(3872) ee B(X(3872) → π + π − J/ψ) 268 = 0.125 eV at the 90% C.L.

270
The luminosity is measured using large angle Bhabha events, and the uncertainty is estimated to 272 be 1% [27]. The uncertainty related to the tracking efficiency is 1% per charged track [6]. Since the final 274 state has four charged tracks, we estimate an uncertainty of 4% for the whole event. Applying our 276 J/ψ selection both to data and the ψ(3686)γ ISR MC simulation, the obtained event yield differs by 0.2%, 278 which we take as systematic uncertainty for the J/ψ selection. To correct for differences between data 280 and MC simulation in the χ 2 2C distribution, an efficiency correction was determined. Varying the χ 2 2C 282 selection and calculating the efficiency correction factor again at each energy, we obtain a correspond-284 ing uncertainty of 0.4% in the luminosity weighted average. The integrals I A have an uncertainty of 286 0.7%, due to the precision of the numerical integration (0.5%) and the calculation of the radiator 288 function (0.5%). The relative uncertainties of the branching fraction B(ψ(3686) → π + π − J/ψ) and 290 B(J/ψ → + − ) are 1.3% and 0.5%, respectively. There is no correlation between these branching 292 fractions [26]. We take 1.4% as the systematic uncertainty from the branching fractions for the 294 electronic width of ψ(3686). In the calculation of Γ X(3872) ee B(X(3872) → π + π − J/ψ) only the branch- ference is found to be 3.4% between them, which is taken as systematic uncertainty for the vectorisr 318 model. atic uncertainties is shown in Table 2. Assuming the sources to be independent, the total systematic 336 uncertainty for the electronic width of X(3872) is 6.1%, while in the case of ψ(3686) we find a sys-338 tematic uncertainty of 4.5%.

340
We have performed a search of the process e + e − → γ ISR X(3872) → γ ISR π + π − J/ψ using the 342 ISR untagged method, where the production of X(3872) in e + e − annihilations is possible via a two-344 photon box diagram. No significant X(3872) signal is observed in the π + π − J/ψ mass spectrum. We set 346 an upper limit for the electronic width of X(3872). By combining all four data sets, we finally obtain 348 Γ X(3872) ee B(X(3872) → π + π − J/ψ) < 0.13 eV at the 90% C.L. Here we have multiplied the upper limit by a factor 1/(1 − σ sys ) in order 350 to take the systematic uncertainties into account. Our measurement improves upon the current limit 352 Γ X(3872) ee B(X(3872) → π + π − J/ψ) < 6.2 eV at the 90% C.L.