Study Of D^0（+）→π^-（0）μ⁺v_μ And D_S^t→τ⁺(ρ⁺（?）v_τ And Test For Lepton Flavor Universality At BESⅢ

Leptonic and semileptonic decays have been well studied in the Standard Model.Their decay rates are proportional to the product of the quark mixing matrix element,which describing the mixing between quark flavor eigenstates and weak interaction eigenstates,and the decay constant or form factor which characterizes the strong in-teraction between initial and final state quarks。The mass of the charm quark is neither light enough for pertubative expansion,nor heavy enough for the application of heavy quark theory,so precision of the theoretical calculations on decay constants and form factors concerning charm mesons have always been limited.In recent years,the rapid development of computer resources has led to great improvement of the Lattice quan-tum chromodynamics(LQCD),which is giving more and more accurate calculations on the decay constants and form factors.As a result,improved study for charm meson lep-tonic and semileptonic decays is needed to calibrate the LQCD calculations and to better determine the quark mixing matrix element with more precise inputs.Meanwhile,in the Standard Model different generations of lepton should couple with the gauge bosons with same strength,known as lepton flavor universality(LFU).By calculating the ratio of the branching fractions(BFs)to different generations of lepton,most of the uncer-tainties introduced in the hardonic current can be cancelled out,making LFU an ideal testbed for the Standard Model.With the evidence of LFU violation observed in recent experiments on B meson semileptonic decays,test for LFU in charm meson decays becomes particularly important.Using a data sample corresponding to an integrated luminosity of 2.93 fb-1 taken at a center-of-mass energy of 3.773 GeV with the BESIII detector operated at the BEPCII collider,we perform an analysis of the semi-leptonic decays D0(+)→π-(0)μ+vμ.The branching fractions of D0→π-μ+vμ and D+→π0μ+vμ are measured to be(0.272±0.008stat.±0.006syst.)%and(0.350±0.011stat.±0.010syst.)%,respectively,where the former is of much improved precision compared to previous results and the latter is determined for the first time.Using these results along with previous BE-SIII measurements of DO(+)→π-(0)e+ve,we calculate the branching fraction ratios to be R0≡BD0→π-μ+vμ/B0→π-e+ve=0.922±0.030stat.±0.022syst.and R+≡BD+→π0μ+vμ/BD+→π0e+ve=0.964±0.037stat.±0.026syst.,which are compatible with the theoretical expectation of lepton flavor universality within 1.7σ and 0.5σ,respec-tively.We also examine the branching fraction ratios in different four-momentum trans-fer square regions,and find no significant deviations from the standard model predic-tionsBy analyzing a data sample of 6.32 fb-1 collected at a center-of-mass energy from 4.18 to 4.23 GeV with the BESIII detector,we measure the branching fraction of Ds+→τ+vτ to be(5.22±0.21stat.±0.17syst.)%with the τ+→ρ+v decay.The measured branching fraction is well consistent with previous measurements from the CLEO-c,Belle,BaBar and BESIII(with other τ decays modes)experiments.Combining with the CKM matrix element|Vcs|given by the CKMFitter,the Ds+ decay constant is calculated to be 255.8±6.1atat.±3.9syst.MeV.Reversely,combining with the fDs calculated by the latest LQCD,|Vcs|is calculated to be 0.997±0.024stat.±0.015syst..We also search for lepton universality,no evidence is found.Our measurements provide important information to calibrate the LQCD calculations on fDs+ and to test the CKM matrix unitarity and the lepton universality with better precision.