A mathematical review on the multiple-solution problem

Understand

The recent multiple-solution problem in extracting physics information from a fit to the experimental data in high energy physics is reviewed in a mathematical viewpoint.

• All these multiple solutions were found via a fit process previously, while in this letter we prove that if the sum of two coherent Breit-Wigner functions is used to fit the measured distribution, there should be two and only two non-trivial solutions, and they are related to each other by analytical formulae.
• For real experimental measurements in more complicated situations, we also provide a numerical method to derive the other solution from the already obtained one.
• The excellent consistency between the exact solution obtained this way and the fit process justifies the method.