Z⁰ Boson Decays To B_c^* Meson And Its Uncertainties

The meson B_c , being a unique and very important meson in the standard model, contains two different heavy flavors. It is stable to the strong and electromagnetic interactions but not to weak interaction, i.e., it mainly decay to a lighter flavor by weak interaction so that it happen to have a typical (quite long) time. Therefore the B_c meson is an ideal platform to test the quantum chromodynamics (QCD) theory. Since it was first observed at TEVATRON by CDF Collaboration in 1998, the B_c meson is attracting more and wide investigation. Especially recent years, many progresses have been made for the theoretical study of B_c physics, some domestic experts deeply and systematical investigate the hadronic production properties of B_c meson at high energy colliders as LHC and TEVATRON, which cause significant international effect. Meanwhile, the world scientists are planning to built higher energy and luminosity e + e? collider, such as the Internal Linear Collider (ILC) and Z -factory, its collision energy will be up to 1 TeV or will restrict to the energy region of Z~0 meson and its luminosity can be raised up to L∝1034 cm ?2 s?1 even higher. Comparing with the hadronic colliders, the e + e? collider have has its own advantages, mainly because of its lower background, so the ILC shall provide another useful platform to study the the properties of the doubly heavy B_c meson. For this purpose, we perform the calculation to the production of B_c meson through Z~0 decays, and discuss the uncertainty of total decay width and differential width in detail. The result will provide important support for the theotists and experimentalists who investigate the properties of B_c meson at the e + e? collider.Recently, physicists have developed an important approach to investigate the production and annihilate of heavy quarkonium. The approach is called Non-relativistic quantum chromodynamics ( NRQCD ). Its core is the NRQCD factorization formulism, In this formulism, the cross section and/or decay width are expressed as the sum of the products of the short distance coefficients and the long distance matrix elements. The short distance coefficients can be calculated perturbatively, while the matrix elements can only be gained by non-perturbative ways such as the potential model, QCD sum rule, lattice QCD and experimental fitting. Researches on the heavy quarkonium production and annihilate with NRQCD factorization formulism are important both for detecting these heavy hadron in experiment and for testing the correctness of NRQCD factorization formulism.In this thesis, we calculate the process Z~0→B_c+b+(c|-) in the framework of the effective theory of NRQCD. Where the B_c and B_c~* is the ground state and the first exited state of (cb)~-quarkonium respectively. In the process of factorization, the short distance coefficients calculated using perturbation-expansion, and the long distance calculated by potential model approximation.Under the'New Trace Amplitude Approach', we calculate the amplitude square and obtain the analytic solution of the amplitude square. Those analytic solution shall provide sound foundation for simulating the production of B_c meson at the e + e? collider in the furture. From the result, we obtain the total decay width for the (cb)-quarkonium production through Z 0 boson decays, i.e. If the Z 0 is enough then we will observe the B_c meson on experiment, the ILC and Z-factory will meet the requirement. At the same time, we study the factors which cause the uncertainty of decay width, especially the both factors mb and mc in detail.