Analytic Structure Of One-loop Coefficients And Cross Section Evaluation Based On Unitarity Cut

In the computation of one-loop scattering amplitudes, the unitarity cut method is a great progress. Based on applications of this method, in this thesis we introduces two aspects of our work. On the one hand, by the unitarity cut method, analytic expressions of one-loop coefficients have been given in spinor forms. In this thesis, we present one-loop coefficients of various bases in Lorentz-invariant contraction forms of external momenta. Using these forms, the analytic structure of these coefficients becomes manifest. Firstly, coefficients of bases contain only second-type singularities while the first-type singularities are included inside scalar bases. Secondly, the highest degree of each singularity is correlated with the degree of the inner momentum in the numerator. Thirdly, the same singularities will appear in different coefficients, thus our explicit results could be used to provide a clear physical picture under various limits (such as soft or collinear limits) when combining contributions from all bases.On the other hand, we propose a new method to calculate cross sections, which is in-spired by the reduced phase space integration of one-loop unitarity cut. The new method re-duces one constrained three-dimension momentum space integration to an one-dimensional integration, plus one possible Feynman parameter integration. There is no need to specify a reference framework in our calculation, since every step is manifestly Lorentz invariant by the new method. Here we have focused on massless and massive particles in4D. There is no need to carve out a complicated integration region because it is only the functions of mass and energy.