Observation of the electromagnetic Dalitz decay $D^{\ast 0}\to D^{0}e^{+}e^{-}$

Based on 3.19 fb$^{-1}$ of $e^+e^-$ collision data accumulated at the center-of-mass energy 4.178 GeV with the BESIII detector operating at the BEPCII collider, the electromagnetic Dalitz decay $D^{\ast 0}\to D^{0}e^{+}e^{-}$ is observed for the first time with a statistical significance of $13.2\sigma$. The ratio of the branching fraction of $D^{\ast 0}\to D^{0}e^{+}e^{-}$ to that of $D^{\ast 0}\to D^{0} \gamma$ is measured to be $(11.08\pm0.76\pm0.49)\times 10^{-3}$. By using the world average value of the branching fraction of $D^{\ast 0}\to D^{0} \gamma$, the branching fraction of $D^{\ast 0}\to D^{0}e^{+}e^{-}$ is determined to be $(3.91\pm0.27\pm0.17\pm0.10)\times 10^{-3}$, where the first uncertainty is statistical, the second systematic and the third external branching fractions.

(Dated: January 7, 2022) Based on 3.19 fb −1 of e + e − collision data accumulated at the center-of-mass energy 4.178 GeV with the BESIII detector operating at the BEPCII collider, the electromagnetic Dalitz decay D * 0 → D 0 e + e − is observed for the first time with a statistical significance of 13.2σ. The ratio of the branching fraction of D * 0 → D 0 e + e − to that of D * 0 → D 0 γ is measured to be (11.08 ± 0.76 ± 0.49) × 10 −3 . By using the world average value of the branching fraction of D * 0 → D 0 γ, the branching fraction of D * 0 → D 0 e + e − is determined to be (3.91 ± 0.27 ± 0.17 ± 0.10) × 10 −3 , where the first uncertainty is statistical, the second is systematic and the third is from external input of the branching fraction for D * 0 → D 0 γ.

I. INTRODUCTION
The conversion decays of a vector resonance (V ) into a pseudoscalar meson (P ) and a lepton pair, V → P γ * → P ¯ , provide a stringent test for theoretical models of the structure of hadrons and the interaction mechanism between photons and hadrons [1]. In these processes, the squared dilepton invariant mass corresponds to the virtual photon 4-momentum transfer squared, q 2 . The q 2 distribution depends on the underlying dynamical electromagnetic structure of the transition V → P γ * . Furthermore, through the vector-meson dominance (VMD) model [1], the virtual photon effectively couples to vector particles, such as the ρ, ω, φ and even the heavier J/ψ particle. However, the off-shell effects cannot be calculated reliably [2]. Experimental measurement of the q 2 distribution is crucial to validate these calculations.
The charmonium electromagnetic (EM) Dalitz decay, ψ(3686) → e + e − η [6], ψ(3686) → e + e − χ cJ [7], and J/ψ → e + e − η [8], have also been reported. The charm meson decay D * + s → D + s e + e − was observed by CLEO [9], and the ratio of the branching fractions is measured to be (0.72 ± 0.18)%, which agrees with theoretical calculation based on the VMD model. However, there is no experimental result for the corresponding EM Dalitz decays of D * 0 and D * + . According to the VMD model, the D * + s → D + s e + e − decay mainly occurs via the coupling of the virtual photon to the vector φ meson, while the D * 0 → D 0 e + e − decay proceeds through the coupling to the ρ or ω meson. Hence, the study of the decay D * 0 → D 0 e + e − , with the diagrams depicted in FIG. 1, provides information on the form factor for the couplings γ * → ρ and γ * → ω. The ratio between branching fractions of D * 0 → D 0 e + e − and D * 0 → D 0 γ is defined as Calculations using the VMD model give R ee = 0.67% along with the following differential decay rate [1]: Here, α is the fine structure constant, is the transition form factor for D * 0 to D 0 , m e is the mass of electron and m D * 0 (m D 0 ) is the mass of D * 0 In this paper, the EM Dalitz decay D * 0 → D 0 e + e − is studied and R ee is measured using 3.19 fb −1 of e + e − collision data collected with the BESIII detector at the center-of-mass energy √ s = 4.178 GeV. To control background contributions, the candidates for both D * 0 → D 0 e + e − and D * 0 → D 0 γ are reconstructed with e + e − → D * 0D * 0 events. The single tag method is used, so that only D * 0 (D * 0 ) is reconstructed and theD * 0 (D * 0 ) on the recoiling side is not detected. The inclusion of chargeconjugate states is implied throughout this paper.

II. DESCRIPTION OF THE BEPCII AND THE BESIII DETECTOR
The BESIII detector [10] records symmetric e + e − collisions provided by the BEPCII storage ring [11], which operates in the center-of-mass energy range from 2.0 − 4.96 GeV. BESIII has collected large data samples in this energy region [12]. The cylindrical core of the BESIII detector covers 93% of the full solid angle and consists of a helium-based multilayer drift chamber (MDC), a plastic scintillator and multi-gap resistive plate chamber timeof-flight system (TOF), and a CsI(Tl) electromagnetic calorimeter (EMC), which are all enclosed in a superconducting solenoidal magnet providing a 1.0 T magnetic field. The solenoid is supported by an octagonal fluxreturn yoke with resistive plate counter muon identification modules interleaved with steel. The charged-particle momentum resolution at 1 GeV/c is 0.5%, and the dE/dx resolution is 6% for electrons from Bhabha scattering. The EMC measures photon energies with a resolution of 2.5% (5%) at 1 GeV in the barrel (end cap) region. The time resolution in the TOF barrel region is 68 ps, while that in the end cap region is 60 ps [13].

III. MONTE CARLO SIMULATION
Simulated data samples produced with a geant4based [14] Monte Carlo (MC) package, which includes the geometric description of the BESIII detector and the detector response, are used to determine detection efficiencies and to estimate backgrounds. The simulation models the beam energy spread and initial state radiation (ISR) in the e + e − annihilations with the generator kkmc [15]. The inclusive MC sample includes the production of open charm processes, the ISR production of vector charmonium(-like) states, and the continuum processes incorporated in kkmc [15]. The known decay modes are modeled with evtgen [16] using branching fractions taken from the Particle Data Group [17], and the remaining unknown charmonium decays are modeled with lundcharm [18]. Final state radiation (FSR) from charged final state particles is incorporated using photos [19].
The MC events of the signal process e + e − → D * 0D * 0 , D * 0 → D 0 e + e − are generated according to the VMD model. Following Ref. [20], the decay D * 0 → D 0 e + e − is described as where θ e is the helicity angle of the electron pair system. The MC samples of the reference process D * 0 → D 0 γ are generated with the kkmc.

IV. EVENT SELECTION
To reconstruct the signal and reference processes, D 0 candidates are selected via three decay modes D 0 → K − π + , K − π + π 0 and K − π + π − π + . For each charged track candidate, the polar angle θ in the MDC is required to be in the range |cos θ| < 0.93, and the distance of closest approach to the interaction point is required to be less than 10 cm along the beam direction and less than 1 cm in the plane perpendicular to the beam. The dE/dx recorded by the MDC and the time-of-flight information measured by the TOF are combined to calculate particle identification (PID) probability for the pion (P π ) and kaon (P K ) hypotheses. Pion candidates are selected by requiring P π > 0 and P π > P K , and kaon candidates are required to satisfy P K > 0 and P K > P π . Photon candidates are reconstructed with isolated clusters in the EMC in the region |cos θ| ≤ 0.80 (barrel) or 0.86 ≤ |cos θ| ≤ 0.92 (end cap). The deposited energy of the cluster is required to be larger than 25 (50) MeV in the barrel (end cap) region, and the angle between the photon candidate and any charged track is larger than 10 • . All γγ combinations are considered as candidate π 0 mesons, and the reconstructed mass M γγ is required to satisfy 0.115 < M γγ < 0.150 GeV/c 2 . A kinematic fit is performed to constrain the γγ invariant mass to the nominal π 0 mass taken from the PDG [17], and candidates with the fit quality χ 2 < 200 are retained. The K − π + , K − π + π 0 , and K − π + π − π + combinations are required to be within the mass windows 1.85< M K − π + < 1.88 GeV/c 2 , 1.84< M K − π + π 0 < 1.89 GeV/c 2 and 1.85< M K − π + π − π + < 1.88 GeV/c 2 , respectively. For each decay mode, all possible combinations are kept for further analysis.
For the D * 0 → D 0 e + e − decay, the electron and positron candidates are identified among the remaining charged tracks with the dE/dx information measured by the MDC. The probability criteria of P e > 0, P e > P π and P e > P K are applied. The energy difference ∆E is defined as ∆E = E D * 0 − E beam , where E D * 0 is the reconstructed energy of D * 0 candidates in the rest frame of the e + e − initial beams and E beam is the beam energy; |∆E| < 0.03 GeV is required to reduce background contributions. If there are multiple candidates (13% of the selected events) in an event, only the one with the minimum |∆E| is accepted. Similarly, for the D * 0 → D 0 γ candidates, if there are multiple combinations (32% of the selected events) in an event, only the candidate with the minimum |∆E| is kept and |∆E| < 0.03 GeV is required to reduce backgrounds. To separate D * 0 candidates produced from e + e − → D * 0D * 0 from backgrounds, the beam-constrained mass M BC is defined as where p D * 0 is the measured total momentum of D * 0 candidates in the rest frame of initial e + e − beams. In addition, a veto for dielectrons from photon conversion is applied to suppress background from D * 0 → D 0 γ, where the dielectron comes from the tran-sition photon interacting with the materials in the beam pipe and the MDC inner wall. The variable of R xy which represents the distance between beam interaction point and vertex of photon-conversion in xy plane [21] is calculated. Figure 2(a) shows the R xy distribution of the D * 0 → D 0 e + e − candidates, where two clear peaks corresponding to the beam pipe position (3 cm) and the MDC inner wall (6 cm) are observed. An additional requirement R xy < 2.0 cm removes the photon-conversion events. Figures 2(b), 2(c) and 2(d) show the distributions of the momentum of the e + e − pair, the opening angle between e + and e − , and the q 2 of the e + e − candidates for the D * 0 → D 0 e + e − , respectively. Good agreement between data and MC simulation is seen in FIG. 3.

V. DETERMINATION OF THE BRANCHING FRACTION
In the data sample, the observed number of signal events is expressed as (4) and the observed number of the reference process as Here, N D * 0D * 0 is the total number of D * 0D * 0 pairs in data, ε sig and ε ref denote the detection efficiencies of the signal and reference processes, respectively, and B int stands for the branching fractions for the three D 0 decay modes and secondary decay of the π 0 meson. For the signal process, the efficiency ε sig has been corrected to account for differences of the photon conversion, tracking and PID efficiencies between data and MC simulation (see discussion of systematic uncertainties below). Thus, the ratio R ee for each decay mode is given as The individual yields of the signal and reference processes are obtained by simultaneous fits to the M BC distributions. The M BC distributions of the accepted candidates for both signal and reference channels are shown in FIG. 4. In the fits, the signal shapes are obtained from the corresponding simulated shapes convolving with Gaussian functions to compensate the resolution difference between data and MC simulation. A common R ee is used for all three tag modes in the simultaneous fit, after the relevant efficiencies and branching fractions for each D 0 mode are taken into account. Note that peaking contributions from the corresponding doubly Cabibbo suppressed modesD 0 → K − π + , K − π + π 0 and K − π + π − π + cancel out in calculating R ee . Background studies indicate no peaking structures in the fit range, as illustrated  The comparison between data and MC components for D * 0 → D 0 e + e − process, where plot (a) is for D 0 → K − π + mode, plot (b) for D 0 → K − π + π 0 mode and plot (c) for D 0 → K − π + π − π + mode. Black dots with error bars are data, the blue lines are signal processes. The shaded histograms are the background processes for D * 0 → D 0 γ (green), open charm (red) and other (yellow) processes, respectively. TABLE I. Yields and efficiencies of the three D 0 tag decay modes and the obtained branching fractions. For the obtained branching fractions, the first uncertainties are statistical and the second systematic, while the uncertainties are statistical only for the other numbers. The third systematic uncertainty is quoted from the uncertainty of D * 0 → D 0 γ in PDG.   Table I. The ratio R ee is determined to be (11.08 ± 0.76) × 10 −3 , where the uncertainty is statistical. The statistical significance is estimated to be 13.2σ. The R ee values obtained separately in the three D 0 tag modes are consistent. By using the world average value of the branching fraction of D * 0 → D 0 γ, the branching fraction of D * 0 → D 0 e + e − is calculated to be (3.91 ± 0.27) × 10 −3 .

VI. SYSTEMATIC UNCERTAINTY
The main sources of systematic uncertainties are summarized in Table II and discussed in detail next. Systematic uncertainties in D 0 reconstruction are canceled in the ratio R ee .
To study the efficiencies of the tracking and PID of low-momentum e ± , a control sample of e + e − → γe + e − is selected. Due to relatively large efficiency differences, a reweighting procedure according to the two-dimensional kinematic distribution in transverse momentum and cos θ is implemented to reweight the MC-determined efficiency of D * 0 → D 0 e + e − . The overall correction factor is estimated to be (108.5 ± 2.9)% for e + e − pair. For e ± PID, the same control sample and reweighting procedure are used. The corresponding overall correction factor is estimated to be (94.1 ± 1.4)%. After correcting the signal efficiencies to data, the uncertainty on the correction factor is assigned as the systematic uncertainties.
In the reference mode D * 0 → D 0 γ, the uncertainty in the reconstruction efficiency of photon is assigned to be 1.0% based on the studies with a control sample of J/ψ → ρ 0 π 0 events [22].
In the nominal analysis, the PDG value of m ρ is used in the form factor of D * 0 → D 0 e + e − in the signal generator. In order to assign an uncertainty, we replace m ρ with m ω in the form factor in Eq. (2). The resultant change on the efficiency, 1.1%, is taken as the systematic uncertainty.
The signal efficiency loss due to vetoing photon conversions (R xy < 2.0 cm) is studied with a control sample of e + e − → γJ/ψ, J/ψ → π 0 π + π − with π 0 decaying to γe + e − final state. The veto efficiency is found to be lower than that determined in MC simulation by a factor (96.4 ± 1.0)%. After correcting the signal efficiencies to data, we assign 1.0% as the corresponding systematic uncertainty.
The efficiencies of the ∆E requirements are estimated by correcting the variable ∆E in the MC sample according to the observed resolution difference between data and MC simulation. The change of the obtained efficiencies of the corrected signal MC samples from the nominal efficiencies is taken as systematic uncertainty. For the fits to the M BC distributions, the signal shapes are varied from the MC-derived shape convolved with a single-Gaussian function to one using MC simulation convolved with a double-Gaussian function, while the background shape is varied from a second-order polynomial function to a linear function. The resultant changes on the final result are adopted as systematic uncertainties.

VII. SUMMARY
Based on 3.19 fb −1 of e + e − collision data collected at √ s =4.178 GeV with the BESIII detector, the EM Dalitz decay D * 0 → D 0 e + e − is observed for the first time. The branching fraction of this decay relative to that of D * 0 → D 0 γ is measured to be (11.08 ± 0.76 ± 0.49)×10 −3 . This result deviates from the ratio of 0.67% according to Eq. (2) with 3.5σ. Using the world average B(D * 0 → D 0 γ) = (35.3 ± 0.9)% [17], we determine B(D * 0 → D 0 e + e − ) = (3.91 ± 0.27 ± 0.17 ± 0.10) × 10 −3 , where the first uncertainty is statistical, the second is systematic and the third is from the uncertainty of the input B(D * 0 → D 0 γ). The obtained distribution of virtual photon 4-momentum transfer square is compatible with the model prediction in Eq. (2), as shown in FIG. 2(d). However, the statistics for now is still low for meaningful measurements of the q 2 -dependent form factor. Better precisions can be achieved with more data taken at BESIII in the future [12], which could be used for more physics goals, such as searching for the light vector boson X17 decaying into the e + e − pairs [23].