Evidence for $X(3872)\rightarrow J/\psi \pi^+\pi^-$ produced in single-tag two-photon interactions

We report the first evidence for $X(3872)$ production in two-photon interactions by tagging either the electron or the position in the final state, exploring the highly virtual photon region. The search is performed in $e^+e^- \rightarrow e^+e^-J/\psi\pi^+\pi^-$, using 825 fb$^{-1}$ of data collected by the Belle detector operated at the KEKB $e^+e^-$ collider. We observe three $X(3872)$ candidates with an expected background of $0.11\pm 0.10$ events, with a significance of 3.2$\sigma$. We obtain an estimated value for $\tilde{\Gamma}_{\gamma\gamma}{\cal B}(X(3872)\rightarrow J/\psi\pi^+\pi^-$) assuming the $Q^2$ dependence predicted by a $c\bar{c}$ meson model, where $-Q^2$ is the invariant mass-squared of the virtual photon. No $X(3915)\rightarrow J/\psi\pi^+\pi^-$ candidates are found.


Abstract
We report the first evidence for X(3872) production in two-photon interactions by tagging either the electron or the positron in the final state, exploring the highly virtual photon region. The search is performed in e + e − → e + e − J/ψπ + π − , using 825 fb −1 of data collected by the Belle detector operated at the KEKB e + e − collider. We observe three X(3872) candidates with an expected background of 0.11 ± 0.10 events, with a significance of 3.2σ. We obtain an estimated value for Γ γγ B(X(3872) → J/ψπ + π − ) assuming the Q 2 dependence predicted by a cc meson model, where −Q 2 is the invariant mass-squared of the virtual photon. No X(3915) → J/ψπ + π − candidates are found. The charmonium-like state X(3872) has been observed in various reactions since its first observation in B → KJ/ψπ + π − decays [1]. Its spin, parity, and charge conjugation were determined to be 1 ++ [2], but its internal structure is still a puzzle [3,4]. Subsequent to the spin-parity determination, the X(3872) has not been searched for in two-photon interactions because axial-vector particles are forbidden to decay to two real photons [5]. However, it has been pointed out that mesons with J P C = 1 ++ could be produced if one or both photons are highly virtual [6]-denoted as γ * .
We have performed the first search for the production of the X(3872) by two photons, using e + e − → e + e − X(3872), where one of the final-state electrons, referred to as a tagging electron, is observed, and the other scatters at an extremely forward (backward) angle and is not detected [7]. Such events are called single-tag events. The X(3872) is reconstructed via its decay to J/ψπ + π − (J/ψ → ℓ + ℓ − ). The two-photon decay width, which is obtained from this measurement, is sensitive to the internal structure of the X(3872). Early attempts to calculate such decay widths for charmonium-like exotic states have been reported in Ref. [8].
The Belle detector is a general-purpose magnetic spectrometer, asymmetrically enclosing the e + e − interaction point [12,13]. Charged-particle momenta are measured by a silicon vertex detector and a cylindrical drift chamber. Electron and charged-pion identification relies on a combination of the drift chamber, time-of-flight scintillation counters, aerogel Cherenkov counters, and an electromagnetic calorimeter made of CsI(Tl) crystals. Muon identification relies on the drift chamber and 14 layers of resistive plate chambers in the iron return yoke.
For Monte Carlo (MC) simulations, used to set selection criteria and derive the reconstruction efficiency, we use TREPSBSS [14,15] to generate single-tag e + e − → e + e − X(3872) events in which the X(3872) decays to J/ψπ + π − and J/ψ decays leptonically. For simulating radiative J/ψ decays, we use PHOTOS [16,17]. A GEANT3-based program simulates the detector response to these events [18].
Since one final-state electron is not detected, we select events with exactly five charged tracks, each coming from the interaction point (IP) and having p T > 0.1 GeV/c, with two or more having p T > 0.4 GeV/c, where p T is the transverse momentum with respect to the e + direction.
J/ψ candidates are reconstructed by their decays to e + e − or µ + µ − pairs. A charged track is identified as an electron (muon) from the J/ψ decay if its electron (muon) likelihood ratio is greater than 0.66 [19,20][21] The invariant mass of the lepton pair is required to be in the range 3.047-3.147 GeV/c 2 . In the calculation of the invariant mass of an e + e − pair, we include the four-momenta of radiated photons, having energy less than 0.2 GeV and angle relative to an electron direction of less than 0.04 radians.
The tagging electron must have an electron likelihood ratio greater than 0.95 or E/p greater than 0.87, where E is the energy measured by the electromagnetic calorimeter and p is the momentum of the particle. We require that the tagging electron have momentum above 1 GeV/c and p T > 0.4 GeV/c. The electron momentum includes the momenta of radiated photons, using the same requirements as for the electrons from J/ψ decays.
We identify a charged track as a pion if its kaon likelihood ratio is less than 0.8, its muon likelihood ratio is less than 0.9, its electron likelihood ratio is less than 0.6, and its E/p is less than 0.8 [22]. We require that events do not have any photons with energy above 0.4 GeV or any π 0 candidates whose χ 2 value in the mass constrained fit is less than 4.0.
As the X(3872) should be back-to-back with the tagging electron projected in the plane perpendicular to the e + e − beam axis, we require the difference between their azimuthal angles be in the range (π ± 0.1) radians.
We require that the total visible transverse momentum of the event, p * T [23], be less than 0.2 GeV/c. We also require that the measured energy of the J/ψπ + π − system, E * obs , be consistent with the expectation, E * exp , calculated from the observed momentum of the tagging electron and the direction and invariant mass of the J/ψπ + π − system, imposing energymomentum conservation. Since the energy and total transverse momentum are correlated, we impose a two-dimensional selection criterion (1) Figure 1 shows the distribution of events and these selection criteria in the p * T vs. E * obs /E * exp plane. Finally, we place a requirement on the missing momentum of the event, which is equal to the momentum of the unmeasured electron that goes down the beam pipe. We require the missing-momentum projection in the e − beam direction in the center-of-mass frame be less than −0.4 GeV/c for e − -tagging events and greater than 0.4 GeV/c for e + -tagging events.
We search for the X(3872) and X(3915) by looking for events in the J/ψπ + π − invariant mass distribution, M(J/ψπ + π − ). The reconstructed mass resolution is expected to be 2.5 MeV/c 2 from the MC simulation. We define two signal regions: 3.867-3.877 GeV/c 2 for the X(3872) and 3.895-3.935 GeV/c 2 for the X(3915). The former accommodates the X(3872) with the known mass of 3871.69 ± 0.17 MeV/c 2 and the small decay width of less than 1.2 MeV [24]; the latter accommodates the X(3915) with the known mass of 3918.4 ± 1.9 MeV/c 2 and the larger decay width of 20 ± 5 MeV. We constrain the J/ψ mass to 3.09690 GeV/c 2 when we calculate M(J/ψπ + π − ) [25]. The dominant background, centered at 3.686 GeV/c 2 , arises from radiatively produced ψ(2S), e + e − → e + e − ψ(2S), with ψ(2S) → J/ψπ + π − . Figure 2 shows the M(J/ψπ + π − ) distribution in data in the vicinity of ψ(2S). Although the width of the ψ(2S) peak is 2.7 MeV/c 2 , its tail extends to the high-mass side. This feature was also seen in previous studies of initial-state-radiation (ISR) production of J/ψπ + π − [26]. To remove ψ(2S) events, we veto events within 0.03 GeV/c 2 of the ψ(2S) mass, 3.686 GeV/c 2 . Figure 3 shows the Q 2 distribution after removing those events, where Q 2 = 2(p in · p out − m 2 e c 2 ) with p in and p out being the four-momenta of the incoming (beam) and outgoing (tagging) electrons and m e being the electron mass. In Fig. 3, data are dominated by background events while MC is pure X(3872). Since two-photon processes are strongly suppressed at high Q 2 , we require Q 2 < 25 GeV 2 /c 2 to suppress non-two-photon background. Our measurement is insensitive for Q 2 < 1.5 GeV 2 /c 2 due to a drop in reconstruction efficiency. mass. A similar distribution was seen in the Belle ISR study [26], suggesting that the main cause of our background is t-channel photon-exchange processes with an emission of a single virtual photon that converts to the hadronic state. To estimate the background level in the X(3872) signal region, we fit a linear function With this background, the significance of three events is 3.2σ. For the X(3872) signal, with three observed and 0.11 expected background events, we calculate the number of signal events, N sig = 2.9 +2.2 −2.0 (stat.) ± 0.1(syst.), using the Feldman-Cousins method [27] at 68% confidence level (C.L.). For the X(3915) signal, with zero observed and 0.3 expected background events, N sig < 2.14 at 90% C.L.
The differential cross section for the production of a resonance (X) in a single-tag twophoton interaction is expressed as [28] dσ ee (X) dQ 2 = 4π 2 1 + where L γ * γ is the single-tag luminosity function, M is the resonance mass, −Q 2 is the invariant mass squared of the virtual photon, Γ γ * γ (Q 2 ) is the γ * γ decay width for the resonance, W is the invariant mass of the γ * γ system, and J is the resonance spin. The factor of two comes from the existence of two production modes: e − γ * and e + γ * scattering.
For a J=1 resonance, spin-parity conservation forbids production at Q 2 = 0. To remove the Q 2 -dependence from Γ γ * γ (Q 2 ), we use the reduced γγ decay widthΓ γγ defined as [6,29] Γ γγ ≡ lim using its Q 2 dependence near zero; Γ LT γ * γ is the γ * γ decay width corresponding to a formation of the resonance from a longitudinal (virtual) photon and a transverse (real) photon. By substituting this expression into Eq. (3), we obtain for qq-type axial-vector mesons, this can be extended to a higher Q 2 region [29] as where accounting for the contributions from helicity 0 and 1.
To obtain the relation between the number of signal events and the decay width,Γ γγ , we use Eqs. (6) and (7) assuming the X(3872) is a pure cc state [6] where ε eff (Q 2 ) is the Q 2 -dependent reconstruction efficiency, L int is the integrated luminosity, B(X → J/ψπ + π − ) is the branching fraction of the X(3872) to J/ψπ + π − , and B(J/ψ → ℓ + ℓ − ) = 0.1193 is the branching fraction of J/ψ to lepton pairs [25]. We estimate the reconstruction efficiency from MC, in which we model the X(3872) decay as X(3872) → J/ψρ 0 with J/ψ → ℓ + ℓ − and ρ 0 → π + π − and with all daughter particles isotropically distributed in the rest frames of their parents. The decay model via ρ is motivated by the measured invariant mass distributions [1,31,32]. It has a reconstruction efficiency 12% higher than that of non-resonantly produced π + π − ; we include a 6% systematic uncertainty to account for this. The angular distribution of the decay products of the X(3872) negligibly affects the reconstruction, as confirmed by simulating with an alternative model with decay angles of daughters from a J P = 1 + resonance with helicities 0 and 1. We estimate the efficiencies for our three center-of-mass beam energies-5.01, 5.29 and 5.43 GeV, corresponding to the Υ(2S), Υ(4S), and Υ(5S) resonance energies-and average the values weighted by their corresponding integrated luminosities. We also average over the four detection modes given the two tagging charges (e + and e − ) and the two J/ψ decay modes (e + e − and µ + µ − ). Figure 5 shows the result. The luminosity functions for our three beam energies are calculated as functions of Q 2 using TREPSBSS. We set ǫ = 1 as a convention for the present application of Eq. (7) [6]. After performing the Q 2 integration in Eq. (8), from Q 2 min = 1.5 GeV 2 /c 2 to Q 2 max = 25 GeV 2 /c 2 , we obtainΓ γγ B(X(3872) → J/ψπ + π − ) = (1.88 ± 0.24) eV × N sig , including the total systematic uncertainty from the integration.
The dominant systematic uncertainty on the productΓ γγ B(X → J/ψπ + π − ) is that on the reconstruction efficiency, primarily due to the differences between MC and data shown in Table I as effects due to selection criteria. The e + e − background uncertainty in the J/ψ selection, 7%, comes from the difference between MC and data in the e + e − background level.
We estimate that the total systematic uncertainty is 13%.