弯曲额外维KK态无穷求和及其对（B|-）→X_sγ的单圈电弱修正
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摘要
近年来,随着欧洲核子中心的大型强子对撞机(LHC)取得的新进展,超出标准模型的新物理研究成为粒子物理学的一个热点。标准模型不仅涵盖了已知的各种基本粒子,也准确解释了除引力之外的强、弱和电磁相互作用。尽管标准模型在过去的半个多世纪中已经取得了巨大的成功,但是也存在与实验不符的地方以及理论自身的困难。额外维理论正是为解决标准模型的能级问题而发展起来的。
本文首先对粒子物理的发展做了简单回顾,介绍了标准模型的相关知识,包括基本粒子的属性、规范不变性和标准模型的拉氏量,并对标准模型的不足和几种新物理模型做了讨论,尤其对含有一个弯曲额外维的Randall-Sundrum模型做了详细介绍,讨论了SU(3)c×SU(2)L×SU(2)R×U(1)X×PLR对称下各粒子场的Kaluze-Klein(KK)分解。
通过Bulk场函数的运动方程和相应的边界条件,我们提出了与KK态本征值相关的三个引理。利用这些引理,用留数定理的方法给出KK态Bulk函数构成的无穷级数收敛的充分条件,并对其求和。本论文还分析了五维基础理论的传播子和四维有效理论中Bulk函数乘以相应KK激发态传播r之间的关系。应用上述方法,我们计算得到ο)(μEW2/∧KK2)阶近似下,满足SU(3)c×SU(2)L×SU(2)R×U(1)X×PLR对称的弯曲额外维模型对B→Xsγ分支比的单圈电弱修正。其中,∧KK表示低激发态的KK能标,μEW表示电弱能标。由此得到的解析结果包含了所有可能的KK激发态的贡献。
在数值分析部分,我们给出了B→Xsγ分支比随模型参数的变化曲线。讨论了分支比随能标∧KK的变化,分析了不同能标下Bulk质量CS,CT,CB和汤川耦合Yu,d的取值对分支比的影响,通过当前的实验结果和理论给出的数值曲线,我们可以得到B→Xsγ对弯曲额外维模型参数的限制。
最后是结论部分,我们概括了所研究的问题和方法,并对解析和数值结果做了总结和讨论。
With the large hadron collider(LHC) of CERN making new progresss in the past few years, the new physics beyond the Standard Model(SM) has been one of the most important issues of particle physics. Although the SM has been extremely successful in describing the all known particles in elementary particle physics and the interactions between them, it possesses some conceptual problems which cann't be solved within the framework of SM. Models with extra dimensions are developed to solve the hierarchy problem in SM.
In this paper, A brief review about the history of Particle Physics is given firstly. Then we introduce the standard model, which including the properties of elementary particle, the gauge invariance and the SM Lagrangian. We also discuss the problems of SM and some new physics models, especially the Randall-Sundrum(RS) model which contains a warped Extra Dimension. The Kaluze-Klein(KK) decompositions of all five dimensional fields with the custodial symmetry SU(3)C×SU(2)L×SU(2)R×U(1)X×PLR are also given in this section.
Applying the equations of motion together with corresponding boundary conditions of bulk profiles, we verify some lemmas on the eigenvalues of KK modes in extension of the stan-dard model with a warped extra dimension and the custodial symmetry SU(3)C×SU(2)L×SU(2)R×U(1)X×PLR. Using the lemmas and performing properly analytic extensions of bulk profiles, we present the sufficient condition for a convergent series of Kaluze-Klein exci-tations and sum over the series through the residue theorem. Furthermore, we analyze the possible connection between the propagators in five dimensional full theory and the product of bulk profiles with corresponding propagators of exciting KK modes in four dimensional effective theory. As an example, we present the electroweak correction from new physics to the branching ratio of B→Xsγ to the order O(μ2EW/A2KK) in extension of the standard model with a warped extra dimension and the custodial symmetry, where AKK denotes the energy scale of low-lying KK excitations and μEW denotes the electroweak energy scale. By doing this, we obtain the corrections from all the possible KK states.
In the numerical section, we present some figures to describe the dependence of the branching ratio on the parameters of new physics. Discussion on the branch ratio varying with Akk and the effection of the bulk mass (CS,CT, and CB) and Yukawa (Yu,d) on branch ratio are given in this section.And we analyze the possible constraint on the parameter space of new physics from experimental data for the branching ratio of B→Xsγ.
本文首先对粒子物理的发展做了简单回顾,介绍了标准模型的相关知识,包括基本粒子的属性、规范不变性和标准模型的拉氏量,并对标准模型的不足和几种新物理模型做了讨论,尤其对含有一个弯曲额外维的Randall-Sundrum模型做了详细介绍,讨论了SU(3)c×SU(2)L×SU(2)R×U(1)X×PLR对称下各粒子场的Kaluze-Klein(KK)分解。
通过Bulk场函数的运动方程和相应的边界条件,我们提出了与KK态本征值相关的三个引理。利用这些引理,用留数定理的方法给出KK态Bulk函数构成的无穷级数收敛的充分条件,并对其求和。本论文还分析了五维基础理论的传播子和四维有效理论中Bulk函数乘以相应KK激发态传播r之间的关系。应用上述方法,我们计算得到ο)(μEW2/∧KK2)阶近似下,满足SU(3)c×SU(2)L×SU(2)R×U(1)X×PLR对称的弯曲额外维模型对B→Xsγ分支比的单圈电弱修正。其中,∧KK表示低激发态的KK能标,μEW表示电弱能标。由此得到的解析结果包含了所有可能的KK激发态的贡献。
在数值分析部分,我们给出了B→Xsγ分支比随模型参数的变化曲线。讨论了分支比随能标∧KK的变化,分析了不同能标下Bulk质量CS,CT,CB和汤川耦合Yu,d的取值对分支比的影响,通过当前的实验结果和理论给出的数值曲线,我们可以得到B→Xsγ对弯曲额外维模型参数的限制。
最后是结论部分,我们概括了所研究的问题和方法,并对解析和数值结果做了总结和讨论。
With the large hadron collider(LHC) of CERN making new progresss in the past few years, the new physics beyond the Standard Model(SM) has been one of the most important issues of particle physics. Although the SM has been extremely successful in describing the all known particles in elementary particle physics and the interactions between them, it possesses some conceptual problems which cann't be solved within the framework of SM. Models with extra dimensions are developed to solve the hierarchy problem in SM.
In this paper, A brief review about the history of Particle Physics is given firstly. Then we introduce the standard model, which including the properties of elementary particle, the gauge invariance and the SM Lagrangian. We also discuss the problems of SM and some new physics models, especially the Randall-Sundrum(RS) model which contains a warped Extra Dimension. The Kaluze-Klein(KK) decompositions of all five dimensional fields with the custodial symmetry SU(3)C×SU(2)L×SU(2)R×U(1)X×PLR are also given in this section.
Applying the equations of motion together with corresponding boundary conditions of bulk profiles, we verify some lemmas on the eigenvalues of KK modes in extension of the stan-dard model with a warped extra dimension and the custodial symmetry SU(3)C×SU(2)L×SU(2)R×U(1)X×PLR. Using the lemmas and performing properly analytic extensions of bulk profiles, we present the sufficient condition for a convergent series of Kaluze-Klein exci-tations and sum over the series through the residue theorem. Furthermore, we analyze the possible connection between the propagators in five dimensional full theory and the product of bulk profiles with corresponding propagators of exciting KK modes in four dimensional effective theory. As an example, we present the electroweak correction from new physics to the branching ratio of B→Xsγ to the order O(μ2EW/A2KK) in extension of the standard model with a warped extra dimension and the custodial symmetry, where AKK denotes the energy scale of low-lying KK excitations and μEW denotes the electroweak energy scale. By doing this, we obtain the corrections from all the possible KK states.
In the numerical section, we present some figures to describe the dependence of the branching ratio on the parameters of new physics. Discussion on the branch ratio varying with Akk and the effection of the bulk mass (CS,CT, and CB) and Yukawa (Yu,d) on branch ratio are given in this section.And we analyze the possible constraint on the parameter space of new physics from experimental data for the branching ratio of B→Xsγ.
引文
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