活跃和惰性中微子振荡的若干研究
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摘要
本文主要研究在考虑轻惰性中微子存在的普适框架下,中微子混合与振荡现象相关的理论推广和实验分析。我们首先仔细回顾中微子物理的发展历史,揭示其来龙去脉,立足现在、展望将来。在对中微子的混合与振荡理论进行简要介绍、为后面章节提供理论基础之后,我们对中微子振荡实验进行分类介绍,并决定对其中引入入胜的热点之一,轻惰性中微子进行系统研究。我们对目前所有短基线实验给出的振荡数据进行全局分析,以此对轻惰性中微子现象学的实验现状进行概括性总结。如果存在额外的惰性中微子,现有的一切振荡理论以及数据分析都必须进行推广扩充,于是我们首先针对太阳中微子实验开展相关的工作,而长基线的大气、反应堆以及加速器的相关工作则是我们计划在不久的将来要完成的。本论文具体由以下六个部分构成：
第一章,导论。我们将介绍中微子物理的发展历史、简要阐述现阶段人们对中微子的基本认识,了解中微子物理学的过去、现在,并尝试藉由五组悬而未决的开放问题对未来的研究热点作一启发性的展望。对于中微子物理和弱相互作用的发展历程,我们进行了相当深入和细致的考证和归纳,在理论和实验两个方面都给出了比较精细、完整的描述,我们还为此专门列出年表以供查阅。
第二章,中微子混合与振荡理论。本章试图对中微子的混合与振荡现象进行简洁明要而又自成体系的完整介绍。我们首先对粒子物理学的标准模型进行介绍,主要包含标准模型的物质场和相互作用拉氏量,生成规范波色场质量的Higgs机制；接着介绍超出标准模型的中微子质量产生机制,以及混合矩阵的定义及参数化；最后,我们将给出中微子真空振荡几率和物质中演化方程的介绍。
第三章,振荡实验和短基线反常。我们首先对中微子振荡实验进行分类介绍,接着对短基线实验反常进行考察,分别在3+1,3+2,3+1+1框架内对全部短基线中微子振荡数据进行全局的振荡参数拟合分析。我们将展示3+1框架下振荡参数的允许区间,其中△m412位于0.82到2.19eV2之间(3σ)。此外,无振荡的情形在6σ置信度下被排除,但如果不把LSND的结果考虑在内,这个结果将令人惊讶的下降到2σ。LSND的结果依然是短基线中微子振荡决定性的主要证据,为此,我们需要其他更高精度的实验去检验LSND的结果。
第四章,活跃-惰性太阳中微子振荡及CP相位。我们将研究包含任意Ns味惰性中微子的,3+Ns味中微子在太阳传播过程中的味演化,并着重研究中微子混合矩阵中各CP相角的效应；计算相应的、描述电子中微子生存几率的Parke公式,计算电子味到惰性味的中微子跃迁几率；更进一步,我们将基于3+1味混合的框架,对所有解析结果进行细致的数值验证,并演示、追踪三个CP相角的贡献和效应。我们所导出推广的Parke公式适用于将来高精度的太阳中微子活跃与惰性振荡实验的测量；在我们基于3+1味典型混合参数给出的例子中,三个未测知的CP相角对电子中微子生存几率造成的改变可以达到1%，而对电子味到惰性味中微子跃迁几率,则高达100%。将来的短基线中微子振荡实验有望对混合矩阵|uα4|(α=e,μ,τ)的绝对值进行精确测量,从而有可能依据这些结果通过太阳中微子实验测量CP相角。
第五章,活跃-惰性太阳中微子振荡中的日夜不对称性。沿用第四章的任意3+Ns味中微子混合框架,我们进一步讨论活跃与惰性太阳中微子振荡中的日夜不对称性,给出微扰和分层两种不同近似下振荡几率的解析表达式。通过与数值结果的比较,我们指出分层近似解析公式的精度是足以信赖的；我们还将分别展示地球物质效应中的活跃及惰性两组中微子混参数的依赖关系以及CP相位对振荡几率的影响。我们发现,年平均重生因子对于实验位址并不敏感,且随着中微子能量递增而变大；对于高能的太阳中微子,其电子味生存几率和电子味到惰性味的转化几率的日夜不对称性Dee。和Des。,幅度可以分别达到10-2和10-3量级；我们还给出了CP相角对Dee和Des。的影响,这个效应在高能区间可以达到10-3的量级。因此,未来的高精度中微子实验有可能探测到活跃与惰性混合以及日夜不对称性中的CP相位。
第六章,回顾和展望。作为结束,本章将对前文内容进行简要梳理和概括,并对惰性中微子现象学的未来发展进行思考和展望。
In this thesis we focus on the phenomenology of neutrino oscillation, assuming the existence of sterile neutrinos. The thesis is organized as follows:
Chap.1, Introduction. In this chapter, we shall give an overview of the history of neutrino physics, outline some fundamental knowledge of neutrinos that we have accumulated until nowadays, and summarize the research frontier by stating five groups of open questions on neutrinos.
Chap.2, Neutrino Oscillation Theory. In this chapter, we first give a brief summary to the standard model of electroweak interaction including introductions of the construction of the Standard Model Lagrangian, and the Higgs mechanism which endows gauge bosons in a gauge theory with mass through absorption of Nambu-Goldstone bosons arising in spontaneous symmetry breaking. We then introduce the description of a massive neutrino in the cases of Dirac/Majorana and the most general Dirac-Majorana mass. After that, we introduce the PMNS matrix which describe the neutrino mixing, and the parameterization of the mixing matrix for arbitrary3+Ns neutrinos where Ns stands for the number of sterile neutrino. Finally, we derive the expressions of neutrino oscillation probabilities and the famous MSW equation which formulize neutrino oscillations in matter.
Chap.3, Oscillation Experiments and SBL anomaly. In this chapter, we first introduce different types of neutrino experiments。We shall introduce carefully the SBL neutrino experiments and anomalies from their recent results. A neutrino oscillation explanation of these anomalies implies the existence of at least one extra mass-squared Difference ΔmS2BL such that ΔmS2OL<<ΔmA2TM< Chap.4, Active-Sterile Solar Neutrino Oscillations and CP-Violating Phases. In this chapter, we extend the discussion of the solar neutrino oscillations in a general scheme of3+Ns mixing, without any constraint on the mixing between the three active and the Ns sterile neutrinos, assuming only a realistic hierarchy of neutrino mass-squared differences. We find that effects of CP-violating phases take place in the oscillation probabilities. A generalized Parke formula describing the neutrino oscillation probabilities inside the Sun is calculated. The validity of the analytical calculation and the probability variation due to the unknown CP-violating phases are illustrated with a numerical calculation of the evolution equation in the case of3+1neutrino mixing.
Chap.5, Day-Night Asymmetries in Active-Sterile Solar Neutrino Oscil-lations. In this chapter, we discuss the day-night asymmetries in active-sterile solar neutrino oscillations in the framework mentioned in Chap.4. Analytical expressions of the probability of neutrino flavor transitions in the Earth in the perturbative approximation and in the slab approximation are presented and the effects of active-sterile mixing and of the CP-violating phases are discussed. The accuracy of the analytical approximations and the properties of the day-night asymmetries are illustrated numerically in the3+1neutrino mixing framework.
Chap.6, Conclusion and Prospect. In this chapter, we shall give a short review and summary of the previous six chapters and try to describe the prospects of sterile neutrino phenomenology.
第一章,导论。我们将介绍中微子物理的发展历史、简要阐述现阶段人们对中微子的基本认识,了解中微子物理学的过去、现在,并尝试藉由五组悬而未决的开放问题对未来的研究热点作一启发性的展望。对于中微子物理和弱相互作用的发展历程,我们进行了相当深入和细致的考证和归纳,在理论和实验两个方面都给出了比较精细、完整的描述,我们还为此专门列出年表以供查阅。
第二章,中微子混合与振荡理论。本章试图对中微子的混合与振荡现象进行简洁明要而又自成体系的完整介绍。我们首先对粒子物理学的标准模型进行介绍,主要包含标准模型的物质场和相互作用拉氏量,生成规范波色场质量的Higgs机制；接着介绍超出标准模型的中微子质量产生机制,以及混合矩阵的定义及参数化；最后,我们将给出中微子真空振荡几率和物质中演化方程的介绍。
第三章,振荡实验和短基线反常。我们首先对中微子振荡实验进行分类介绍,接着对短基线实验反常进行考察,分别在3+1,3+2,3+1+1框架内对全部短基线中微子振荡数据进行全局的振荡参数拟合分析。我们将展示3+1框架下振荡参数的允许区间,其中△m412位于0.82到2.19eV2之间(3σ)。此外,无振荡的情形在6σ置信度下被排除,但如果不把LSND的结果考虑在内,这个结果将令人惊讶的下降到2σ。LSND的结果依然是短基线中微子振荡决定性的主要证据,为此,我们需要其他更高精度的实验去检验LSND的结果。
第四章,活跃-惰性太阳中微子振荡及CP相位。我们将研究包含任意Ns味惰性中微子的,3+Ns味中微子在太阳传播过程中的味演化,并着重研究中微子混合矩阵中各CP相角的效应；计算相应的、描述电子中微子生存几率的Parke公式,计算电子味到惰性味的中微子跃迁几率；更进一步,我们将基于3+1味混合的框架,对所有解析结果进行细致的数值验证,并演示、追踪三个CP相角的贡献和效应。我们所导出推广的Parke公式适用于将来高精度的太阳中微子活跃与惰性振荡实验的测量；在我们基于3+1味典型混合参数给出的例子中,三个未测知的CP相角对电子中微子生存几率造成的改变可以达到1%，而对电子味到惰性味中微子跃迁几率,则高达100%。将来的短基线中微子振荡实验有望对混合矩阵|uα4|(α=e,μ,τ)的绝对值进行精确测量,从而有可能依据这些结果通过太阳中微子实验测量CP相角。
第五章,活跃-惰性太阳中微子振荡中的日夜不对称性。沿用第四章的任意3+Ns味中微子混合框架,我们进一步讨论活跃与惰性太阳中微子振荡中的日夜不对称性,给出微扰和分层两种不同近似下振荡几率的解析表达式。通过与数值结果的比较,我们指出分层近似解析公式的精度是足以信赖的；我们还将分别展示地球物质效应中的活跃及惰性两组中微子混参数的依赖关系以及CP相位对振荡几率的影响。我们发现,年平均重生因子对于实验位址并不敏感,且随着中微子能量递增而变大；对于高能的太阳中微子,其电子味生存几率和电子味到惰性味的转化几率的日夜不对称性Dee。和Des。,幅度可以分别达到10-2和10-3量级；我们还给出了CP相角对Dee和Des。的影响,这个效应在高能区间可以达到10-3的量级。因此,未来的高精度中微子实验有可能探测到活跃与惰性混合以及日夜不对称性中的CP相位。
第六章,回顾和展望。作为结束,本章将对前文内容进行简要梳理和概括,并对惰性中微子现象学的未来发展进行思考和展望。
In this thesis we focus on the phenomenology of neutrino oscillation, assuming the existence of sterile neutrinos. The thesis is organized as follows:
Chap.1, Introduction. In this chapter, we shall give an overview of the history of neutrino physics, outline some fundamental knowledge of neutrinos that we have accumulated until nowadays, and summarize the research frontier by stating five groups of open questions on neutrinos.
Chap.2, Neutrino Oscillation Theory. In this chapter, we first give a brief summary to the standard model of electroweak interaction including introductions of the construction of the Standard Model Lagrangian, and the Higgs mechanism which endows gauge bosons in a gauge theory with mass through absorption of Nambu-Goldstone bosons arising in spontaneous symmetry breaking. We then introduce the description of a massive neutrino in the cases of Dirac/Majorana and the most general Dirac-Majorana mass. After that, we introduce the PMNS matrix which describe the neutrino mixing, and the parameterization of the mixing matrix for arbitrary3+Ns neutrinos where Ns stands for the number of sterile neutrino. Finally, we derive the expressions of neutrino oscillation probabilities and the famous MSW equation which formulize neutrino oscillations in matter.
Chap.3, Oscillation Experiments and SBL anomaly. In this chapter, we first introduce different types of neutrino experiments。We shall introduce carefully the SBL neutrino experiments and anomalies from their recent results. A neutrino oscillation explanation of these anomalies implies the existence of at least one extra mass-squared Difference ΔmS2BL such that ΔmS2OL<<ΔmA2TM<
Chap.5, Day-Night Asymmetries in Active-Sterile Solar Neutrino Oscil-lations. In this chapter, we discuss the day-night asymmetries in active-sterile solar neutrino oscillations in the framework mentioned in Chap.4. Analytical expressions of the probability of neutrino flavor transitions in the Earth in the perturbative approximation and in the slab approximation are presented and the effects of active-sterile mixing and of the CP-violating phases are discussed. The accuracy of the analytical approximations and the properties of the day-night asymmetries are illustrated numerically in the3+1neutrino mixing framework.
Chap.6, Conclusion and Prospect. In this chapter, we shall give a short review and summary of the previous six chapters and try to describe the prospects of sterile neutrino phenomenology.
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