Establishment of numerical analysis methods in high energy physics

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In order to extract physics information as much as possible from experimental data contaminated by huge backgrounds, a standard method to analyze the experimental data simply compared with analytical prediction of the theory is not sufficient. In order to extract physically meaningful results from such a complicated data and to measure parameters in the model, it is necessary to perform larger scale numerical calculations for both of signal and background channels. This kind of large-scale high-quality numerical method is named "the numerical analysis method".The background of the proton-proton colliding experiment must be completely predicted by QCD. However the lowest level (tree-level) calculation does not have any predictive power for the probability of the event rate. We need both higher order perturbation and non-perturbative calculations for precise predictions of the background behavior. One of the main achievement of the numerical analysis is to establish the method to perform calculations based on the perturbative QCD very efficiently with a numerically stable manner. It includes automatic generation of the scattering amplitudes, loop integration appeared in the radiative corrections and so on.It is also clarified that the numerical analysis method is effective for the higher radiative correction beyond 1-loop level in the electro-weak processes. We apply the numerical analysis method for this subject to pursue the loop integral directly numerically in systematic way. It is confirmed that the loop integration can be performed with more than 10 digit accuracy by using a precision-preserved floating-point calculation and improved numerical integration method. It is improved about 5 digit precision compared with the Monte Carlo integration method. We are ready to approach 2-loop calculations with a systematic way using the numerical analysis method.