Search for the semileptonic decay $D^{0(+)}\to b_1(1235)^{-(0)} e^+\nu_e$

Using $2.93~\mathrm{fb}^{-1}$ of $e^+e^-$ annihilation data collected at a center-of-mass energy $\sqrt{s}=3.773$ GeV with the BESIII detector operating at the BEPCII collider, we search for the semileptonic $D^{0(+)}$ decays into a $b_1(1235)^{-(0)}$ axial-vector meson for the first time. No significant signal is observed for either charge combination. The upper limits on the product branching fractions are ${\mathcal B}_{D^0\to b_1(1235)^- e^+\nu_e}\cdot {\mathcal B}_{b_1(1235)^-\to \omega\pi^-}<1.12\times 10^{-4}$ and ${\mathcal B}_{D^+\to b_1(1235)^0 e^+\nu_e}\cdot {\mathcal B}_{b_1(1235)^0\to \omega\pi^0}<1.75\times 10^{-4}$ at the 90\% confidence level.


I. INTRODUCTION
Semileptonic decays of the D 0(+) provide an outstanding platform to explore the dynamics of both weak and strong interactions in the charm sector. The semileptonic D 0(+) decays into pseudoscalar and vector mesons have been widely studied in both experiment [1] and theory.
In this paper, we report the first search for the semileptonic decays D 0 → b 1 (1235) − e + ν e and D + → b 1 (1235) 0 e + ν e .
The data used in this analysis, corresponding to an integrated luminosity of 2.93 fb −1 [12], was accumulated at a center-of-mass energy of 3.773 GeV with the BESIII detector. Throughout this paper, charge conjugate channels are always implied.

II. BESIII DETECTOR AND MONTE CARLO SIMULATION
The BESIII detector is a magnetic spectrometer [13] located at the Beijing Electron Positron Collider (BEPCII) [14]. The cylindrical core of the BESIII detector consists of a helium-based multilayer drift chamber (MDC), a plastic scintillator time-of-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 flux-return yoke with resistive plate counter muon identifier modules interleaved with steel.
The acceptance of charged particles and photons is 93% over 4π solid angle. The charged-particle momentum resolution at 1 GeV/c is 0.5%, and the dE/dx resolution is 6% for the 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 of the TOF barrel part is 68 ps, while that of the end cap part is 110 ps.
Simulated samples produced with the geant4based [15] Monte Carlo (MC) package which includes the geometric description of the BESIII detector and the detector response, are used to determine the detection efficiency and to estimate the backgrounds.
The simulation includes the beam energy spread and initial state radiation (ISR) in the e + e − annihilations modeled with the generator kkmc [16]. The inclusive MC samples consist of the production of DD pairs with consideration of quantum coherence for all neutral D modes, the non-DD decays of the ψ(3770), the ISR production of the J/ψ and ψ(3686) states, and the continuum processes. The known decay modes are modeled with evtgen [17] using the branching fractions taken from the Particle Data Group [1], and the remaining unknown decays from the charmonium states with lundcharm [18]. The final state radiations from charged final state particles are incorporated with the photos package [19]. The signal process D 0(+) → b 1 (1235) −(0) e + ν e is simulated with b 1 (1235) −(0) decaying into ωπ −(0) , using the ISGW2 model [3]. A relativistic Breit-Wigner function is used to parameterize the resonance b 1 (1235) −(0) , the mass and width of which are fixed to the world-average values of 1229.5 ± 3.2 MeV/c 2 and 142 ± 9 MeV, respectively [1].

III. DATA ANALYSIS
The process e + e − → ψ(3770) → DD provides an ideal opportunity to study semileptonic D 0(+) decays with the double-tag (DT) method, because there are no additional particles that accompany the D mesons in the final states [20]. Throughout the paper, D denotes D 0 or D + . At first, single-tag (ST)D 0 mesons are reconstructed by using the hadronic decay modes of D 0 → K + π − , K + π − π 0 , and K + π − π − π + ; while ST D − mesons are reconstructed via the decays D − → K + π − π − , K 0 S π − , K + π − π − π 0 , K 0 S π − π 0 , K 0 S π + π − π − , and K + K − π − . Then the semileptonic D candidates are reconstructed with the remaining tracks and showers. The candidate event in which D decays into b 1 (1235)e + ν e andD decays into a tag mode is called a DT event.
Since the branching fraction of the subsequent decay b 1 (1235) → ωπ is not well measured, the product of the branching fractions of the decay D → b 1 (1235)e + ν e (B SL ) and its subsequent decay b 1 (1235) → ωπ (B b1 ) is determined using where N tot ST and N DT are the yields of the STD mesons and the DT signal events in data, respectively; B ω and B π 0 are the branching fractions of ω → π + π − π 0 and π 0 → γγ, respectively; k is the component, which corresponds to the number of π 0 mesons in the final states andε SL is the average efficiency of reconstructing D → b 1 (1235)e + ν e . The average signal efficiency, weighted over the tag modes i, is calculated byε DT is the detection efficiency of reconstructinḡ D → i and D → b 1 (1235)e + ν e at the same time.
The STD candidates are selected with the same criteria employed in our previous works [9,[21][22][23][24][25][26][27][28][29]. For each charged track (except for those used for reconstructing K 0 S meson decays), the polar angle with respect to the MDC axis (θ) is required to satisfy | cos θ| < 0.93, and the point of closest approach to the interaction point (IP) must be within 1 cm in the plan perpendicular to the MDC axis and within ±10 cm along the MDC axis. Charged tracks are identified by using the dE/dx and TOF information, with which the combined confidence levels under the pion and kaon hypotheses are computed separately. A charged track is assigned as the particle type which has a larger probability.
Candidate K 0 S mesons are formed from pairs of oppositely charged tracks. For these two tracks, the distance of closest approach to the IP is required to be less than 20 cm along the MDC axis. No requirements on the distance of closest approach in the transverse plane or on particle identification (PID) criteria are applied to these tracks. The two charged tracks are constrained to originate from a common vertex, which is required to be away from the IP by a flight distance of at least twice the vertex resolution. The invariant mass of the π + π − pair is required to be within (0.486, 0.510) GeV/c 2 .
Photon candidates are chosen from the EMC showers. The EMC time deviation from the event start time is required to be within [0, 700] ns. The energy deposited in the EMC is required to be greater than 25 (50) MeV if the crystal with the maximum deposited energy in that cluster is in the barrel (end cap) region [30]. The opening angle between the photon candidate and the nearest charged track is required to be greater than 10 • . For any π 0 candidate, the invariant mass of the photon pair is required to be within (0.115, 0.150) GeV/c 2 . To improve the momentum resolution, a mass-constrained (1-C) fit to the nominal π 0 mass [1] is imposed on the photon pair. The four-momentum of the π 0 candidate returned by this kinematic fit is used for further analysis.
In the selection ofD 0 → K + π − events, the back-grounds from cosmic rays and Bhabha events are rejected by using the same requirements described in Ref. [31].
To separate the STD mesons from combinatorial backgrounds, we define the energy difference ∆E ≡ ED − E beam and the beam-constrained mass where E beam is the beam energy, and ED and pD are the total energy and momentum of the STD meson in the e + e − center-of-mass frame. If there is more than oneD candidate in a specific ST mode, the one with the least |∆E| is kept for further analysis.
To suppress combinatorial backgrounds, the STD candidates, which are reconstructed by using the modes with and without π 0 in the final states, are imposed with the requirements of ∆E ∈ (−0.055, 0.045) GeV and ∆E ∈ (−0.025, 0.025) GeV, respectively. For each ST mode, the yield of STD mesons is extracted by fitting the corresponding M BC distribution. The signal is described by an MC-simulated shape convolved with a double-Gaussian function which compensates the resolution difference between data and MC simulation. The background is parameterized by the ARGUS function [32]. All fit parameters are left free in the fits.  We require that there are four and three charged tracks reconstructed in D 0 → b 1 (1235) − e + ν e and D + → b 1 (1235) 0 e + ν e candidates, respectively. These tracks exclude those used to form the STD candidates. For each candidate, one charged track is identified as a positron and the others are required to be identified as pions. The selection criteria of charged and neutral pions are the same as those used in selecting the STD candidates. To suppress fake π 0 candidates, the decay angle of π 0 , defined as cos θ π 0 = |E γ1 − E γ2 |/| p π 0 · c|, is required to be less than 0.9. The requirement has been optimized using the inclusive MC sample. E γ1 and E γ2 are the energies of the two daughter photons of the π 0 , and p π 0 is the reconstructed momentum of the π 0 . For the selected D 0 → π + π − π − π 0 e + ν e and D + → π + π − π 0 π 0 e + ν e candidates, there are always two possible π + π − π 0 combinations to form the ω. The invariant masses of both combinations are required to be greater than 0.6 GeV/c 2 to suppress the backgrounds from D → a 0 (980)e + ν e . One candidate is kept for further analysis if either of the combinations has an invariant mass falling in the ω mass signal region of (0.757, 0.807) GeV/c 2 . To form a b 1 (1235) candidate, the ωπ invariant mass is required to be within (1.080, 1.380) GeV/c 2 . The background from D 0(+) → K 1 (1270)[K 0 S π +(0) π −(0) ]e + ν e is rejected by requiring the invariant masses of any π + π − (π 0 π 0 ) combinations to be outside (0.486, 0.510) GeV/c 2 ((0.460, 0.510) GeV/c 2 ). These requirements correspond to three times the invariant mass resolution about the nominal K 0 S mass [1]. The e + candidate is required to have a charge of opposite sign to that of the charm quark in the ST D meson. The e + candidate is identified by using the combined dE/dx, TOF, and EMC information. The combined confidence levels for the positron, pion, and kaon hypotheses (CL e , CL π , and CL K ) are computed. The positron candidate is required to satisfy CL e > 0.001 and CL e /(CL e +CL π +CL K ) > 0.8. Its deposited energy in the EMC is required to be greater than 0.8 times its momentum reconstructed by the MDC, to further suppress the background from misidentified hadrons and muons.
The peaking backgrounds from hadronic D decays with multiple pions in the final states are rejected by requiring that the invariant mass of b 1 (1235)e + (M b1e + ) is less than 1.80 GeV/c 2 . To suppress backgrounds with extra photon(s), we require that the energy of any extra photon (E γ extra ) is less than 0.30 GeV and there is no extra π 0 (N π 0 extra ) in the candidate event. The neutrino is not detectable in the BESIII detector. To distinguish semileptonic signal events from backgrounds, we define U miss ≡ E miss − | p miss | · c, where E miss and p miss are the missing energy and momentum of the DT event in the e + e − center-of-mass frame, respectively. They are calculated as E miss ≡ E beam − E b1 − E e + and p miss ≡ p D − p b1 − p e + , where E b1 (e + ) and p b1 (e + ) are the measured energy and momentum of the b 1 (1235) (e + ) candidates, respectively, and p D ≡ −pD · E 2 beam /c 2 − m 2 D · c 2 , wherepD is the unit vector in the momentum direction of the STD meson and mD is the nominalD mass [1]. The use of the beam energy and the nominal D mass for the magnitude of the ST D mesons improves the U miss resolution. For the correctly reconstructed signal events, U miss peaks at zero. Figure 2 shows the U miss distributions of the accepted candidate events. Unbinned maximum likelihood fits are performed on these distributions. In the fits, the signal and background are modeled by the simulated shapes obtained from the signal MC events and the inclusive MC sample, respectively, and the yields of the signal and background are left free. Since no significant signal is observed, conservative upper limits will be set by assuming all the fitted signals are from b 1 (1235).
The detection efficienciesε SL are estimated to be 0.0704 ± 0.0006 and 0.0412 ± 0.0002 for the D 0 → b 1 (1235) − e + ν e and D + → b 1 (1235) 0 e + ν e decays, respectively. The blue dotted curves in Fig. 3 show the raw likelihood distributions versus the corresponding product of branching fractions.

IV. SYSTEMATIC UNCERTAINTY
With the DT method, many systematic uncertainties on the ST side mostly cancel. The sources of the systematic uncertainties in the measurements of the product of branching fractions are classified into two cases. The first one is from the uncertainties relying on effective efficiencies and are assigned relative to the measured branching fractions. The uncertainty associated with the ST yield N tot ST is estimated to be 0.5% [21][22][23]. The uncertainty from the quoted branching fraction of the ω → π + π − π 0 decay is 0.8%. The uncertainties from the tracking and PID of e ± are studied with a control sample of e + e − → γe + e − . The uncertainties from the tracking and PID of π ± and π 0 reconstruction are obtained by studing a DT control sample ψ(3770) → DD with hadronic D decays [21,22]. The systematic uncertainties from the tracking (PID) efficiencies are assigned as 1.0% (1.0%) per e ± and 1.0% (1.0%) per π ± , respectively. The π 0 reconstruction efficiencies include photon finding, the π 0 mass window, and the 1-C kinematic fit, the systematic uncertainty of which is taken to be 2.0% per π 0 . The systematic uncertainty from the π 0 decay angle requirement is determined to be 2.0% per π 0 by studying the DT events of D 0 → K − π + π 0 versusD 0 → K + π − and K + π − π − π + . The systematic uncertainty associated with the ω mass window is assigned to be 1.2% using a control sample of D 0 → K 0 S ω reconstructed versus the sameD 0 tags as those used in the nominal analysis. The systematic uncertainties from the E max extra γ and N extra,π 0 requirements are estimated to be 1.4% and 2.0% for D 0 → b 1 (1235) − e + ν e and D + → b 1 (1235) 0 e + ν e , respectively, which are estimated using DT samples of D 0 → K − e + ν e and D + → K 0 S e + ν e decays reconstructed versus the same tags as the nominal analysis. The systematic uncertainty related to the MC generator is The points with error bars are data, the red dashed curve is the signal, the gray filled histogram is the background contribution, and the blue solid curve shows the total fit. estimated using alternative signal MC samples, which are produced by varying the mass and width of the b 1 (1235) by ±1σ.
The second kind of systematic uncertainty originates from the fit to the U miss distribution of the semileptonic D decay candidates. It is dominated by the uncertainty from imperfect knowledge of the background shape. The uncertainty associated with the signal shape is negligible. The background shape is obtained from the inclusive MC sample using a kernel estimation method [33] implemented in RooFit [34]. Unlike the other sources of uncertainties, the background shape directly affects the likelihood function. The smoothing parameter of RooKeysPdf is varied within a reasonable range to obtain alternative background shapes. The absolute change of the signal yield, which gives the largest upper limit on the branching fraction, is taken as the systematic uncertainty (σ n ). It is found to be 1.7 for D 0 → b 1 (1235) − e + ν e and 1.1 for D + → b 1 (1235) 0 e + ν e .

V. RESULTS
To take into account the first kind of systematic uncertainty in the calculation of the upper limits, the raw likelihood distribution versus the product of branching fractions is smeared by a Gaussian function with a mean of 0 and a width equal to σ ǫ according to Refs. [35,36].
To incorporate the second kind of systematic uncertainty, the updated likelihood is then convolved with another Gaussian function with mean of 0 and a width equal to σ B similarly. Here σ B is an uncertainty of the product of the branching fractions calculated with Eq. (1) by replacing N DT with σ n .

VII. ACKNOWLEDGEMENT
The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. This work is supported in part by National QYZDJ-SSW-SLH003, QYZDJ-SSW-SLH040;