Study of J / ψ and ψ ( 3686 ) → ( 1385 ) 0 ̄ ( 1385 ) 0 and 0 ̄ 0 BESIII Collaboration

M. Ablikim a, M.N. Achasov i,5, S. Ahmed n, X.C. Ai a, O. Albayrak e, M. Albrecht d, D.J. Ambrose aw, A. Amoroso bb,bd, F.F. An a, Q. An ay,1, J.Z. Bai a, O. Bakina y, R. Baldini Ferroli t, Y. Ban ag, D.W. Bennett s, J.V. Bennett e, N. Berger x, M. Bertani t, D. Bettoni v, J.M. Bian av, F. Bianchi bb,bd, E. Boger y,3, I. Boyko y, R.A. Briere e, H. Cai bf, X. Cai a,1, O. Cakir ap, A. Calcaterra t, G.F. Cao a, S.A. Cetin aq, J. Chai bd, J.F. Chang a,1, G. Chelkov y,3,4, G. Chen a, H.S. Chen a, J.C. Chen a, M.L. Chen a,1, S. Chen at, S.J. Chen ae, X. Chen a,1, X.R. Chen ab, Y.B. Chen a,1, X.K. Chu ag, G. Cibinetto v, H.L. Dai a,1, J.P. Dai aj,10, A. Dbeyssi n, D. Dedovich y, Z.Y. Deng a, A. Denig x, I. Denysenko y, M. Destefanis bb,bd, F. De Mori bb,bd, Y. Ding ac, C. Dong af, J. Dong a,1, L.Y. Dong a, M.Y. Dong a,1, Z.L. Dou ae, S.X. Du bh, P.F. Duan a, J.Z. Fan ao, J. Fang a,1, S.S. Fang a, X. Fang ay,1, Y. Fang a, R. Farinelli v,w, L. Fava bc,bd, F. Feldbauer x, G. Felici t, C.Q. Feng ay,1, E. Fioravanti v, M. Fritsch n,x, C.D. Fu a, Q. Gao a, X.L. Gao ay,1, Y. Gao ao, Z. Gao ay,1, I. Garzia v, K. Goetzen j, L. Gong af, W.X. Gong a,1, W. Gradl x, M. Greco bb,bd, M.H. Gu a,1, Y.T. Gu l, Y.H. Guan a, A.Q. Guo a, L.B. Guo ad, R.P. Guo a, Y. Guo a, Y.P. Guo x, Z. Haddadi aa, A. Hafner x, S. Han bf, X.Q. Hao o, F.A. Harris au, K.L. He a, F.H. Heinsius d, T. Held d, Y.K. Heng a,1, T. Holtmann d, Z.L. Hou a, C. Hu ad, H.M. Hu a, T. Hu a,1, Y. Hu a, G.S. Huang ay,1, J.S. Huang o, X.T. Huang ai, X.Z. Huang ae, Z.L. Huang ac, T. Hussain ba, W. Ikegami Andersson be, Q. Ji a, Q.P. Ji o, X.B. Ji a, X.L. Ji a,1, L.W. Jiang bf, X.S. Jiang a,1, X.Y. Jiang af, J.B. Jiao ai, Z. Jiao q, D.P. Jin a,1, S. Jin a, T. Johansson be, A. Julin av, N. Kalantar-Nayestanaki aa, X.L. Kang a, X.S. Kang af, M. Kavatsyuk aa, B.C. Ke e, P. Kiese x, R. Kliemt j, B. Kloss x, O.B. Kolcu aq,8, B. Kopf d, M. Kornicer au, A. Kupsc be, W. Kühn z, J.S. Lange z, M. Lara s, P. Larin n, H. Leithoff x, C. Leng bd, C. Li be, Cheng Li ay,1, D.M. Li bh, F. Li a,1, F.Y. Li ag, G. Li a, H.B. Li a, H.J. Li a, J.C. Li a, Jin Li ah, K. Li m, K. Li ai, Lei Li c, P.R. Li g,at, Q.Y. Li ai, T. Li ai, W.D. Li a, W.G. Li a, X.L. Li ai, X.N. Li a,1, X.Q. Li af, Y.B. Li b, Z.B. Li an, H. Liang ay,1, Y.F. Liang al, Y.T. Liang z, G.R. Liao k, D.X. Lin n, B. Liu aj,10, B.J. Liu a, C.X. Liu a, D. Liu ay,1, F.H. Liu ak, Fang Liu a, Feng Liu f, H.B. Liu l, H.H. Liu a, H.H. Liu p, H.M. Liu a, J. Liu a, J.B. Liu ay,1, J.P. Liu bf, J.Y. Liu a, K. Liu ao, K.Y. Liu ac, L.D. Liu ag, P.L. Liu a,1, Q. Liu at, S.B. Liu ay,1, X. Liu ab, Y.B. Liu af, Y.Y. Liu af, Z.A. Liu a,1, Zhiqing Liu x, H. Loehner aa, Y.F. Long ag, X.C. Lou a,1,7, H.J. Lu q, J.G. Lu a,1, Y. Lu a, Y.P. Lu a,1, C.L. Luo ad, M.X. Luo bg, T. Luo au, X.L. Luo a,1, X.R. Lyu at, F.C. Ma ac, H.L. Ma a, L.L. Ma ai, M.M. Ma a, Q.M. Ma a, T. Ma a, X.N. Ma af, X.Y. Ma a,1, Y.M. Ma ai, F.E. Maas n, M. Maggiora bb,bd, Q.A. Malik ba, Y.J. Mao ag, Z.P. Mao a, S. Marcello bb,bd, J.G. Messchendorp aa, G. Mezzadri w, J. Min a,1, T.J. Min a, R.E. Mitchell s, X.H. Mo a,1, Y.J. Mo f, C. Morales Morales n, G. Morello t, N.Yu. Muchnoi i,5, H. Muramatsu av, P. Musiol d, Y. Nefedov y, F. Nerling j, I.B. Nikolaev i,5, Z. Ning a,1, S. Nisar h, S.L. Niu a,1, X.Y. Niu a, S.L. Olsen ah, Q. Ouyang a,1, S. Pacetti u, Y. Pan ay,1, P. Patteri t, M. Pelizaeus d, H.P. Peng ay,1, K. Peters j,9, J. Pettersson be, J.L. Ping ad, R.G. Ping a, R. Poling av, V. Prasad a, H.R. Qi b, M. Qi ae, S. Qian a,1, C.F. Qiao at, L.Q. Qin ai, N. Qin bf,


Introduction
The decays of the charmonium resonances J /ψ and ψ(3686) [in the following, ψ denotes both charmonium states J /ψ and ψ(3686)] into baryon anti-baryon pairs (BB) in e + e − annihilation have been extensively studied as a favorable test of perturbative quantum chromodynamics (QCD) [1]. These decays are assumed to proceed via the annihilation of the constituent cc pair into three gluons or a virtual photon.
It is interesting that the ψ(3686) decay to a specific final state is strongly suppressed relative to the same final state in J /ψ decay according to the annihilation decay of heavy quarkonium. The ratio of branching fractions for ψ decaying into the same final states is predicted from factorization [2]  This rule was first observed to be violated in the decay of ψ into the final state ρπ . A broad variety of reviews of the relevant theoretical and experimental results [3] conclude that the current theoretical explanations are unsatisfactory. Although the branching fractions for ψ decays into baryon pairs have been measured extensively [4], uncertainties are still large for many decays; e.g.
the world average values of the branching fractions for J /ψ and ψ(3686) → 0¯ 0 are (1.20 ± 0.24) × 10 −3 and (2.07 ± 0.23) × 10 −4 [4], respectively. In particular, ψ → (1385) 0¯ (1385) 0 has not yet been observed. By hadron helicity conservation, the angular distribution of the process e + e − → ψ → BB is expressed as dN d cos θ where θ is the angle between the baryon and the beam directions in the e + e − center-of-mass (CM) system and α is a constant, which has widely been investigated in theory and experiment [5].

BESIII detector and Monte Carlo simulation
BEPCII is a double-ring e + e − collider that has reached a peak luminosity of 10 33 cm −2 s −1 at a CM energy of 3.773 GeV. The cylindrical core of the BESIII detector consists of a helium-based main drift chamber (MDC), a plastic scintillator time-of-flight (TOF) system, and a CsI(Tl) electromagnetic calorimeter (EMC), which are all enclosed in a superconducting solenoidal magnet with a field strength of 1.0 T for the ψ(3686) data and J /ψ data taken in 2009, and 0.9 T for the J /ψ data taken in 2012. The solenoid is supported by an octagonal flux-return yoke with resistive plate counter modules interleaved with steel as muon identifier. The acceptance for charged particles and photons is 93% of the 4π stereo angle, and the charged-particle momentum resolution at 1 GeV/c is 0.5%. The photon energy resolution is 2.5% (5%) at 1.0 GeV in the barrel region (end caps regions). More details about the experimental apparatus can be found in Ref. [17].
The response of the BESIII detector is modeled with Monte Carlo (MC) simulations using a framework based on geant4 [18].
The production of ψ resonances is simulated with the kkmc generator [19], the subsequent decays are processed via evtgen [20] according to the measured branching fractions provided by the Particle Data Group (PDG) [4], and the remaining unmeasured decay modes are generated with lundcharm [21]. To determine the detection efficiencies for ψ → (1385) 0¯ (1385) 0 and 0¯ 0 , one million MC events are generated for each mode taking into account for the angular distribution with α value measured in this analysis. The decays of the baryons (1385) 0 , 0 , and in the signal channels are simulated exclusively, taking into account the angular distributions via evtgen [20], while the anti-baryons are set to decay inclusively.
To achieve higher efficiency and reduce the systematic uncertainty, a single baryon (1385) 0 / 0 tag technique is employed, without including the anti-baryon mode tag due to the imperfection of the simulation related to the effect of annihilation for antiproton. The (1385) 0 / 0 is reconstructed in its decay to π 0 with the subsequent decays → pπ − and π 0 → γ γ . The charged tracks are required to be reconstructed in the MDC with good helix fits and within the angular coverage of the MDC (| cos θ| < 0.93, where θ is the polar angle with respect to the e + beam direction).
Information from the specific energy loss measured in the MDC (dE/dx) and from the TOF are combined to form particle identification (PID) confidence levels for the hypotheses of a pion, kaon, and proton. Each track is assigned to the particle type with the highest confidence level. At least one negatively charged pion and one proton are required. Photons are reconstructed from isolated showers in the EMC. The energy deposited in the nearby TOF counter is included to improve the reconstruction efficiency and energy resolution. Photon energies are required to be greater than 25 MeV in the EMC barrel region (| cos θ| < 0.8) or greater than 50 MeV in the EMC end cap (0.86 < | cos θ| < 0.92). The showers in the angular range between the barrel and the end cap are poorly reconstructed and are excluded from the analysis. Furthermore, the EMC timing of the photon candidate must be in coincidence with collision events, 0 ≤ t ≤ 700 ns, to suppress electronic noise and energy deposits unrelated to the collision events. At least two good photon candidates are required.
In order to reconstruct the π 0 candidates, a one-constraint (1C) kinematic fit is employed for all γ γ combinations, constraining the invariant mass of two photons to the π 0 nominal mass, combined with the requirement of | E|/P π 0 < 0.95, where E is the energy difference between the two photons and P π 0 is the π 0 momentum, and the χ 2 1C < 20 to suppress non-π 0 backgrounds.
where E π 0 and p π 0 are the energy and momentum of the selected π 0 system, and E CM is CM energy. Fig. 1 shows

Background study
The data collected at CM energies of 3.08 GeV (30 pb −1 ) [14]  from the anti-baryon can be wrongly combined with the in the (1385) 0 / 0 reconstruction. As a result, the wrong combination background (WCB) in the π 0 mass spectrum is inevitable. This background is studied by the MC simulation.

Branching fraction
The signal yields for the decays ψ → (1385) 0¯ (1385) 0 and 0¯ 0 are extracted by performing an extended maximum likelihood fit to the M recoil π 0 spectrum. In the fit, the signal shape is represented by the simulated MC shape convolved with a Gaussian function to take into account the mass resolution difference between data and MC simulation. The peaking backgrounds and the wrong combination background are described by the individual shape taken from MC simulation, and the corresponding numbers of background events are fixed according to the individual detection efficiencies and branching fractions [4]. The remaining backgrounds are found to be distributed smoothly in the M recoil π 0 spectrum and are therefore described by a second-order polynomial function. Fig. 3 shows the projection plots of M recoil π 0 for the decays ψ → (1385) 0¯ (1385) 0 and 0¯ 0 , respectively.

The branching fraction can be calculated by
where X stands for the (1385) 0 or 0 baryon, denotes the detection efficiency obtained with the measured α value, N obs is the number of observed signal events, B(X → π 0 ), B( → pπ ) and B(π 0 → γ γ ) are the branching fractions of X → π 0 , → pπ and π 0 → γ γ taken from PDG [4], N ψ is the total number of J /ψ or ψ(3686) events [14,16]. Table 1 summarizes the numbers of observed signal events, the corresponding efficiencies, and branching fractions for the various decays in this measurement with the statistic uncertainty only.

Angular distribution
The values of α for the four decay processes are determined by performing a least squares fit to the cos θ distribution in the range from −0.  Table 1.

Branching fraction
Systematic uncertainties on the branching fractions are mainly due to efficiency differences between data and MC simulation.
They are estimated by comparing the efficiencies of photon, π 0 , and 0 reconstruction between the data and the MC simulation. Additional sources of systematic uncertainties are the fit range, wrong combination, the background shape, and the angular distributions. In addition, the uncertainties of the decay branching fractions of intermediate states and uncertainties of the total number of ψ events are also accounted for in the systematic uncertainty. All of the systematic uncertainties are discussed in detail below.  1. The uncertainty associated with photon detection efficiency is 1.0% per photon, which is determined using the control sample J /ψ → ρπ . Hence, for ψ → (1385) 0¯ (1385) 0 , the value 2.0% is taken as the systematic uncertainty. 2. The systematic uncertainty due to the 1C kinematic fit for the π 0 reconstruction is estimated to be 1.0% with the control sample J /ψ → ρπ .

The uncertainty related to the reconstruction efficiency in
(1385) decays is estimated using the control sample ψ → −¯ + . Here, the reconstruction efficiency includes systematic uncertainties due to tracking, PID, and the vertex fit. A detailed description of this method can be found in Ref. [22]. 4. The 0 reconstruction efficiency, which includes the two photon efficiencies, π 0 reconstruction efficiency and the reconstruction efficiency, is studied with the control sample J /ψ → 0¯ 0 via single and double tag methods. The selection criteria of the charged tracks, and the reconstruction of and 0 candidates are exactly same as those described in Sec. 3.
The 0 reconstruction efficiency is defined as the ratio of the number of events from the double tag 0¯ 0 to that from the single tag. The difference in the 0 reconstruction efficiency between data and MC samples is taken as the systematic uncertainty. 5. In the fits of the M recoil π 0 signal, the uncertainty due to the fitting range is estimated by varying the mass range by ±10 MeV/c 2 for two sides. The resulting differences of signal yields are taken as the systematic uncertainty. 6. The uncertainties due to the background shape arise from the polynomial function and the peaking shape. The former is estimated by the alternative fits with a first or a third-order polynomial function. The latter is estimated by varying the number of normalized events by 1σ . The larger difference is taken as the systematic uncertainty. The total uncertainty related to the background shape is obtained by adding all contributions in quadrature. 7. The systematic uncertainty due to the wrong combination background is estimated by comparing the signal yields between the fits with and without the corresponding component included in the fit. The differences of signal yields are taken as systematic uncertainties.  10. The systematic uncertainties due to the total number of J /ψ or ψ(3686) events are determined with the inclusive hadronic ψ decays. They are 0.5% and 0.6% in [14,16], respectively.
The various systematic uncertainties on the branching fraction measurements are summarized in Table 2. The total systematic uncertainty is obtained by summing the individual contributions in quadrature. 3. In the analysis, the α values are obtained by fitting the cos θ distribution corrected by the detection efficiency. To estimate the systematic uncertainty related to the imperfect simulation of the detection efficiency, the ratio of detection efficiencies as function of cos θ between data and MC simulation is obtained based on the control sample J /ψ → 0¯ 0 with a full event reconstruction. Then, the efficiency corrected cos θ distribution scaled by the ratios of detection efficiencies is refitted. The resulting differences in α are taken as the systematic uncertainty.

Angular distribution
All the systematic uncertainties for the α measurement are summarized in Table 3. The total systematic uncertainty is the quadratic sum of the individual values.
Mode   [7] 0.19 0.28 0.46 0.53 Table 6 Summary of the ratios of branching fraction for testing isospin symmetry. The first uncertainties are the statistical, and the second systematic. J /ψ 1.12 ± 0.01 ± 0.07 0.98 ± 0.01 ± 0.08 0.85 ± 0.02 ± 0.09 ψ(3686) 0.98 ± 0.02 ± 0.07 0.81 ± 0.12 ± 0.12 0.82 ± 0.11 ± 0.11 (1385) 0¯ (1385) 0 and 0¯ 0 are measured. A comparison of the branching fractions between our measurement and previous experiments (PDG average) is summarized in Table 4. The branching fractions for ψ → (1385) 0¯ (1385) 0 are measured for the first time, and the branching fractions for ψ → 0¯ 0 are measured with a good agreement and a much higher precision than the previous results. The measured α values are also compared with the predictions of the theoretical models from Refs. [6,7]. As indicated in Table 5, some of our results disagree significantly with the theoretical predictions, which may imply that the naive prediction of QCD suffers from the approximation that higher-order corrections are not taken into account. As calculated in Ref. [9], the sign for parameter α in ψ → 0¯ 0 mode could be negative if re-scattering effects in the final states are taken into account. However, our results show that α for J /ψ is negative, and is different to the other decay processes in this measurement, which is hard to explain within the existing models. We, therefore, believe that it is of utmost importance to improve the theoretical models to shed further light on the origin of these discrepancies. To test the "12% rule", the ratios of the branching fractions To test isospin symmetry, the ratios of the branching fractions listed in Table 6 are also calculated based on the measurements between the neutral mode and the corresponding charged modes [13] taking into account the cancelation of the common systematic uncertainties. All ratios are within 1σ of the expectation of isospin symmetry.