中微子振荡现象学中的若干研究
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摘要
中微子振荡是最近十年粒子物理领域最重要的成就之一。太阳中微子实验(SNO),大气中微子实验(SK),反应堆中微子实验(KamLAND)以及加速器中微子实验(K2K,MINOS)都给出了中微子味转化的确实证据,这就意味着中微子具有非零的质量和非平庸的混合结构。现在中微子质量和混合的标准图像是亚电子伏特质量的三味中微子间的双大混合。
在本论文,我们主要讨论了中微子振荡和中微子质量三个不同方面的问题。论文第一个讨论的问题是三双最大混合(TriBimaxmal)的修正。我们讨论了三种有代表性的修正,包括带电轻子部分的修正,辐射修正以及右手中微子部分的修正。此外,在讨论此问题之前,在第2章的前半部分,我们简单介绍了粒子物理标准模型和产生中微子质量的跷跷板(Seesaw)机制的基础知识。
我们讨论的第二个问题是量子场论中的中微子振荡理论。在第3章,我们首先回顾中微子真空振荡的标准处理方法,然后介绍在量子场论中的两个中微子振荡模型,其中一个模型被用来定义相互作用相关的味态,而另一个模型是利用中微子混合来构造味态。我们使用后者的模型来定义的味态来研究标准模型中相互作用顶点的振幅。我们发现在数图阶会出现味改变的荷流相互作用。这意味着我们无法通过伴随而生的带电轻子来定义中微子的味量子数,从而导致物理上一致性的矛盾。
第三个问题我们讨论了太阳中微子的物质效应和试验的统计分析。在第4章中,我们介绍了中微子穿越太阳内部的共振加强效应(MSW效应)。在给出两味混合近似和三味中微子混合条件下的MSW效应后,我们详细讨论了存在三个活跃中微子和Ns个惰性中微子混合的一般情况下的MSW效应,我们使用解析和数值计算相对比的方法来验证结果的正确性。此外,我们还在此章的末尾处讨论了中微子穿过地球内部的物质重生效应。在第5章中,我们使用最小方差方法对若干太阳中微子和反应堆(KamLAND)中微子实验的结果进行统计分析。在两味混合近似下,我们给出两个振荡参数(△m2和tan2θ)的全局拟合结果,结果验证了太阳中微子丢失问题的大角混合MSW共振解。在三味中微子混合的拟合中我们主要关注可能的非零θ13的信息,我们的结果给出了1.2ρ置信水平的显著性。
在第6章中,我们给出了结论和展望。
Neutrino oscillation is one of the most important achievements in particle physics in last ten years. Compelling evidences of neutrino flavor transformations are obtained in many experiments, such as solar neutrino experiments(SNO), atmospheric neutrino experiments(SK), reactor neutrino experiments(KamLAND) and accelerator neutrino experiments(K2K,MINOS), which indicate that neutrinos have non-zero masses and non-trivial mixing. Now the standard picture of neutrino masses and mixing is three neutrinos with sub-eV masses and bi-large mixing.
The main parts of this dissertation include three topics on different aspects of neu-trino oscillation and neutrino masses. The first one is devoted to the discussion of tribimaxmal pattern of neutrino mixing. We investigate three different methods of the deviation of the tribimaxmal mixing matrix, including charged lepton section correc-tions, radiative corrections and right-handed sector corrections. Before this, in chap-ter 2, we also discussed the main fundamentals of the standard model(SM) in particle physics and the Seesaw mechanism of neutrino mass generation.
The second topic is about neutrino oscillation theory in quantum field theory(QFT). In chapter 3, after we reviewed the standard treatment of neutrino vacuum oscillation, we introduce two different models of neutrino oscillation in QFT, one is used to de-fine process-dependent flavor states and another proposed by Blasone and Vitiello(BV) is focused on the construction of flavor Fock states from mixing. Using these flavor states in the latter model, We check the consistency of the two models by calculating the amplitudes of interaction vertex in SM. We find that, at tree level, flavor changing charge(CC) current interactions emerge even if we carry out everything correctly. This means that we cannot define a neutrino flavor by the flavor of associated charged lepton and results in contradictions.
We discuss the matter effects and statistical analysis of solar neutrinos as our third topic. In chapter 4, we discuss the resonance enhancement mechanism(MSW effect) which happens when neutrino propagates inside the Sun. After derived this effect in two-neutrino mixing approximation and in-three neutrino mixing, we discuss in de-tail the MSW effect with the generic mixing of three active neutrinos and Ns sterile neutrinos. We employ both analytical and numerical analysis to check the accuracy of our results. We also take into account the earth re-generation effects of solar neu- trinos at the end of this chapter. In chapter 5, we present our data analysis results of solar neutrino and reactor(KamLAND) neutrino experiments by using the least squares methods. In two-neutrino approximation, we give the global fit of the two oscillation parameters(△m2 and tan2θ), which exhibits the main feature of the LMA-MSW solu-tion of solar neutrino problem. In three-neutrino mixing hypothesis, we focus on the possible hint of non-zeroθ13. Our results give a significance of 1.2σ.
Conclusions and future prospects are summarized in chapter 6.
在本论文,我们主要讨论了中微子振荡和中微子质量三个不同方面的问题。论文第一个讨论的问题是三双最大混合(TriBimaxmal)的修正。我们讨论了三种有代表性的修正,包括带电轻子部分的修正,辐射修正以及右手中微子部分的修正。此外,在讨论此问题之前,在第2章的前半部分,我们简单介绍了粒子物理标准模型和产生中微子质量的跷跷板(Seesaw)机制的基础知识。
我们讨论的第二个问题是量子场论中的中微子振荡理论。在第3章,我们首先回顾中微子真空振荡的标准处理方法,然后介绍在量子场论中的两个中微子振荡模型,其中一个模型被用来定义相互作用相关的味态,而另一个模型是利用中微子混合来构造味态。我们使用后者的模型来定义的味态来研究标准模型中相互作用顶点的振幅。我们发现在数图阶会出现味改变的荷流相互作用。这意味着我们无法通过伴随而生的带电轻子来定义中微子的味量子数,从而导致物理上一致性的矛盾。
第三个问题我们讨论了太阳中微子的物质效应和试验的统计分析。在第4章中,我们介绍了中微子穿越太阳内部的共振加强效应(MSW效应)。在给出两味混合近似和三味中微子混合条件下的MSW效应后,我们详细讨论了存在三个活跃中微子和Ns个惰性中微子混合的一般情况下的MSW效应,我们使用解析和数值计算相对比的方法来验证结果的正确性。此外,我们还在此章的末尾处讨论了中微子穿过地球内部的物质重生效应。在第5章中,我们使用最小方差方法对若干太阳中微子和反应堆(KamLAND)中微子实验的结果进行统计分析。在两味混合近似下,我们给出两个振荡参数(△m2和tan2θ)的全局拟合结果,结果验证了太阳中微子丢失问题的大角混合MSW共振解。在三味中微子混合的拟合中我们主要关注可能的非零θ13的信息,我们的结果给出了1.2ρ置信水平的显著性。
在第6章中,我们给出了结论和展望。
Neutrino oscillation is one of the most important achievements in particle physics in last ten years. Compelling evidences of neutrino flavor transformations are obtained in many experiments, such as solar neutrino experiments(SNO), atmospheric neutrino experiments(SK), reactor neutrino experiments(KamLAND) and accelerator neutrino experiments(K2K,MINOS), which indicate that neutrinos have non-zero masses and non-trivial mixing. Now the standard picture of neutrino masses and mixing is three neutrinos with sub-eV masses and bi-large mixing.
The main parts of this dissertation include three topics on different aspects of neu-trino oscillation and neutrino masses. The first one is devoted to the discussion of tribimaxmal pattern of neutrino mixing. We investigate three different methods of the deviation of the tribimaxmal mixing matrix, including charged lepton section correc-tions, radiative corrections and right-handed sector corrections. Before this, in chap-ter 2, we also discussed the main fundamentals of the standard model(SM) in particle physics and the Seesaw mechanism of neutrino mass generation.
The second topic is about neutrino oscillation theory in quantum field theory(QFT). In chapter 3, after we reviewed the standard treatment of neutrino vacuum oscillation, we introduce two different models of neutrino oscillation in QFT, one is used to de-fine process-dependent flavor states and another proposed by Blasone and Vitiello(BV) is focused on the construction of flavor Fock states from mixing. Using these flavor states in the latter model, We check the consistency of the two models by calculating the amplitudes of interaction vertex in SM. We find that, at tree level, flavor changing charge(CC) current interactions emerge even if we carry out everything correctly. This means that we cannot define a neutrino flavor by the flavor of associated charged lepton and results in contradictions.
We discuss the matter effects and statistical analysis of solar neutrinos as our third topic. In chapter 4, we discuss the resonance enhancement mechanism(MSW effect) which happens when neutrino propagates inside the Sun. After derived this effect in two-neutrino mixing approximation and in-three neutrino mixing, we discuss in de-tail the MSW effect with the generic mixing of three active neutrinos and Ns sterile neutrinos. We employ both analytical and numerical analysis to check the accuracy of our results. We also take into account the earth re-generation effects of solar neu- trinos at the end of this chapter. In chapter 5, we present our data analysis results of solar neutrino and reactor(KamLAND) neutrino experiments by using the least squares methods. In two-neutrino approximation, we give the global fit of the two oscillation parameters(△m2 and tan2θ), which exhibits the main feature of the LMA-MSW solu-tion of solar neutrino problem. In three-neutrino mixing hypothesis, we focus on the possible hint of non-zeroθ13. Our results give a significance of 1.2σ.
Conclusions and future prospects are summarized in chapter 6.
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