| Charm baryon ?c+is the lightest member of the charm baryon family.Its quark components are a pair of light quarks(u,d)and a heavy charm quark(c).In the naive spectator model,?c+ decays proceed only through the weak amplitudes,namely at leading order c?W+s and c? W+d.Therefore,the study of ?c+ decay is helpful to understand the dynamic mechanism of weak interaction in baryon decay.The knowledge of the ?c+charm baryon and the charm baryon spectrum will provide important input information to the study of the bottom baryon spectrum and the decay of the bottom baryon into the ?c+charm baryon.The hadronic weak decay of the single charm baryon does not conserve the parity.The two-body decay ?c+? A7r+is dominated by the weak interaction mediated by a W boson,namely c?W+s.The final state of ? and ? particles can be in S-wave and P-wave.Through the final state of the charm baryon decay,the polarization of the charm baryon can be studied by measuring its decay asymmetry parameter.The angular distribution of the decayed ? particle takes the the form of dN/d cos?? ? 1+???+cos??,where ??? is a decay asymmetric parameter.Baryons composed of u,d,s and c quarks belong to the SU(4)group.The subscript c in ?c+ means it carries a single c quark,and the superscript+means it carries a positive charge.It belongs to 20 mixed multiplets in the SU(4)group,and the quark model assign its spin as JP=1/2+.The spin of ?c+ was once measured by the NA32 experimental group.The charm baryon ?c+ they detected was produced in the fixed target experiment ?-Cu??c+ DX,and the decay ?c+?pK-?+was used to reconstruct the charm baryon,and a total of 160 ?c+ candidates were selected.Due to the limited statistics of experimental data,the spin of ?c+ cannot be determined conclusively as J=1/2.Now,the ?c+ particle spin quantum number in the particle data group(PDG)comes from the quark model prediction.So far,there is no direct experimental measurement of its spin information.The helicity amplitude method was commonly used in experimental data,and we use this method to analyze the spin hypothesis of ?c+.The advantage of the helicity amplitude is that the energy dependence part and the angular dependence part can be separated,and the angular distribution formalism can be derived independently,so that it is applicable to the study of cascade decay.The experimental data used in the measurement was collected by the BES? at the center of mass energy(?)=4.6GeV with integral luminosity 587 pb-1,we use the reaction e+e-? ?c+?c-to select the ?c+?c-charm baryon pair.The single-tag method is used to reconstruct the ?c+?c-baryon pair,via the ?c+ decays to pKS0,??+,?0?+and ?+?0.We use the maximum likelihood method to determine the spin J of ?c+.The formula of the joint angular distribution is obtained by performing the helicity amplitude analysis.After fitting the experimental data and obtained the model parameters,we use the TOY MC method to test the spin hypotheses.It is found that the spin 1/2 hypothesis is more preferable than the spin 3/2,and its statistical significance is determined to be 6 standard deviations.This is for the first time to determine the spin of?c+as 1/2.which is consistent with the expectation of the naive quark model.By taking into consideration of systematic uncertainties,the significance of ?c+ spin J=1/2 determined to be 6.07-0.30+0.38 standard deviations.The establishment of ?c+spin quantum number helps us to study the properties of the charm baryon and the bottom quark baryon.Below the DD threshold,the charmonium states include ?c,J/?,hc,?cJ(J=0,1,2)and ?(2S),and most branching fractions of their decays have been well measured exper-imentally.The charmonium decays play an important role to study the strong interaction and non-perturbation QCD properties.For example,looking for a new charm elemen-t state,determining the internal structure of the established charmonium states,precise measurement of their masses and widths,searching for the transition between charmoni-um states(radiation transition or hadron transition),and searching for new decay channel,will help us to understand the strong interactions in the charmonium decays and their decay mechanism.The BESIII is particularly suitable for the study of light and heavy charmonium states.The research on the lower charmonium states below the ?(2S)de-cay enjoy the large statistics and the clean background.One main physical goals of the BESIII is to study the decay properties of the charmonium state below the open char-m threshold.?/(2S)can radioactively decay to ?cJ,J/? and ?c with large branching fractions,which makes it especially suitable for studying the spectrum and transition be-tween charmonium states.The constituent quark bound in ?cJ is cc,which constitutes the spin triplet state of the charmonium state.We will detect ?cJ from the radiation de-cay of ?(2S),and then study ?cJ??? strong decay.The spin parity of ?cJ is J++.In the leading order of pQCD theory,the hadron decay of ?cJ described as annihila-tion of cc into two gluons,and then followed by the hadronization into a light hadronic final state.If the mass of the strange quark is ignored,the decay branching fraction of?cJ??? is governed by the law of conservation of helicity,and the decay branching fraction of ?cJ will be greatly suppressed.This leads to the difficulty that theoretical cal-culation of the branching fraction is much smaller than the experimental measurement.Especially for the decay of ?c1???,considering the requirement of identical particle symmetry,the decay branching fraction is further suppressed.The theoretical calculation is more than an order of magnitude lower than the branching fraction of the experimental measurement.We use the helicity amplitude to analyze the four-level cascade decay of?(2S)???cJ,?cJ???,??K+K-K+K-,and consider subtracting non-resonant contributions and the interference between them.The data in this analysis includes a total of 447 million ?(2S)data collected by the BESIII detector at the center of mass energy of 3.686 GeV.Then we use the maximum likelihood method to fit the data.The measured branching fraction of ?cJ??? are listed as follows,in which the second and third term are statistical and systematic uncertainties.The decay of the XcJ meson will help us to examine QCD and understand the internal structure of the charm.Br[?c0???]=(8.1±0.2±0.4)×10-4,Br[?c1???]=(4.5 ± 0.1 ± 0.3)×10-4,Br[?c2???]=(12.6±0.2±1.0)×10-4.The mass and width of ?c0 measurement results are:?c0 mass:3414.60 ± 0.30 ± 0.95 MeV,?c0 width:10.98 ± 0.55 ± 1.81 MeV.Correspondingly,the PDG value of the mass of ?c0 is 3414.71±0.30 MeV and width is 10.8±0.6 MeV.It can be seen that the statistical uncertainty of ?c0 mass is comparable to the accuracy of the PDG average value,while the statistical accuracy of width is better than PDG value,and the measurement result is consistent with the PDG value within one standard deviation if the system uncertainty is involved.For the ?c0???(0+?1-1-)decay channel,the measurement result of the helicity amplitude ratio is:|F1,1|/|F0,0|=0.274± 0.003±0.001.The measurement results of ?c2???(2+?1-1-)are as follows:|F0,1|/|F0,0|=1.285±0.217 ± 0.039,|F0,0|/|F0,0|=1.365±0.206 ± 0.058,|F1,1|/|F0,0|=1.011±0.175±0.126.The measurement result of the helicity amplitude ratio of ?0??? are consistent with the pQCD prediction within one standard deviation.But the prediction results of pQCD theory and 3P0 model are both quite different from the measurement results of ?c2???decay.The measurement of the branching fractions of ?cJ help us to understand its decay mechanism.The mass and width of ?c0 will help us to understand the structure of the charmonium.The measurements of the helicity amplitude ratio can be used to test the pQCD and 3P0 model predictions.These will improve our understanding of the physics of ?cJ. |
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