A mathematical solution for the parameters of three interfering resonances

X. Han; C. P. Shen

doi:10.1088/1674-1137/42/4/043001

Chinese Physics C> 2018, Vol. 42> Issue(4) : 043001 DOI: 10.1088/1674-1137/42/4/043001

A mathematical solution for the parameters of three interfering resonances

X. Han ,
C. P. Shen ^,

1.
School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China

Abstract
HTML
Reference
Related

PDF

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.
- multiple solutions ,
- three interfering resonances ,
- high energy physics experiments

References

[1]	X. L. Wang et al (Belle Collaboration), Phys. Rev. D, 91:112007 (2015)
[2]	C. Z. Yuan, X. H. Mo, and P. Wang, Int. J. Mod. Phys. A, 25:5963 (2010)
[3]	K. Zhu, X. H. Mo, C. Z. Yuan, and P. Wang, Int. J. Mod. Phys. A, 26:4511 (2011)
[4]	A. D. Bukin, arXiv:0710.5627
[5]	C. Patrignani et al (Particle Data Group), Chin. Phys. C, 40:100001 (2016) and 2017 update

[1]	Yuanning Gao , Tianze Rong , Zhenwei Yang , Chenjia Zhang , Yanxi Zhang . A scheme to fix multiple solutions in amplitude analyses. Chinese Physics C, 2024, 48(5): 053001. doi: 10.1088/1674-1137/ad2674
[2]	Taejin Lee . Covariant open string field theory on multiple Dp-branes. Chinese Physics C, 2018, 42(11): 113105. doi: 10.1088/1674-1137/42/11/113105
[3]	Ayan Banerjee , J. R. Villanueva , Phongpichit Channuie , Kimet Jusufi . Stable gravastars: Guilfoyle's electrically charged solutions. Chinese Physics C, 2018, 42(11): 115101. doi: 10.1088/1674-1137/42/11/115101
[4]	Hui Jia , Bin Qi , Shou-Yu Wang , Shuo Wang , Chen Liu . Electromagnetic transitions in multiple chiral doublet bands. Chinese Physics C, 2016, 40(12): 124103. doi: 10.1088/1674-1137/40/12/124103
[5]	Hao Zhang , Qibo Chen . Chiral geometry in multiple chiral doublet bands. Chinese Physics C, 2016, 40(2): 024102. doi: 10.1088/1674-1137/40/2/024102
[6]	Chun-Jie Wang , Zhen-An Liu , Jing-Zhou Zhao , Zhao Liu . Design of a high throughput electronics module for high energy physics experiments. Chinese Physics C, 2016, 40(6): 066102. doi: 10.1088/1674-1137/40/6/066102
[7]	HUANG Xi-Ru , CAO Ping , ZHENG Jia-Jun . A data transmission method for particle physics experiments based on Ethernet physical layer. Chinese Physics C, 2015, 39(11): 116102. doi: 10.1088/1674-1137/39/11/116102
[8]	HUANG Xi-Ru , CAO Ping , GAO Li-Wei , ZHENG Jia-Jun . A data readout approach for physics experiments. Chinese Physics C, 2015, 39(7): 076102. doi: 10.1088/1674-1137/39/7/076102
[9]	Eef van , George Rupp . Evidence for further charmonium vector resonances. Chinese Physics C, 2011, 35(4): 319-324. doi: 10.1088/1674-1137/35/4/001
[10]	Dmitri Diakonov . Exotic pentaquarks as Gamov—Teller resonances. Chinese Physics C, 2010, 34(9): 1298-1302. doi: 10.1088/1674-1137/34/9/028
[11]	ZHOU Dai-Cui , WAN Ren-Zhuo , MAO Ya-Xian , WANG Meng-Liang , MA Ke , WANG Ya-Ping , YIN Zhong-Bao , CAI Xu , for the , ALICE collaboration . High pt and photon physics with ALICE at LHC. Chinese Physics C, 2010, 34(9): 1383-1386. doi: 10.1088/1674-1137/34/9/048
[12]	HAO Xi-Qing , KE Hong-Wei , DING Yi-Bing , SHEN Peng-Nian , LI Xue-Qian . Testing Bell inequality at experiments of high energy physics. Chinese Physics C, 2010, 34(3): 311-318. doi: 10.1088/1674-1137/34/3/002
[13]	Jamil Aslam . B→0⁺(1⁺)+ missing energy in unparticle physics. Chinese Physics C, 2009, 33(5): 332-339. doi: 10.1088/1674-1137/33/5/003
[14]	T. Hyodo , D. Jido , H.-Ch. Kim , H. Nagahiro , S.I. Nam , M. Oka . Reaction dynamics for photoproductions of baryon resonances. Chinese Physics C, 2009, 33(12): 1167-1174. doi: 10.1088/1674-1137/33/12/019
[15]	SUN Bao-Xi , Vicente Vacas . Dynamically generated resonances. Chinese Physics C, 2009, 33(12): 1132-1139. doi: 10.1088/1674-1137/33/12/014
[16]	FU Cheng-Dong , MO Xiao-Hu . Significance of absolute energy scale for physics at BESⅢ. Chinese Physics C, 2008, 32(10): 776-780. doi: 10.1088/1674-1137/32/10/002
[17]	WANG Ya-Ping , ZHOU Dai-Mei , HUANG Rui-Dian , CAI Xu . Collision geometry and particle production in high energy heavy ion collision experiments. Chinese Physics C, 2008, 32(4): 308-328. doi: 10.1088/1674-1137/32/4/014
[18]	ZHOU Dai-Mei , WANG Ya-Ping , WEI Li-Hua , CAI Xu . Correlations and fluctuations in high energy heavy ion collision experiments. Chinese Physics C, 2008, 32(5): 400-418. doi: 10.1088/1674-1137/32/5/016
[19]	WANG Ya-Ping , ZHOU Dai-Mei , CAI Xu . Collective expansion and hadronization in high energy heavy ion collision experiments. Chinese Physics C, 2008, 32(9): 714-727. doi: 10.1088/1674-1137/32/9/008
[20]	Xia Keding , Cai Yanhuang . Multipole Giant Resonances in Highly Excited Nuclei. Chinese Physics C, 1989, 13(S1): 79-86.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2018-01-20

Fund

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)

Article Metric

Article Views(1735)
PDF Downloads(22)
Cited by(0)

Policy on re-use

To reuse of Open Access content published by CPC, for content published under the terms of the Creative Commons Attribution 3.0 license (“CC CY”), the users don’t need to request permission to copy, distribute and display the final published version of the article and to create derivative works, subject to appropriate attribution.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

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

Received Date: 2018-01-20

Available Online: 2018-04-05

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.

HTML

Reference (5)

A mathematical solution for the parameters of three interfering resonances

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article