| The decay of unstable particles is one of the two fundamental processes in advanced physics(the other is collision).The main property of particle decay to the final state is its lifetime τ or decay width Γ=1/τ,which is determined by the interaction dynamics mechanism.For weak coupling,S-matrix element can be treated with perturbation approximation method.But in the case of strong coupling,the higher order term is not necessarily much smaller than the lower order term.In principle,we must add up the contributions of all orders,so perturbed calculations requiring only a few lower-order terms are not reliable.On the other hand,even if we could give the interaction Hamiltonian in its original form,it would be difficult to calculate the S-matrix and compare its predicted results with experimental results.In this work,the effective Hamiltonian Heff for the three decay modes of charmonium is derived from the basic principle of the equivalent interaction model,which belong to the two-body decay problem and are represented by three-wire vertices in Feynman diagrams.The first pattern is a pair of turns the vector meson decay is standard meson,it indicates that the V→PP:1--→0-c+0-c;The second model is a vector meson decay into constraint with vector meson and a standard meson,it indicates that the V→VP:1--→1-c+0-c;The third kind of pattern is a vector meson decay into a pair of vector meson,it indicates that the V→VV:1--→1-c+1-c.Previous studies have given the first two decay modes of mesons,while the analysis and calculation of the third mode are still blank.In this paper,all possible effective Hamiltonian Heff forms of the third decay mode are written out according to the basic principle of equivalent interaction.It satisfies the requirements of charge C conjugate transformation parity P transformation symmetry and Lorentz transformation in strong interaction and electromagnetic interaction.Then,the matrix element Mif of S matrix is obtained from the effective Hamiltonian Heff,and the analytical expression of ΓV→PP,ΓV→PP,ΓV→VV for the decay modes of heavy charmonium is calculated by using the method of calculating Feynman graphs in quantum field theory.The three decay widths obtained above are put into the Breit-Wigner formula describing the generation and decay properties of resonance states,in which the phenomenological parameters contained in the expression of energy correlation of the three decay widths are determined by the experimental data(such as hadron case number,integral brightness,etc.)measured by fitting BESII scanning.Since the experimental measurement of R-value requires radiation correction factor as input,and the radiation correction factor requires resonance parameter value,we will adopt the iterative fitting method,and the experimental value obtained thus has self-consistency.The fitting tool we adopted was MINUIT software package in CERN library.Its principle was to use data-driven method to carry out least square fitting,so as to get the shape of the objective function near its minimum value.The parameter value of the objective function χ2 was the global minimum(or local minimum)by iterating the principle of least square method.It is obtained that the value of the fitting parameter under the convergence of the objective function χ2 is the result of the physical parameter we want to measure.Other models,such as the potential model,can also be used for the energy correlation of heavy charmonium decay width.In this paper,the energy correlation using the potential model is compared with the energy correlation using the equivalent interaction model.In addition,we also discuss the influence of experimental errors on the experimental accuracy. |
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