Search for the light hadron decay

With a data sample corresponding to an integrated luminosity of 11.5 fb − 1 collected with the BESIII detector operating at the BEPCII storage ring, for the ﬁrst time the light hadron decay χ c 1 (3872) → π + π − η is searched for. While no signiﬁcant signal is observed, the upper limits at the 90% conﬁdence level for σ [ e + e − → γχ c 1 (3872)] B [ χ c 1 (3872) → π + π − η ] at

h Also at School of Physics and Electronics, Hunan University, Changsha 410082, China i Also at Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, China j Also at Frontiers Science Center for Rare Isotopes, Lanzhou University, Lanzhou 730000, People's Republic of China k Also at Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou 730000, People's Republic of China l Also at the Department of Mathematical Sciences, IBA, Karachi 75270, Pakistan m Also at Hubei University of Automotive Technology, Shiyan 442002, People's Republic of China (Dated: January 22, 2024) With a data sample corresponding to an integrated luminosity of 11.5 fb −1 collected with the BESIII detector operating at the BEPCII storage ring, for the first time the light hadron decay χc1(3872) → π + π − η is searched for.While no significant signal is observed, the upper limits at the 90% confidence level for σ[e + e − → γχc1(3872)]B[χc1(3872) → π + π − η] at center-of-mass energies from 4.13 to 4.34 GeV are determined.By normalizing to the χc1(3872) → π + π − J/ψ decay channel, a 90% confidence level upper limit for the branching fraction ratio R = B[χc1(3872) → π + π − η]/B[χc1(3872) → π + π − J/ψ] < 0.12 is given.These measurements provide important inputs for understanding the internal structure of the χc1(3872) resonance.
Since its discovery in 2003 [1], the χ c1 (3872) resonance has been widely considered an exotic hadron state beyond the conventional baryon and meson picture [2].At the moment, several theoretical models have been proposed that describe the χ c1 (3872) as a tetraquark state [3], a P -wave radially excited charmonium state [4], or a D 0 D * 0 meson molecule [5,6], the latter one being favored due to the χ c1 (3872) mass being very close to the D 0 D * 0 mass threshold [7].However, the production rate of χ c1 (3872) in high energy pp/pp collisions is comparable to that of the ψ(2S) [8], which does not agree with a pure molecule prediction [9].To explain this, the χ c1 (3872) has been proposed to be a charmonium-hadronic molecule mixture state [10].
To further understand the nature of the χ c1 (3872), more experimental studies about its decay channels are required.By taking measurements from several experiments into account, Ref. [21] has performed a global analysis on the BFs of its decays, which indicates that (32 +18 −32 )% of the BFs have not yet been observed in experiment.The BESIII experiment accumulated the world's largest e + e − annihilation data from √ s = 4.01 to 4.95 GeV and offers an opportunity to further investigate decays of χ c1 (3872), shedding light on the wave function of the χ c1 (3872) state.Previously, the BESIII collaboration has already established the e + e − → γχ c1 (3872) production method with large significance [14,15].
The BESIII detector [26] records symmetric e + e − collisions provided by the BEPCII storage ring [27], which operates in the c.m. energy range from 2.0 to 4.95 GeV.BESIII has collected large data samples in this energy region [28].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 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 (0.9 T in 2012) magnetic field.The solenoid is supported by an octagonal flux-return 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 110 ps.The end-cap TOF system was upgraded in 2015 using multi-gap resistive plate chamber technology, providing a time resolution of 60 ps [29].
Simulated data samples produced with a GEANT4based [30] Monte Carlo (MC) package, which includes the ge-ometric description of the BESIII detector and the detector response, are used to determine detection efficiencies, optimize event selection, and estimate backgrounds.For the signal process, 100,000 e + e − → γχ c1 (3872) events are generated at each c.m. energy, assuming an E1 radiative transition process which has been verified by BESIII data [17].The possible Initial-State-Radiation (ISR) is simulated with KKMC [31], incorporating the √ s-dependent production cross section of e + e − → γχ c1 (3872) [17].The maximum ISR photon energy is set according to the production threshold (3.9 GeV) of the γχ c1 (3872) system.The decay of χ c1 (3872) → π + π − η and η → γγ is generated by EVTGEN [32] with the phasespace model.The other decay η → π + π − π 0 is generated according to the Dalitz-distribution measured by BESIII [33].The final-state-radiation of charged particles is simulated with the PHOTOS package [34].
To study the possible background, an inclusive MC sample is used, including the production of open charm processes, the ISR production of vector charmonium(-like) states, and the continuum processes incorporated in KKMC [31].All particle decays are modeled with EVTGEN [32] using BFs taken from the Particle Data Group (PDG) [7], when available, or otherwise modelled with LUNDCHARM [35] for charmonium states and PYTHIA [36] for other hadrons.The equivalent integrated luminosity of the inclusive MC sample is 10 times that of data at √ s = 4178.0MeV, and is of equal size to data at other c.m. energies.
Charged tracks detected in the MDC are required to be within a polar angle (θ) range of |cosθ| < 0.93, where θ is defined with respect to the z-axis, which is the symmetry axis of the MDC.For each charged track, the distance of closest approach to the interaction point must be less than 10 cm along the z-axis, |V z |, and less than 1 cm in the transverse plane, |V xy |.Photon candidates are identified using showers in the EMC.The deposited energy of each shower must be more than 25 MeV in the barrel region (| cos θ| < 0.80) and more than 50 MeV in the end cap region (0.86 < | cos θ| < 0.92).To exclude showers that originate from charged tracks, the angle subtended by the EMC shower and the position of the closest charged track at the EMC must be greater than 10 degrees.To suppress electronic noise and showers unrelated to the event, the EMC time with respect to the event start time is required to be within [0, 700] ns.
For the process of e + e − → γχ c1 (3872) → γπ + π − η with η → γγ, the number of charged tracks is required to be two with zero net charge in an event, and both tracks are assigned as pion candidates.We also require at least three good photon candidates for each event.To improve the resolution and reduce backgrounds, a five-constraint (5C) kinematic fit is performed.Four constraints come from the four-momentum conservation of the final state particles equal to the initial e + e − colliding beams, and the additional one comes from the η mass.For possible multi-combination of photon candidates, the one with the minimum χ 2 5C is retained, and χ 2 5C < 16 is further required.This value is determined by optimizing the Figure-of-Merit (FOM) S/ √ S + B, where S represents the number of signal events from signal MC simulation, and B is the number of background events estimated from the inclusive MC sample.
For the process of e + e − → γχ c1 (3872) → γπ + π − η with η → π + π − π 0 and π 0 → γγ, the number of charged tracks is required to be four with zero net charge in an event.Due to possible kaon background contamination, particle identification (PID) for charged tracks, combining measurements of the ionization energy loss (dE/dx) in the MDC and the flight time in the TOF to evaluate the likelihoods L(h) (h = p, K, π) for each hadron (h) hypothesis, is applied.At least one of the pion candidates is required to satisfy L(π) > L(K).We also require at least three good photon candidates for each event.To improve the resolution and reduce backgrounds, a 5C kinematic fit is performed, where four constraints come from the four-momentum conservation of the final state particles equal to the initial e + e − colliding beams, and the additional one comes from the η mass.For possible multicombination due to multi-pion and multi-photon candidates in an event, the one with the minimum χ 2 5C is retained and χ 2 5C < 30 is further required.This value is determined by optimizing the FOM.The π 0 mass window is defined as Through the study of the inclusive MC sample, we find that the main backgrounds come from e + e − → π + π − π + π − π 0 .Events satisfying 125.6 < M (γ rad γ 1 ) < 150.0 MeV/c 2 and 115.7 < M (γ rad γ 2 ) < 160.0 MeV/c 2 are rejected to suppress this background, where γ 1(2) denote the two photons from π 0 decay (sorted by energies) and M (γ rad γ 1(2) ) is the invariant mass of γ rad and γ 1(2) combination.The different mass window vetos are optimized by FOM.After imposing the selection criteria above, the obtained M (π + π − η) distribution from the full data set is shown in Fig. 1 (b).There is no obvious χ c1 (3872) signal observed, and the background level is lower than that of the η → γγ mode.The background also produces a smooth distribution in the signal region from the study of the inclusive MC sample.
For the two decay channels of η, a simultaneous fit to the M (π + π − η) distribution is performed to extract the signal yield at each c.m. energy.In the fit, the signal probabilitydensity-function is parameterized with an MC simulated shape (with χ c1 (3872) mass and width taken from PDG [7]), convolved with a Gaussian function which represents the resolution difference between data and MC simulation.The mean and standard deviation of the Gaussian function are fixed to the values obtained from a control sample of χ c1 (1P ) → π + π − η.The background shape is parameterized as a 2ndorder polynomial function.In the simultaneous fit, the production rate for e + e − → γχ c1 (3872) → γπ + π − η is a common parameter, and the signal yields for η → γγ and π + π − π 0 modes are weighted according to the detection efficiencies and BFs.Appendix A shows the fit results at each c.m. energy, and the fit results to the full data set are shown in Fig. 1.

The production cross section
where N obs i is the number of observed signal events from the i-th data set, L int is the corresponding integrated luminosity, (1 + δ) is the radiative correction factor calculated by the KKMC MC generator [31], ε j B j (j = 1, 2) is the product of detection efficiency and BF for the η → γγ and π + π − π 0 modes, and N sig i is the number of produced signal events after considering the detection efficiencies and BFs.Since no obvious signal is seen in the M (π + π − η) distribution, an upper limit for σ[e + e − → γχ c1 (3872)]B[χ c1 (3872) → π + π − η] is set using the Bayesian approach [37].By scanning the likelihood function L(n) in the fit, the number of events corresponding to 90% of the integral ) is estimated as the upper limit (N up ) for the signal yield.The systematic uncertainty is considered by applying a Gaussian (with standard deviation equal to the total systematic uncertainty) smearing to the likelihood function.The systematic uncertainties in the cross section measurement come from integrated luminosity measurements, photon detection, tracking efficiencies, PID, η/π 0 reconstruction, kinematic fit, quoted BFs, radiative correction factor, signal extraction, and MC decay model.
The integrated luminosities of the data sets are measured using large-angle Bhabha scattering events, with a systematic uncertainty of 0.66% [38].The photon detection uncertainty is estimated to be 1.0% per photon by studying J/ψ → ρπ events [39].The tracking efficiency uncertainty is estimated to be 1.0% per pion by studying J/ψ → ppπ + π − events [40].For the decay with η → π + π − π 0 , we use PID for the pion selection, and at least one of the pion candidates is required to be identified.The PID efficiency of pions can be calculated as 1 − (1 − p) 4 , where p represents the PID efficiency for a single pion.Since p is very high (> 0.8) at BESIII, the uncertainty due to PID can be safely ignored [41].
The systematic uncertainty due to η/π 0 reconstruction is estimated to be 1.0% per η/π 0 , by studying a high purity control sample of J/ψ → ppη (ppπ 0 ) events [42].For the uncertainty from the kinematic fit, we use a helix parameter correction method [43].A correction is performed on the track parameters and half of the efficiency difference with and with-out the correction is taken as the systematic uncertainty.
For the radiative correction factor calculation, the cross section of e + e − → γχ c1 (3872) is input from Ref. [17], where a Breit-Wigner resonance Y (4200) (M [Y (4200)] = 4200.6+7.9 −13.3 ± 3.0 MeV/c 2 and Γ[Y (4200)] = 115 +38 −26 ± 12 MeV) is employed to describe the cross section line shape.To estimate the potential effect due to the uncertainty of the resonance, a two-dimensional Gaussian sampling (possible correlation has been considered) method is used.We generate 300 groups of Y (4200) resonance parameters (mass and width) and recalculate the (1 + δ)ε.With the weighting method given in Ref. [44], we get the distribution of (1+δ)ε according to the Gaussian sampling.A fit to this distribution yields the standard deviation of (1+δ)ε, which is taken as the corresponding systematic uncertainty.
The systematic uncertainty due to signal extraction is dominated by the signal and background shapes.For the signal shape, the χ c1 (3872) is simulated with resonance parameters (mass and width) taken from PDG.We vary the resonance parameters by ±1σ in the simulation.The background shape is varied from a first-order polynomial to a second-order polynomial.By repeating these fits, we conservatively take the largest upper limit for signal yield as the final result.
Appendix B summarizes the systematic uncertainties at each c.m. energy.To combine the systematic uncertainties between two η decay modes, a weighted average is taken as where ∆ tot is the combined total systematic uncertainty for each source, ω i and ∆ i are the corresponding weight and systematic uncertainty, ǫ i and B i are the efficiency and BF for the i-th decay mode of η, and ρ ij is the correlation coefficient between them.We take ρ ij = 1 for the same systematic source, otherwise ρ ij = 0. Assuming all these sources are independent, the total systematic uncertainties are added in quadrature for different sources, which is around 7%. Table I lists the total systematic uncertainties in the cross section measurement.is the integrated luminosity, ε η→γγ (π + π − π 0 ) is detection efficiency for η → γγ (π + π − π 0 ) modes, (1 + δ) is the radiative correction factor, Nsig is the efficiency and branching fraction corrected production yield of χc1(3872) → π + π − η signal events in e + e − → γχc1(3872) and N up sig is the corresponding upper limit at the 90% C.L., (σB) is the product of the cross section σ[e + e − → γχc1(3872)] and BF B[χc1(3872) → π + π − η] and (σB) up is the corresponding upper limit at the 90% C.L., and ∆ denotes the total systematic uncertainty in the cross section measurement.
In the BF ratio measurement, systematic uncertainties in- cluding the integrated luminosity, e + e − → γχ c1 (3872) production cross section, radiative correction factor, tracking efficiency and photon detection, are cancelled.The remaining systematic uncertainties come from extra photon and track detection, BF, η (π 0 ) reconstruction, J/ψ mass window, MC decay model, signal extraction, and the uncertainty of χ c1 (3872) signal events in the π + π − J/ψ mode.
All the systematic uncertainties for the R measurement are listed in Table II.The contributions from η → γγ and π + π − π 0 modes are combined using the same method as the cross section measurement.Assuming all these sources are independent, the total systematic uncertainty is calculated by adding each individual source in quadrature.Since our measurement obviously finds the BF to be lower than 1%, this could have an impact on the explanation of the internal structure of the χ c1 (3872) .
The BESIII Collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support.

a
Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia b Also at the Novosibirsk State University, Novosibirsk, 630090, Russia c Also at the NRC "Kurchatov Institute", PNPI, 188300, Gatchina, Russia d Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany e Also at Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education; Shanghai Key Laboratory for Particle Physics and Cosmology; Institute of Nuclear and Particle Physics, Shanghai 200240, People's Republic of China f Also at Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern Physics, Fudan University, Shanghai 200443, People's Republic of China g Also at State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, People's Republic of China

FIG. 1 .
FIG.1.The M (π + π − η) distributions from η → γγ mode (a) and π + π − π 0 mode (b) with fit curves overlaid.Dots with error bars are data, the blue solid curves are the MC signal with arbitrary normalization, the red solid curves are the fit result, the blue dashed curves are the background components, and the green shaded histograms are the backgrounds estimated from the inclusive MC sample.

4 FIG. 2 .
FIG.2.The production cross section of e + e − → γχc1(3872) times the BF of χc1(3872) → π + π − η as a function of center-of-mass energy.Blue triangles are the upper limit for (σB) up at 90% C.L., and the red dots with error bars are the nominal result.

1 FIG. 3 .
FIG.3.The likelihood curve obtained by scanning various R values in the fit.The red dot-dashed curve is from the nominal fit, the blue solid curve is the corresponding distribution smeared by a Gaussian function with resolution equal to the total systematic uncertainty, and the gray shaded area indicates 90% of the likelihood integral.

2 )FIG. 4 .
FIG. 4. The fit results at c.m. energies ranging from√ s = 4128.8 to 4244.0 MeV.The signal MC shape convolved with a Gaussian function is used to fit the invariant mass spectrum of π + π − η at each energy.Black dots with error bars are data, the red solid curve shows the fit result, the blue dashed curve is the signal shape with arbitrary normalization and the green dashed curve is the background contribution.

FIG. 5 .
FIG. 5.The fit results at c.m. energies ranging from√ s = 4258.0 to 4337.9 MeV.The signal MC shape convolved with a Gaussian function is used to fit the invariant mass spectrum of π + π − η at each energy.Black dots with error bars are data, the red solid curve shows the fit result, the blue dashed curve is the signal shape with arbitrary normalization and the green dashed curve is the background contribution.