Analytical Calculation of Reaction Cross Section of e+e-→W+W- with Correction of Hybrid Chain Propagators

CHEN Xue-wen; ZHANG Jia-wei; FANG Zhen-yun

doi:10.13718/j.cnki.xdzk.2021.05.013

2021 Volume 43 Issue 5

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CHEN Xue-wen, ZHANG Jia-wei, FANG Zhen-yun. Analytical Calculation of Reaction Cross Section of e+e-→W+W- with Correction of Hybrid Chain Propagators[J]. Journal of Southwest University Natural Science Edition, 2021, 43(5): 96-103. doi: 10.13718/j.cnki.xdzk.2021.05.013

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CHEN Xue-wen, ZHANG Jia-wei, FANG Zhen-yun. Analytical Calculation of Reaction Cross Section of e⁺e^-→W⁺W^- with Correction of Hybrid Chain Propagators[J]. Journal of Southwest University Natural Science Edition, 2021, 43(5): 96-103. doi: 10.13718/j.cnki.xdzk.2021.05.013

Analytical Calculation of Reaction Cross Section of e⁺e^-→W⁺W^- with Correction of Hybrid Chain Propagators

1.
School of Mathematics, Physics and Data Science, Chongqing University of Science and Technology, Chongqing 401331, China
2.
School of Physics, Chongqing University, Chongqing 400030, China

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Received Date: 25/07/2019
Available Online: 20/05/2021
MSC: O413

Abstract

The framework of γ and Z hybrid chain propagators which are formed by photon and intermediate boson, respectively, is analyzed in the electroweak standard model (SM). The corresponding series expressions of the hybrid chain propagators are obtained by re-classifying and combining the propagators of each loop propagator, and analytical results of renormalized chain propagators are obtained through the introduction of the counter terms in the on-shell renormalization scheme. Based on the same treatment, the renormalized electron neutrino chain propagator is obtained. Furthermore, this result is applied to the particle reaction of e⁺e^-→W⁺W^-, and the reaction cross section is obtained under the hybrid chain propagators' correction. The numerical results show that the reaction cross section of hybrid chain propagators has a suppression effect on the tree-level cross section. Finally, the effect of W boson's mass near the W⁺W^- threshold on the total cross section is discussed. Combined with the Circular Electron Positron Collider (CEPC) experiment, the numbers of W⁺W^- that can be generated near the W⁺W^- threshold and in the region of 240 GeV collision energy are discussed, respectively.
- standard model,
- hybrid chain propagator,
- radiation correction,
- reaction cross section

References

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电弱统一标准模型(the electroweak standard model，SM)是20世纪粒子物理学中颇具影响的唯象理论之一，在描述电磁与弱相互作用中取得了巨大成功，被标准模型预言的基本粒子都已经得到了实验数据的支持与验证，尤其是2012年人们用大型强子对撞机发现了标准模型预言的Higgs玻色子. 自标准模型提出以来，国际上出现许多相关理论研究工作，其中涉及“精确”检验标准模型的理论计算工作一直备受学术界关注，而这些理论计算工作本身也对标准模型理论的发展起到了十分重要的推动作用.

e⁺e^-→W⁺W^-反应可以精确确定W^±玻色子的质量，许多物理学家在理论上从不同侧面对e⁺e^-→W⁺W^-反应做过研究. Lemoine M等人^[1-5]曾讨论过e⁺e^-→W⁺W^-过程电弱修正和软光子修正；Beenakker W等人^[6-8]针对特定的极化态计算了硬光子韧致辐射修正；Hagiwara K等人^[9-10]基于最小超对称模型讨论了e⁺e^-→W⁺W^-过程；Aeppli A等人^[11]初步讨论了e⁺e^-→W⁺W^-→4fermions过程，实验上，LEP实验组也对此过程做过观测.

在e⁺e^-碰撞中，W玻色子主要是通过e⁺e^-→W⁺W^-过程产生的. 当质心能量在W⁺W^-阈值处附近时，总截面对m_W非常敏感，因而可以通过阈值扫描测量m_W. 当质心能量在W⁺W^-阈值以上时，W玻色子的质量可以通过测量其衰变产物的动量来确定. 大型正负电子对撞机(the large electron-positron collider，LEPC)曾采用阈值扫描和直接测量对W玻色子进行了测量. 其中，阈值扫描法具有较大的统计不确定性(~200 MeV)；由于直接测量的数据统计有限，W玻色子质量不确定度约为33 MeV^[12]. 结合LEPC，Tevatron和ATLAS的测量结果，目前W玻色子的质量为m_W=(80.379±0.012) GeV^[13]. 随着北京正负电子对撞机(Beijing Electron-Positron Collider，BEPC)于2022年左右关闭，为了在国际高能物理领域占有一席之地，我国科学家提出建设下一代环形正负电子对撞机(the circular electron positron collider，CEPC). 在CEPC上可以对W玻色子的质量和衰变宽度等物理量进行更加精确的测量，在CEPC上采用阈值扫描可获得2.5 MeV的测量精度，采用直接测量可获得3 MeV的测量精度，且测量可以直接在CEPC对撞能量区($\sqrt s $~240 GeV)进行.

现有研究工作大多从有限高阶圈图角度研究e⁺e^-→W⁺W^-过程反应截面，并未涉及无穷高阶修正. 相对于已有的研究工作，本研究将从另一角度——即考虑混合链图传播子修正下e⁺e^-→W⁺W^-反应截面的解析计算. 在SM理论框架下讨论e⁺e^-→W⁺W^-反应，相应的传播子为光子γ，中间玻色子Z和电子中微子ν_e. 此外，由于γ和Z参与多种不同物理过程的电弱相互作用，因而若要考虑由γ和Z以及它们之间的混合圈构成的混合链图传播子，其构架问题将十分复杂. 本研究首先分析了SM中γ-Z混合链图传播子的构架方式，通过对各圈图传播子重新归类和组合，得到了相应的链图传播子的解析表达式，再通过在壳重整化方案中引入抵消项，从而获得重整化链混合链图传播子的严格解析结果. 同样本研究还给出了电子中微子链图传播子的严格解析结果. 进而，本研究将此结果应用到粒子反应e⁺e^-→W⁺W^-中，获得了在重整化链图传播子传递电弱作用时e⁺e^-→W⁺W^-的反应截面. 最后，结合CEPC实验，讨论了在W⁺W^-产生能量阈值附近W玻色子质量不确定度对反应截面的影响，并讨论了在CEPC对撞能区可产生的W⁺W^-事例数.

4. 结论

本研究首先在标准模型理论框架下讨论了γ，Z，ν_e混合链图传播子的构架方式，并获得了相应的重整化混合链图传播子的严格解析结果. 进而，采用“混合链图传播子修正下的反应截面”这种计算模式，讨论了混合链图传播子修正下的e⁺e^-→W⁺W^-反应截面，获得了相应的解析结果和数值结果. 最后，结合CEPC对撞亮度和运行时间，讨论了CEPC在W⁺W^-阈值附近和240 GeV两个对撞能区可产生W⁺W^-的事例数.

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Analytical Calculation of Reaction Cross Section of e⁺e^-→W⁺W^- with Correction of Hybrid Chain Propagators

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