A mathematical solution for the parameters of three interfering resonances

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X. Han and C. P. Shen. A mathematical solution for the parameters of three interfering resonances[J]. Chinese Physics C, 2018, 42(4): 043001. doi: 10.1088/1674-1137/42/4/043001
X. Han and C. P. Shen. A mathematical solution for the parameters of three interfering resonances[J]. Chinese Physics C, 2018, 42(4): 043001.  doi: 10.1088/1674-1137/42/4/043001 shu
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Received: 2018-01-20
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    Supported by National Natural Science Foundation of China (NSFC) (11575017, 11761141009), the Ministry of Science and Technology of China (2015CB856701) and the CAS Center for Excellence in Particle Physics (CCEPP)

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A mathematical solution for the parameters of three interfering resonances

    Corresponding author: C. P. Shen,
  • 1. School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China
Fund Project:  Supported by National Natural Science Foundation of China (NSFC) (11575017, 11761141009), the Ministry of Science and Technology of China (2015CB856701) and the CAS Center for Excellence in Particle Physics (CCEPP)

Abstract: 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.

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