Study Of Semi-leptonic Decays D_s⁺→η^’e⁺v_e And Radiative Leptonic Decay D_s⁺→γe⁺v_e At BESⅢ

In the Standard Model(SM)of particle physics,Cabibbo-Kobayashi-Maskawa(CKM) matrix which contains information of the strength of the flavour-changing weak^nterac-tion and describes the quark coupling is one of the very important and based parts in SM.semileptonic(leptonic)decays are the prior way to study due to their relatively large branch-ing fraction and simple decay processes.In the Semi-leptonic(leptonic)decay,the strong and weak interaction could be divided well,so that the product of the form factor(decay constant)and the module of CKM matrix can be extracted Parametrically by study their de-cay rates.It could provide important test and calibration for QCD calculation and the unitary of CKM matrix.BESIII has collected e+e-annihilation data corresponding to an integrated luminosity of 3.19 fb-1 at a center-of-mass energy of 4.178 GeV,which is the largest sample of Ds+ Ds-*pair in the world.Both the normal mode and rare mode including new physics will have chance gaining successes.In the ground-states of charmed hadrons,the study of Ds+ is limited by the statistics comparing to the robust experiment analysis of D0/+.So we study the dynamics of Ds+→η(1)+ve to better understand the underlying mechanism of Ds+ decay attributed by the above two aspects.The leptonic and neutrinos don’t exchange the gluon with η(1),the form factor of Ds+→η(1)e+ve could be extracted independently.Recently,multiple theory models are used to calculated f+Ds+→η(1))(0),like Lattice QCD,QCD sum rule assuming the mixing of quark and gluon and light cone QCD sum rule.The measurement of form factor is very crucial to constraint the theory models.Another intriguing thing in this decay is that gluons play an important role in the mech-anism of η-η1 mixing.The mechanism of η-η1 mixing in SU(3)is always interesting,they could express as the octet-single mixing or quark-basis qq(q=u,a)and ss mixing.Due to the U(1)anomaly of QCD,η1 may have a strong coupling to gluons.But present result of determining the existence of gluon from KLOE and LHCb is not precise enough.Using the possible gluon-independent formula cot φp=ΓDs→η′e+ve/ΓDs+→ηe+ve/ΓD+→η′e+ve/ΓD+→ηe+ve,we could measure the mixing angle φp,and help to understand the mechanism of η-η1-gluons mixing.In the prior analysis of Ds+—>η(1)e+ve in the CLEO-c and BESIII experiments,no form factor results but branching fractions are obtained due to the poor statistics.In this analysis,we measure the dynamics of semileptonic decay Ds+→η(1)e+ve,Using differ-ent parameterization method and combination,the product of form factor f+η(1)(0)and |Vcs|can be determined.With the two parameters of series expansion we obtain f+η(0)|Vcs|=0.4455 ± 0.0053stat ± 0.0044syst,f+η1(0)|Vcs|=0.477±0.049stat ± 0.011syst.Imple-mented with double tag technique,we obtain the absolute branching fraction BDs+→ηe+ve=(2.323 ± 0.063stat ± 0.063syst)%,BDs+→η1e+ve=(0.824 ± 0.073stat±0.027syst)%,the precision is improved with a factor of 2 comparing the world average result.Combing the BD+-η(1)e+ve measured by BESIII and a possible gluon-independent formula cot φP=ΓDs→η′e+ve/ΓDs+→ηe+ve/ΓD+→η′e+ve/ΓD+→ηe+ve,φp=(40.1±2.1stat ± 0.7syst)°is determined.In the research of dynamics of particles decay,pure leptonic decay is the simplest way for theoretical calculations and experiment measurement.In the SM,pure leptonic decay P→e+ve is helicity suppressed by a factor me due to the smallness of the positron.The helicity suppression in these processes can be overcome by emitting a radiative photon which makes the process obey conservation of spin,because the photon has spin.As a result,the decay rate of the purely leptonic radiative decay P→γe+ve may be 103—105 times larger than P→ e+ve.Due to the absence of hadrons in the final state,the non-perturbative strong interaction effects in these decays can be factorized and their BF can be calculated.With prediction of the BF sensitivity of 10-3—10-5,it may be detectable at BESIII.BESIII has searched for the D+→γe+ve decay at a center-of-mass(?)=3.773 GeV in 2016.Withe no signal found,they report a upper limit of branching fraction BD+→γe+ve<3.0 x 10-5 based on the Eγ＞0.01 GeV.D+→γe+ve is Cabibbo suppressed decay,while Ds+→γe+ve is Cabibbo favored.The full BF of Ds+→γe+ve is predicted to be of order 10-5—10-4 in the light front quark model,and in the nonrelativistic constituent quark model.The theoretical study indicates that the long-distance contribution described by the vector meson dominance model,may further enhance this decay BF up to order 10-4.More-over,it is predicted to be of order 10-3 within the perturbative quantum chro1odynamics method combining heavy quark effective theory.New physics could be found if the obtained branching fraction is deviated largely from the theoretical calculation.Using the data sample above,we do not observe the signal of D+→γe+ve.The upper limit of partial branching fraction is determined BDs+→γe+ve<1.3 ×10-4 based on Eγ>0.01 GeV.