The adjacent matrix method for identifying isomorphism to planar kinematic chain with multiple joints and higher pairs is presented. The topological invariants of the planar kinematic chain can be calculated and compa...The adjacent matrix method for identifying isomorphism to planar kinematic chain with multiple joints and higher pairs is presented. The topological invariants of the planar kinematic chain can be calculated and compared by adjacent matrix. The quantity of calculation can be reduced effectively using the several divisions of bars and the reconfiguration of the adjacent matrix. As two structural characteristics of adjacent matrix, the number of division and division code are presented. It can be identified that two kinematic chains are isomorphic or not by comparing the structural characteristics of their adjacent matrixes using a method called matching row-to-row. This method may be applied to the planar linkage chain too. So, the methods of identifying isomorphism are unified in the planar kinematic chain that has or hasn＇t higher pairs with or without multiple joints. And it has some characters such as visual, simple and convenient for processing by computer, and so on.展开更多
The heavy constituent quark pair of the heavy quarkonium is produced perturbatively and subsequently undergoes hadronization into the bound state non-perturbatively.The production of the heavy quarkonium is essential ...The heavy constituent quark pair of the heavy quarkonium is produced perturbatively and subsequently undergoes hadronization into the bound state non-perturbatively.The production of the heavy quarkonium is essential to testing our understanding of quantum chromodynamics(QCD)in both perturbative and non-perturbative aspects.The electron-positron collider will provide a suitable platform for the precise study of the heavy quarkonium.The higher excited heavy quarkonium may contribute significantly to the ground states,which should be considered for sound estimation.We study the production rates of the higher excited states quarkonium pair in■at the future Z factory under the non-relativistic QCD(NRQCD)framework,where the■represents the color-singlet states■The differential angle distribution of cross sections■is given.We also discuss the uncertainties of cross sections caused by the varying quark masses and the renormalization scaleμ.We show that significant numbers of events for pairs of higher excited state quarkonia can be generated at the super Z factory.展开更多
文摘The adjacent matrix method for identifying isomorphism to planar kinematic chain with multiple joints and higher pairs is presented. The topological invariants of the planar kinematic chain can be calculated and compared by adjacent matrix. The quantity of calculation can be reduced effectively using the several divisions of bars and the reconfiguration of the adjacent matrix. As two structural characteristics of adjacent matrix, the number of division and division code are presented. It can be identified that two kinematic chains are isomorphic or not by comparing the structural characteristics of their adjacent matrixes using a method called matching row-to-row. This method may be applied to the planar linkage chain too. So, the methods of identifying isomorphism are unified in the planar kinematic chain that has or hasn＇t higher pairs with or without multiple joints. And it has some characters such as visual, simple and convenient for processing by computer, and so on.
基金Supported by the Scientific Research Fund of Chengdu University of Information Technology(KYTZ2022113)the National Key Research and Development Plan of China,Key Project of Cyberspace Security Governance(2022YFB3103103)。
文摘The heavy constituent quark pair of the heavy quarkonium is produced perturbatively and subsequently undergoes hadronization into the bound state non-perturbatively.The production of the heavy quarkonium is essential to testing our understanding of quantum chromodynamics(QCD)in both perturbative and non-perturbative aspects.The electron-positron collider will provide a suitable platform for the precise study of the heavy quarkonium.The higher excited heavy quarkonium may contribute significantly to the ground states,which should be considered for sound estimation.We study the production rates of the higher excited states quarkonium pair in■at the future Z factory under the non-relativistic QCD(NRQCD)framework,where the■represents the color-singlet states■The differential angle distribution of cross sections■is given.We also discuss the uncertainties of cross sections caused by the varying quark masses and the renormalization scaleμ.We show that significant numbers of events for pairs of higher excited state quarkonia can be generated at the super Z factory.
