A mathematical solution for the parameters of three interfering resonances

作者：Han, X.; Shen, C. P.^*

来源：Chinese Physics C, 2018, 42(4): 043001.

DOI：10.1088/1674-1137/42/4/043001

• multiple solutions
• three interfering resonances
• high energy physics experiments

The multiple-solution problem in determining the parameters of three interfering resonances from a fit to an experimentally measured distribution is considered from a mathematical viewpoint. It is shown that there are four numerical solutions for a fit with three coherent Breit-Wigner functions. Although explicit analytical formulae cannot be derived in this case, we provide some constraint equations between the four solutions. For the cases of nonrelativistic and relativistic Breit-Wigner forms of amplitude functions, a numerical method is provided to derive the other solutions from that already obtained, based on the obtained constraint equations. In real experimental measurements with more complicated amplitude forms similar to Breit-Wigner functions, the same method can be deduced and performed to get numerical solutions. The good agreement between the solutions found using this mathematical method and those directly from the fit verifies the correctness of the constraint equations and mathematical methodology used.

• 出版日期2018-4
• 单位北京航空航天大学