Higgs物理在LHC和ILC上的唯象研究
摘要
粒子物理的标准模型(SM)成功的将强相互作用、弱相互作用和电磁相互作用三种相互作用有机的统一起来，并在过去的几十年里被大量精确实验所检验。可以说，标准模型是迄今描述微观粒子相互作用规律最完美的理论之一。标准模型虽然取得了巨大的成功，但其理论体系仍有一些不足之处。如精细调节问题，不能为暗物质提供候选者，引力相互作用也没有纳入到其理论体系之中。所以，人们更倾向于视标准模型为某一高能标新物理模型下的低能有效理论，这就为超出标准模型之外的新物理提供了发展空间。也就是说，在某一高能标下应该存在更基本的理论。在众多的更基本的新物理模型中，低能超对称模型是比较流行的新物理模型之一，它可以很好的解决标准模型所存在的一些问题。因此，对低能超对称模型的唯象学研究一直是一个比较热门和前沿的领域。
无论在标准模型中，还是在新物理模型中，Higgs物理都是一个研究热点。这是因为Higgs粒子在质量起源问题上扮演着一个很重要的角色。一方面，它通过自发破缺，也就是Higgs机制为矢量玻色子提供质量；另一方面，它通过Yukawa耦合为费米子提供质量。因此，Higgs粒子也被称为是“上帝粒子”，Higgs粒子的重要性决定了它受关注的程度。从1964年Higgs机制的首次提出，到2012年7月，欧洲核子研究组织（CERN）发现Higgs存在的迹象,再到2013年3月确认发现Higgs[1]，人类走过了漫长的半个世纪。虽然Higgs已经发现，但是关于Higgs的研究依然在继续，Higgs的性质还有待进一步研究，并没有直接证据证明已发现的Higgs是标准模型中的Higgs粒子。我们期待着这些问题会随着欧洲大型强子对撞机（LHC）的再运行而逐步解开。
本文主要是在最小超对称模型（MSSM）和次最小超对称模型（NMSSM）,结合LHC和未来的直线对撞机ILC的运行环境，对Higgs的一些产生及衰变过程进行研究。主要包含以下几部分：
（1）我们基于125GeV Higgs粒子的发现，利用Manohar-Wise模型来解释Higgs数据。Manohar-Wise模型是在SM的基础上，加入了一个色八重态电弱二重态。这么做会明显的改变Higgs粒子与胶子对和光子对的耦合强度。首先我们看当前实验限制对Manohar-Wise模型的参数空间有何限制，这些限制主要包括LHC寻找Higgs的实验限制，电弱精确测量的限制，同时有幺正性限制。施加幺正性限制是工作的一个亮点，主要是利用群论的知识，将SU(3)群的高维表示约化成多个低维表示，之后再施加幺正限制，我们在第四章中给予具体介绍。在存活的参数空间中，用最新的ATLAS和CMS的实验数据来做ft，我们发现Manohar-Wise模型可以很好的拟合Higgs的实验数据。
（2）在LHC上，基于MSSM和NMSSM两种模型，对Higgs对的产生进行了研究。该过程对研究Higgs的自耦合作用帮助很大，而Higgs自耦合可用来重构Higgs势，Higgs质量确定以后，SM中Higgs自耦合已经确定，但在SUSY中Higgs自耦合还不确定。另外，在标准模型中Higgs对的产生的主要贡献来自于单圈图，而在MSSM和NMSSM中Higgs对的产生的主要贡献也来自于单圈图。在主要贡献来自同一级次时，在SUSY中该过程的结果相对于标准模型可能会有比较大的改变。再次，该过程涉及到非退耦效应，非退耦效应会使重粒子对Higgs对产生过程的影响不容忽视。通过我们的研究，发现Higgs对的产生主要来源于胶子湮灭，其产生截面在SUSY中的值可为标准模型中的10倍，即使stop质量在TeV能标，抬高效应也能达30%。如此大的抬高作用，有可能会随着LHC的发展使通过gg→hh过程来研究Higgs成为可能。具体研究情况见本论文第五章。
（3）同样，我们在ILC上，对Higgs对的产生也进行了研究。同样分析了在MSSM和NMSSM两种模型下Higgs对产生截面相对于标准模型的变化程度。相对于标准模型，在MSSM中Higgs对产生截面的提高效应可达18倍，主要贡献来自于stau圈，这点和LHC上的情况不同；在NMSSM中抬高效应可达2倍，主要贡献来自于top-squark圈，这点和LHC上的情况相似。其具体内容见本论文第六章。
During the past40years, the Standard Model(SM) of elementary particle successfully uni-fed strong and electroweak interaction, and it has been tested by the precise experimental data.We can say that the SM is one of the best theories to describe the interaction of fundamentalparticles. The SM is a good theory but not a perfect one. Because there are several problemsthat have not been solved, for example,fne-tuning problem, candidate for dark matter problemand gravity problem. So, the SM is generally considered to be an efective theory at a low scale,leaving room for developing new physics beyond SM, i.e. there should been some more basictheory at a higher scale. In so many new physics, one of the most popular new physics is lowenergy supersymmetric model, which can solve the problems in the SM. So, the phenomenologystudy of supersymmetric model has attracted more and more attention.
Higgs plays a very important role in SM and new physics beyond SM――the mass origina-tion. On the one hand, Higgs give the boson particles mass through mechanism of spontaneoussymmetry breaking–Higgs mechanism；on the other hand, Higgs give fermion mass throughY ukawa coupling. So, Higgs is considered to be“god particle”. The study of Higgs bosonis always hot. From the frst appearance of Higgs concept in1964, to Higgs may exist in July2012, fnally to Higgs announced to be found by CERN in March2013, almost half century havepassed. The study of Higgs is not end, but going on. We do not know the founded Higgs isunder which model, i.e. there is no robust evidence to say the Higgs is in SM. We hope theseproblems will be solved together with the second running of LHC.
In this thesis, we focus on Higgs and Higgs pair production in diferent colliders underlow energy efective theory such as minimal supersymmetric standard model(NMSSM), nextto minimal supersymmetric standard model(NMSSM). The diferent colliders are mainly LargeHadron Collider (LHC) and International Linear Collider (ILC). Our work is as follows:
(1) In light of the signifcant progress of the LHC to determine the properties of the Higgsboson, we investigate the capability of the Manohar-Wise model to explain the Higgs data. Thismodel extends the SM by one family of color-octet and isospin-doublet scalars, and it can sizablyalter the coupling strengths of the Higgs boson with gluons and photons. We frst examine thecurrent constraints on the model, which are from unitarity, the LHC searches for the scalars and the electroweak precision data (EWPD).In implementing the unitarity constraint, we usethe properties of the SU(3) group to simplify the calculation. Then in the allowed parameterspace we perform a ft of the model using the latest ATLAS and CMS data. We fnd thatthe Manohar-Wise model is able to explain the data with χ2signifcantly smaller than the SMvalue.For elaborate details see chapter4.
(2)In MSSM and NMSSM, we focus on Higgs pair production at LHC. This work is helpfulfor studying Higgs self-coupling while Higgs self-coupling can be used to reconstruct the Higgspotential。After125GeV Higgs discovered,the Higgs self-coupling in SM is fxed while in SUSYis not fxed,yet.In SM, the mainly contribution of Higgs pair production is from one loop topquark diagram; in SUSY, the mainly contribution is also from one loop diagram. They arethe same order, so the production of Higgs pair in SUSY may greatly alter the productionin SM. And in this process,the non-decoupling efect may be strong, we could not ignore itsefect. Based on our research, we found that the the dominant contribution to the Higgs pairproduction comes from the gluon fusion process and the production rate can be greatly enhanced,maximally10times larger than SM prediction (even for a TeV-scale stop the production ratecan still be enhanced by a factor of1.3). Such large enhancement may help people to use thisprocess research Higgs.For elaborate details see chapter5.
(3)It is the same with (2), we also study the production of Higgs pair at ILC. We found thatthe large enhancement of the cross section in the MSSM is mainly due to the contributions fromthe loops mediated by the stau, while in the NMSSM it is mainly due to the contributions fromthe top-squark loops. The normalized production rate σSUSY/σSMcan reach18in MSSM whilecan reach2in NMSSM. Such enhancement may be detected in the future collider to researchthe property of Higgs boson.For elaborate details see chapter6.
无论在标准模型中，还是在新物理模型中，Higgs物理都是一个研究热点。这是因为Higgs粒子在质量起源问题上扮演着一个很重要的角色。一方面，它通过自发破缺，也就是Higgs机制为矢量玻色子提供质量；另一方面，它通过Yukawa耦合为费米子提供质量。因此，Higgs粒子也被称为是“上帝粒子”，Higgs粒子的重要性决定了它受关注的程度。从1964年Higgs机制的首次提出，到2012年7月，欧洲核子研究组织（CERN）发现Higgs存在的迹象,再到2013年3月确认发现Higgs[1]，人类走过了漫长的半个世纪。虽然Higgs已经发现，但是关于Higgs的研究依然在继续，Higgs的性质还有待进一步研究，并没有直接证据证明已发现的Higgs是标准模型中的Higgs粒子。我们期待着这些问题会随着欧洲大型强子对撞机（LHC）的再运行而逐步解开。
本文主要是在最小超对称模型（MSSM）和次最小超对称模型（NMSSM）,结合LHC和未来的直线对撞机ILC的运行环境，对Higgs的一些产生及衰变过程进行研究。主要包含以下几部分：
（1）我们基于125GeV Higgs粒子的发现，利用Manohar-Wise模型来解释Higgs数据。Manohar-Wise模型是在SM的基础上，加入了一个色八重态电弱二重态。这么做会明显的改变Higgs粒子与胶子对和光子对的耦合强度。首先我们看当前实验限制对Manohar-Wise模型的参数空间有何限制，这些限制主要包括LHC寻找Higgs的实验限制，电弱精确测量的限制，同时有幺正性限制。施加幺正性限制是工作的一个亮点，主要是利用群论的知识，将SU(3)群的高维表示约化成多个低维表示，之后再施加幺正限制，我们在第四章中给予具体介绍。在存活的参数空间中，用最新的ATLAS和CMS的实验数据来做ft，我们发现Manohar-Wise模型可以很好的拟合Higgs的实验数据。
（2）在LHC上，基于MSSM和NMSSM两种模型，对Higgs对的产生进行了研究。该过程对研究Higgs的自耦合作用帮助很大，而Higgs自耦合可用来重构Higgs势，Higgs质量确定以后，SM中Higgs自耦合已经确定，但在SUSY中Higgs自耦合还不确定。另外，在标准模型中Higgs对的产生的主要贡献来自于单圈图，而在MSSM和NMSSM中Higgs对的产生的主要贡献也来自于单圈图。在主要贡献来自同一级次时，在SUSY中该过程的结果相对于标准模型可能会有比较大的改变。再次，该过程涉及到非退耦效应，非退耦效应会使重粒子对Higgs对产生过程的影响不容忽视。通过我们的研究，发现Higgs对的产生主要来源于胶子湮灭，其产生截面在SUSY中的值可为标准模型中的10倍，即使stop质量在TeV能标，抬高效应也能达30%。如此大的抬高作用，有可能会随着LHC的发展使通过gg→hh过程来研究Higgs成为可能。具体研究情况见本论文第五章。
（3）同样，我们在ILC上，对Higgs对的产生也进行了研究。同样分析了在MSSM和NMSSM两种模型下Higgs对产生截面相对于标准模型的变化程度。相对于标准模型，在MSSM中Higgs对产生截面的提高效应可达18倍，主要贡献来自于stau圈，这点和LHC上的情况不同；在NMSSM中抬高效应可达2倍，主要贡献来自于top-squark圈，这点和LHC上的情况相似。其具体内容见本论文第六章。
During the past40years, the Standard Model(SM) of elementary particle successfully uni-fed strong and electroweak interaction, and it has been tested by the precise experimental data.We can say that the SM is one of the best theories to describe the interaction of fundamentalparticles. The SM is a good theory but not a perfect one. Because there are several problemsthat have not been solved, for example,fne-tuning problem, candidate for dark matter problemand gravity problem. So, the SM is generally considered to be an efective theory at a low scale,leaving room for developing new physics beyond SM, i.e. there should been some more basictheory at a higher scale. In so many new physics, one of the most popular new physics is lowenergy supersymmetric model, which can solve the problems in the SM. So, the phenomenologystudy of supersymmetric model has attracted more and more attention.
Higgs plays a very important role in SM and new physics beyond SM――the mass origina-tion. On the one hand, Higgs give the boson particles mass through mechanism of spontaneoussymmetry breaking–Higgs mechanism；on the other hand, Higgs give fermion mass throughY ukawa coupling. So, Higgs is considered to be“god particle”. The study of Higgs bosonis always hot. From the frst appearance of Higgs concept in1964, to Higgs may exist in July2012, fnally to Higgs announced to be found by CERN in March2013, almost half century havepassed. The study of Higgs is not end, but going on. We do not know the founded Higgs isunder which model, i.e. there is no robust evidence to say the Higgs is in SM. We hope theseproblems will be solved together with the second running of LHC.
In this thesis, we focus on Higgs and Higgs pair production in diferent colliders underlow energy efective theory such as minimal supersymmetric standard model(NMSSM), nextto minimal supersymmetric standard model(NMSSM). The diferent colliders are mainly LargeHadron Collider (LHC) and International Linear Collider (ILC). Our work is as follows:
(1) In light of the signifcant progress of the LHC to determine the properties of the Higgsboson, we investigate the capability of the Manohar-Wise model to explain the Higgs data. Thismodel extends the SM by one family of color-octet and isospin-doublet scalars, and it can sizablyalter the coupling strengths of the Higgs boson with gluons and photons. We frst examine thecurrent constraints on the model, which are from unitarity, the LHC searches for the scalars and the electroweak precision data (EWPD).In implementing the unitarity constraint, we usethe properties of the SU(3) group to simplify the calculation. Then in the allowed parameterspace we perform a ft of the model using the latest ATLAS and CMS data. We fnd thatthe Manohar-Wise model is able to explain the data with χ2signifcantly smaller than the SMvalue.For elaborate details see chapter4.
(2)In MSSM and NMSSM, we focus on Higgs pair production at LHC. This work is helpfulfor studying Higgs self-coupling while Higgs self-coupling can be used to reconstruct the Higgspotential。After125GeV Higgs discovered,the Higgs self-coupling in SM is fxed while in SUSYis not fxed,yet.In SM, the mainly contribution of Higgs pair production is from one loop topquark diagram; in SUSY, the mainly contribution is also from one loop diagram. They arethe same order, so the production of Higgs pair in SUSY may greatly alter the productionin SM. And in this process,the non-decoupling efect may be strong, we could not ignore itsefect. Based on our research, we found that the the dominant contribution to the Higgs pairproduction comes from the gluon fusion process and the production rate can be greatly enhanced,maximally10times larger than SM prediction (even for a TeV-scale stop the production ratecan still be enhanced by a factor of1.3). Such large enhancement may help people to use thisprocess research Higgs.For elaborate details see chapter5.
(3)It is the same with (2), we also study the production of Higgs pair at ILC. We found thatthe large enhancement of the cross section in the MSSM is mainly due to the contributions fromthe loops mediated by the stau, while in the NMSSM it is mainly due to the contributions fromthe top-squark loops. The normalized production rate σSUSY/σSMcan reach18in MSSM whilecan reach2in NMSSM. Such enhancement may be detected in the future collider to researchthe property of Higgs boson.For elaborate details see chapter6.
引文
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