Multiple Solutions in Extracting Physics Information From Experimental Data

Yuan, C. Z.; Mo, X. H.; P.Wang,

doi:10.1142/s0217751x10051153

Cited by 11 publications

(3 citation statements)

References 35 publications

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“…However, if we come across the case where the parameters contained in the objective function have multiple solution [38,39,40,41], optimization procedure can only be applied for one set of parameters. For the general case involving all sets of parameters, it is a topic for the further investigation.…”

Section: Optimization Issuementioning

confidence: 99%

Theory of second optimization for scan experiment

2015

Int. J. Mod. Phys. A

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In many high energy experiments, the physics quantities are obtained by measuring the cross sections at a few energy points over an energy region. This was referred to as scan experiment. The optimal design of the scan experiment (how many energy points, what the energies are, and what is the luminosity at each energy point) is of great significance both for scientific research and from economical viewpoint. Two approaches, one has recourse to the sampling technique and the other resorts to the analytical proof, are adopted to figure out the optimized scan scheme for the relevant parameters. The final results indicate that for n parameters scan experiment, n energy points are necessary and sufficient for optimal determination of these n parameters; each optimal position can be acquired by single parameter scan (sampling method), or by analysis of auxiliary function (analytic method); the luminosity allocation among the points can be determined analytically with respect to the relative importance between parameters. By virtue of the second optimization theory established in this paper, it is feasible to accommodate the perfectly optimal scheme for any scan experiment.

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Section: Optimization Issuementioning

confidence: 99%

Theory of second optimization for scan experiment

2015

Int. J. Mod. Phys. A

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“…The existence of multiple solutions is one of the amazing features of quantum mechanics when more than one coherent amplitudes are considered to describe an observed distribution. This feature has been noticed for a long while in both theoretical and experimental sides [1][2][3][4], and in Ref. [5] it has been proved that there must be two solutions when the number of amplitudes are two for some specific forms.…”

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confidence: 91%

Selecting the physical solution via $η$-$η'$ mixing

Zhu

2021

Preprint

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A novel and simple method is proposed to select the physics solution in the decays of Y (4230) → ηJ/ψ and Y (4230) → η ′ J/ψ, where multiple solutions have been reported in the experimental measurements. Based on an η-η ′ mixing analysis, a unique solution is determined for the decay of Y (4230) → η ′ J/ψ. But no conclusion can be drawn for Y (4230) → ηJ/ψ yet due to the large uncertainties in experimental results. It turns out reducing the uncertainty of the η-η ′ mixing angle is crucial for solving this problem, and will provide indication on whether Y (4230) contains substantial ss quark component or not.

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“…Another example is presented in Ref. [2], where two solutions are found in the branching fraction measurement for the φ→ωπ 0 process and the study of ρ−ω mixing.…”

Section: Introductionmentioning

confidence: 99%

A mathematical solution for the parameters of three interfering resonances

Han

Shen

2018

Chinese Phys. C

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The multiple-solution problem in determining the three-interfering-resonances' parameters from a fit to an experimentally measured distribution is considered in a mathematical viewpoint. In this paper it is shown that there are four numerical solutions for the fit with three coherent Breit-Wigner functions. Although the explicit analytical formulae can not 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, numerical method is provided to derive the other solutions from the already obtained one 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 well agreement between the solved solutions using this mathematical method and those from the fit directly verifies the correctness of the supplied constraint equations and mathematical methodology.

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Multiple Solutions in Extracting Physics Information From Experimental Data

Cited by 11 publications

References 35 publications

Theory of second optimization for scan experiment

Theory of second optimization for scan experiment

Selecting the physical solution via $η$-$η'$ mixing

A mathematical solution for the parameters of three interfering resonances

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