The Strong Interactions Potential For Two Quarks

In this paper, with the aid of the ripe theory of quantum field, and with the same way we detruded the analytic expression of interaction potential functions between different fermions for the tree diagram in the momentum space, then transit it into expression in the spatial space via Fourier transform. Considering the interaction between color factors and the symbol of the electrons, we can get the analytic Coulomb potential expression for the strong interactions between the two quarks (quark-antiquark pairs). We obtain the energtic formula of quark and antiquark system through calculating the Schrodinger equation for two quarks. Taking the three heavy flavor quarks (c, b, and t).as example and comparing with the ionization potential of the H atom, we obtain the ground state energy for the three heavy flavor quarks for the tree diagram.Considering that the one loop diagram correction has important influence to theoretical results, the strong interactions potential of the dominant one-loop diagrams for quark-antiquark pairs must to be computed. Using the FeynArts software, we drawn all the effective one-loop diagrams with two or more gluons exchanging. According to the perturbative QCD, the one-loop diagrams of strong interactions for quark-antiquark pairs to be analyzed detailedly. At last, with the help of LoopTools, we simplify expressions and calculate the functions under the apt parameters, and finally get the numerical result for contributions of the potential from the tree diagram and one-loop diagrams in quark and antiquark system.In this paper, it can be found that the obtained Coulomb potential of strong interactions is not infinite in the quark-antiquark systems, even if putting the corrections of the dominate one-loop diagrams, the Coulomb potential is still limited. So, it can not cause the "quark confinement" only by the strong interactions. However, by the same time there is a deep Coulomb potential in the quark-antiquark pairs which makes us to discover the free quark quite difficult.This work have a deep sense for the potential model that is very popular at present, which results only think over the tree diagram, our result given the correction of the dominate one-loop diagrams. Besides, our work helps to select the parameters in confinement potential which has a connection with Coulomb potential.