Tau Lepton Decay And Its Application In Resonances Problem

Tau lepton is the only lepton that is heavy enough to decay into hadrons.The study of tau lepton decay is helpful to learn about weak interaction as well as strong interaction,so it is a significant research direction.However,there has been a lack of relevant research work in the world.Recently,we proposed a novel algebraic method to study tau lepton decay process by using the algebraic technique of angular momentum coupling.This method is very important in deriving the analytical expression of the scattering amplitudes and further to correlate different reactions.In our calculation,only one experimental data is needed and no any other adjustable parameter,then we correlate to study and also predict other branching ratios.Another important discovery is the G-parity,the scattering amplitudes for different G-parity can be obtained due to the analytical expressions,which is particularly important to filter different reactions,so as to investigate the nature of resonances in the tau decay.In the chiral unitary approach,the scalar resonances and the axial vector resonances are dynamically generated in the interactions between the pseudoscalar-pseudoscalar and pseudoscalar-vector mesons,respectively.Based on the above,in this work we further discuss some related and interesting problems.Firstly,we study the process of tau decay into a neutrino and two mesons,the analytical scattering amplitudes are given for different cases.Only one experimental branch ratio is used to obtain other branch ratios due to the correlation.We also compare with experimental data and predict the invariant mass distributions for some reactions.Secondly,we apply the analytical amplitudes to study the final state interaction in the tau decay by G-parity conservation to filter different isospin = 0 and = 1 scalar resonances,and calculate the differential cross section and further the branching ratios.Finally,the process of tau decay into a neutrino and an axial vector meson is discussed,the different isospin = 1 and = 1/2 axial vector resonant are investigated due to G-parity,the branch ratios for different reactions are predicted and some interesting results are obtained.In this paper,the novel algebraic method is utilized to study the tau decays and applications,which is helpful to further explore other interesting resonant states in different reactions from a new perspective.