Renormalization Chain Effect Of The Cross Section Of Nucleon-Meson Reaction With Nucleon-Antinucleon Mixed Loop-Chain Contribution

SU(2) invariant coupling model which based on the invariance of isotopic spin symmetry in strong interaction has been a great success in vicarious kinds of model theories that describing the strong reaction between nucleon and meson. In the theoretical research of SU(2) invariant coupling model, it will be encountered with the divergence difficulty when take account of higher order correction. Theoretically, the divergent terms can be eliminated by renormalization procedures. The key features of renormalization theory are most clearly exhibited in the framework of the so-called chain approximation.This thesis made a study of the differential cross section of elastic collision between proton andπ~- meson, and had an emphasis on the topic of renormalization under mixed chain propagator. Respectively; the thesis dealt the calculation of nucleon under tree-level, loop diagram and chain diagram, and derived an available computation expression of nucleon propagator under chain approximation. It is a hard work to get a precise expression of the propagator function about nucleon propagator with loop diagram and chain diagram contribution. Adopting momentum renormalization program, and with the matrix function expansion method, the physical finite quantity be isolated from unphysical divergence successfully. And then, with the large momentum integral limit method; get the formula about renormalized finite quantity of nucleon propagator with single-loop in a one-dimensional integral form. Then, with the trick of complex variable of function integral, we worked out the renormalized finite quantity of nucleon propagator with single-loop. Furthermore, by utilizing of this result, the circumstance of nucleon propagator with complex chain also is taken into consideration; the convergence of the matrix function on loop propagator is discussed exhaustive, and the precise result of nucleon propagator with complex chain is given. As obtaining the result of single-loop and chain propagator, we have the result plugged in the differential cross section formula. Finally, we get the accurate expression with loop diagram and chain diagram contribution.Radiative correction of the single-loop diagram and complex loop-chain diagram also is discussed in this paper. Since the expression of fermion propagator involves matrix, we have their corrections discussed apart: one is about the 4×4 dimensionγ-p matrix; the other is a four dimensions identity matrix. And we get the information that in lower energy region, the correction is appropriately in tiny value. At last, this thesis made a numeric analysis and comparisons among differential cross sections of tree-level, loop diagram and chain diagram, and gave a graph based on computer plotting. We get a conclusion that it is accurate to describe strong interaction with quantum field perturbation theory in middle-low energy area.This study would offer certain academic references to the further research on SU(2) invariant coupling model and the nuclear physics in terms of theoretical calculations. In addition, it will also provide something valuable to refer on relevant physical process, and on the renormalization calculation orderly with different approaches in perturbation theory of QFT.