The Theoretical Study Of The Form Factors Of B_c Into Charmonium Or ?^'

In this paper,we investigate the decays of Bc meson into charmonium or ?(')within the nonrelativistic QCD effective theory.The main content includes:(1)introductions of NRQCD theory;(2)relativistic corrections to the form factors of Bc into S-wave charmo-nium and some calculations of decay rates;(3)form factors of Bc into ?(')and the related semi-leptonic decay rates.B meson physics is an important part of our physics research.We do the main research on the decay properties of Bc mesons.Bc meson is the only meson made up of two different flavors of heavy quarks(bottom quark and charm quark).The research on its production and decay is undoubtedly a good choice and it provides a certain way to the research of heavy quark physics.At present,it has caused extensive theoretical and experimental research.Due to the "color confining principle",we can only observe the bound state of gluons and quarks in the experiment.And quarks cannot come in the form of freedom.Calculation in the effective field theory when dealing with the bound states is a hot spot in the research of QCD.Because NR.QCD is easy to calculate and the theory is strict,it will be the most widely applied research theory for the research on the productions and decays of the heavy quarkonium states.NRQCD is now widely accepted as the main theoretical model of the research on heavy quarkonium.In this article,we investigate the form factors of Bc meson into S-wave charmoni-um within the nonrelativistic QCD effective theory where both the Bc meson and the charmonium are treated as the nonrelativistic bound states.And then we obtain the next-to-leading order relativistic corrections to the form factors of Bc into S-wave char-monium.In the limit mc/mb?0,we treat the charm quark as a light quark and then at,the maximum recoil point,some form factors are identical which are consistent with the predictions in the large-energy effective theory and the heavy-quark effective theory.In the O(|k|2)and O{|k'|2).we calculate the relativistic corrections to the form factors of Bc into S-wave charmonium and give the specific analytic expression.We study the rela-tivistic corrections of form factors and find that there will be an increase of 15%?25%in the form factors.Considering that the LHCb and ATLAS Collaborations have measured the branching ratios of Bc?J/?Ds+ and Bc?J/?Ds*+,we investigate the channel of Bc?J/?Ds(*)decay within the NRQCD.We apply the form factors of Bc into S-wave charmonium on the next-to-leading order accuracy to these two decay channels,and then we will obtain more accurate results of these decay rates.In these two decay channels,numerical results indicate that the factorizablc diagrams dominate the contribution while the annihilation diagrams and the colour-suppressed diagrams contribute only less than 10 percent.Our results are consistent with the LHCb and ATLAS data results.Besides,we calculate the form factors of Bc meson into ?(')where the Bc meson is treated in NRQCD approach and the light mesons ?(')are treated as light-cone objects.For the form factors of Bc decays into ?('),the mechanism of two gluon transition into?(')dominates the contribution.Here,we consider the ?-?' mixing effect and then we find that there is only qq contribution in the ? while there are qq and gg contributions in the ?'.We give the expression of the form factors at the maximum momentum recoil point,,and give the form factors of Bc into ?(')dependences on the meson momentum fraction and recoil momentum squared.At last,we get the semi-leptonic decay width and branching ratios.