The Spinor Helicity Amplitudes Method In High-energy Physics

Particle physics arise from exploration of the fundamental particle and its construction. After decades of development, physicists established the big bang theory, quantum field theory, quantum chromodynamics and the standard model theory, which generalize the most microscopic particles and forces. The standard model provides a great support for the further development of particle physics. The standard model predicts a set of new fundamental particles. But the standard model is not perfect enough, for the standard model unable to describe the dark matter dark energy and unknown substances.The best experiment device for the fundamental particles structure exploration is the accelerator. Particle physicists found a series of new unknown particle through accelerator, these new findings verify the predictions of the standard model particles. Meanwhile, the new discoveries of accelerator, in turn, promote further development of the standard model of particle physics theory. Among the accelerators, the large hadron collider’s(LHC) contribution to the particle physics is outstanding. The fundamental goal of the large hadron collider is to find the Higgs boson. After running few years, the experimental group of the large hadron collider announced the discovery of the "God particle"-the Higgs boson.We need to compute a lot of the multi-particle’s amplitudes in quantum field theory. After Feynman developed Feynman diagram method, greatly simplifies the calculation of the multi-particle’s amplitudes. But this technique is generally infeasible for complex processes. Calculation items is propotional to the square of the nmber of Feynman diagrams’items. The helicity amplitudes method was first used in papers by J.D. Bjorken and M. Chen.We have calculated three kinds of the helicity amplitudes in the paper. For the massless fermions situation, we handle it very easy through spinor helicity amplitude method, and we also deal with scattering amplitudes with polarization vectors by following the definition of Xu, Zhang and Chang. However, for the massive spinor case, we used a special representation in the Ref. to define massive spinor products. In this approach, information with respect to the polarization of the fermion spins is contained in the definition of the spinor products. In this paper we only discussed the simple situations for the tree-level amplitude. For the one-loop amplitudes, one can find more details in these papers. The purpose of this paper is to provide a brief and basic introduction to spinor helicity amplitude method, which is widely used in the calculation of high energy physics.