t-(?)-γ耦合及(?)衰变的精确研究
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摘要
虽然标准模型(SM)被认为是迄今为止最为成功的粒子物理模型,但由其基石之一(Higgs机制)所引入的Higgs粒子至今未在实验上被发现,探索电弱对称性破缺(EWSB)的起源进而寻找新物理成为当前粒子物理学界的最重要目标。美国费米国家实验室的Tevatron对撞机以及欧洲核子中心的大型强子对撞机(LHC)为我们精确研究标准模型以及探索新物理提供了非常好的实验平台。本论文紧跟当前粒子物理学理论和实验的热点进行选题,精确研究了t-t-γ耦合及g衰变。
作为标准模型中最重的费米子,顶夸克的质量最接近电弱对称性破缺能标,研究与顶夸克相关的性质被认为最可能发现电弱对称性破缺机制的秘密。强子对撞机会产生大量的顶夸克事例,其中对撞能量最高的LHC被称为顶夸克工厂,在强子对撞机上ttγ的强产生仅对t-t-γ的耦合敏感,不会引入t-t-Z耦合的信息,所以在强子对撞机上对ttγ伴随产生过程的精确研究能为我们精确检验顶夸克与光子的规范耦合提供更好的理论支撑。在论文第三章,我们研究了强子对撞机上顶夸克(top-quark)对伴随光子产生过程(pp/pp→ttγ+X)的次领头阶(NLO)QCD修正。给出了该过程领头阶(LO)和NLO QCD修正后的顶夸克和光子的横动量分布,并且计算了Tevatron上pp→ttγ+X过程的顶夸克电荷前后不对称性(AFB)。研究结果表明,包含了NLO QCD修正后,散射截面对非物理能标μ的依赖比LO有了很大的改善；当取μ=mt时,LHC上ttγ伴随产生过程的NLO QCD修正超过了50%,如此显著的效应在LHC的实验上是必须考虑的。我们的文章发表后,被Tevatron上的CDF实验组引用,同时也得到了LHC上ATLAS实验组的重视,根据ATLAS实验组的需要,我们将pp→ttγ+X过程的精确研究拓展到LHC当前对撞能量7TeV下,同时深入研究了低光子横动量截断(pT,cut(γ))以及奇异顶夸克(qt=-4e/3)所带来的影响,研究结果表明pp→ttγ+X过程的K-因子[K≡σ-NLO/σ-LO]对pT,cut(γ)以及顶夸克带电量(qt)都不敏感。当我们将qt从2e/3变为-4e/3时,K-因子仅变化了约3%,但是总的散射截面却强烈依赖pY,cut(γ)和qt的取值。
为了解决标准模型的一些根本不足,物理学家提出了各种新的理论模型,比如Little Higgs模型,大额外维模型(LED)和最小超对称模型(MSSM)等,其中最小超对称模型(MSSM)不仅拥有优美的对称性而且具有丰富的物理内涵,被认为是最有希望的新物理模型。根据MSSM,所有SM粒子都有其超对称伴随子。在R宇称守恒的MSSM中,通常认为χ10(最轻的neutralino)是最轻的超对称粒子(LSP),除LSP外的超对称粒子都不稳定,在对撞机上产生后,它们会迅速衰变到更轻的粒子。顶夸克的超对称伴随子标量顶夸克t1被认为是最轻的标量夸克(squarks)。χ10和t1都很可能在实验上被发现。做为带色的超对称粒子,标量夸克和g会在强子对撞机上大量产生,而这些粒子一旦产生就会衰变。根据参数选取的不同,g会有很多衰变道,就像人们期待t1是最轻的标量夸克一样,衰变道g→ttχ102是g最主要的衰变道,因此精确计算该衰变道的NLO修正就非常必要。在本论文第四章,我们给出了超对称粒子g(gluino)的三体衰变过程(g→ttχ10)的包括QCD修正在内的精确计算。关于超对称参数的选取,我们紧贴实验选择了由SPA方案给出的SPS6参数基准点,关于共振粒子的处理方法,我们选择了能保证规范不变性的复质量方案(CMS),并且首次给出了在复质量方案下标量顶夸克部分的抵消项的表达式和推导过程。在上述选择下,我们精确计算了该过程在参数基准点SPS6处的LO和NLO QCD修正后的衰变宽度,并且研究了它们对真空期望值(VEVs)tanβ、g的质量mg、标量顶夸克的质量(mt1、mt2)以及χ10的质量mχ10的依赖关系,同时给出了该过程LO和NLO QCD修正后的宽度随tt不变质量Mtt和χ10的能量Emiss (missing energy)的微分分布((?)和(?))。我们的研究结果表明,在某些参数空间,NLO QCD修正的绝对值超过了30%,这个效应是相当可观的,为实验上寻找相关超对称粒子提供了很好的理论依据。
本论文中创新之处主要在如下几点：
·本论文首次对强子对撞机上pp/pp→ttγ+x过程进行了系统的研究,准确计算了该过程的NLO QCD修正,给出了该产生过程目前最精确的理论预言,为LHC和Tevatron上精确研究ttγ的产生信号提供了理论依据,对于检验顶夸克与光子的耦合性质有着非常重要的意义。并且我们的计算结果被美国费米实验室的CDF实验组采用。
·我们发表的文章"Phys. Rev. D80(2009)014022",在本领域得到了广泛的重视,截止目前他引已达十余次。根据ATLAS实验组的需要,我们对LHC上ttγ伴随产生过程进行了更加深入的研究,给出了该过程在7TeV对撞能量下的目前最精确的理论预言,同时我们还研究了低光子横动量截断以及奇异顶夸克对该过程的影响。我们的计算结果得到了ATLAS实验组的认可,并被ATLAS实验组采用。
·本论文首次对g→ttχ10过程进行了精确的研究,准确计算了该过程的NLO QCD修正,给出了该衰变过程目前最精确的理论预言,这为实验上寻找超对称粒子提供了重要的理论依据,对我们更加深入的研究MSSM具有重要的意义。
·本论文在g→ttχ10过程的精确计算中引入了复质量方案(CMS)来解决遇到的有多个超对称粒子共振的问题。同时我们还首次给出了在复质量方案下标量顶夸克部分的抵消项的表达式和推导过程。对待不稳定粒子的共振,直接使用窄宽度近似、有效拉氏量方法无法保证理论的规范不变性,而复质量方案不仅解决了多粒子的共振问题,而且能保证规范不变性。
Although the standard model(SM) is considered as the most successful model of particle physics, the Higgs boson from Higgs Mechanism which is one of the SM corner-stones, has not been discovered yet. Thus probing the origin of electroweak symmetry breaking(EWSB) and searching for new physics are the most important goals in modern particle physics. Fortunately, the Tevatron at Fermilab and the Large Hardon Collider (LHC) at CERN provide us good plats to test the SM precisely and probe new physics. The topic of this thesis follows the trends in both theoretical and experimental particle physics. We study precisely the t-t-γ coupling and gluino Decay.
The top-quark is the heaviest elementary fermion in SM whose mass is close to the scale of EWSB. It is natural to assume that the top-quark is most sensitive to EWSB. Hadron colliders can produce copious top events, and the LHC is called a top facto-ry, ttγ hadronic production is sensitive only to t-t-γ coupling and free from t-t-Z coupling at Hadron colliders. Thus precision study on ttγ associated production can support precision test on t-t-γ coupling in theoretical aspect. In chapter3, we present the precision study on associated production of ttγ at hadron colliders including the next-to-leading order(NLO) QCD corrections. We provide the leading order(LO) and NLO cross sections, distributions of the transverse momenta of top-quark and photon. We also study the LO and NLO top-quark charge forward-backward asymmetry(AFB) at the Tevatron. We find that the NLO corrections improve obviously the indepen-dence of the LO cross sections on the unphy sical scale μ. Our numerical results show that the NLO QCD corrections can surpass50%assuming μ=mt at the LHC. Such a remarkable effect must be taken into account for the precise experimental measure-ment at the LHC. Our first published paper was cited by the Tevatron CDF experi-mental group and drew great attentions of the LHC ATLAS experimental group. Ac-cording to the needs of the LHC ATLAS experimental group, we extend the study on ttγ associated production to the7TeV LHC, and probe the impacts from the lower PT,cut(γ) and the exotic top-quark(qt=-4e/3). Our further studies turn out that the K-factor[K≡σNLO/σLO] varies only slightly with the variation of either the PT,cut(γ) or the top-quark electric charge(qt)(about3%for the latter). However the LO and NLO cross sections strongly depend on the pT,cut(γ) and qt.
Various new models, such as the Little Higgs Models (LH), the Large Extra Di-mension Model (LED) and the Minimal Supersymmetiy Standard Model (MSSM), are raised to solve the fundamental problems in the SM. Among these new models, the MSSM was regarded as the most promising candidate due to its elegant symmetry and rich physics meaning. According to the MSSM, all the SM particles have their su-persymmetric partners. In the R-conserving MSSM, the lightest neutralino is usually thought to be the lightest supersymmetry particle (LSP). The supersymmetric particles are unstable and decay into lighter particles immediately after productions except L-SP. The supersymmetry partner t1of top quark is regarded as the lightest scalar quark (squark). Thus x10and t1can be probably discovered in experiments. Colored supersym-metry scalar quarks and gluinos can be copiously produced at hardon colliders and de-cay immediately. Depending on the mass spectrum of supersymmetry particles, gluinos may have many decay modes. As one expects that t1is the lightest squark, the decay mode g→ttχ10could have major contribution to the total decay width of gluino. Therefore, the accurate calculations including the NLO corrections to this decay mode are necessary. In chapter4, we present the precision study on the decay of the super-symmetry particle gluino (g→ttχ10) including the NLO QCD corrections. We select the scenario SPS6point as proposed in the SPA project as the supersymmetry parame-ters. In dealing with resonant propagators, we adopt the complex-mass scheme (CMS) which can guarantee gauge invariance. And also we present firstly the corresponding counter-terms in the scalar top sector and their deduction in the CMS. Then, using the SPS6reference point and CMS, we present the LO and NLO QCD width of the decay g→ttχ10. Meanwhile, we study their dependence on the vacuum expectation val-ue(VEVs)(tan β), the mass of gluino(mg), the masses of scalar top quarks (mt1, mt2) and the mass of χ10(mχ1o). We present the LO and NLO width distributions of the tt invariant mass (Mtt) and the missing energy (Emiss). Our numerical results show that, in some parameter space, the absolute relative correction can exceed30%. Such con-siderable effect can provide excellent theoretical foundation for supersymmetry particle hunting.
The innovative points in this thesis are mainly listed below:
· This is the first systematic study of pp/pp→ttγ+X, including the NLO QCD corrections and the most precise theoretical predictions until now. It provides theoretical foundation for studying ttγ events at the Tevatron and the LHC, espe-cially for the precise measurement of top-photon coupling. Our results have been adopted by Tevatron CDF experiment group at Fermilab.
· Our publication "Phys. Rev. D80(2009)014022" has drawn attention in the field of particle physics and has been cited more than10times by others until now. According to the needs of the Atlas experimental group at the LHC, we studied further on this topic and gave the most precise theoretical predictions at the7TeV LHC so far. We also explored the impacts from the exotic top-quark and lower PT,cut(γ) Our results have been adopted by the LHC ATLAS experimental group at CERN.
· This is the first precision study on g→ttχ10, including the NLO QCD correc-tions and the most precise theoretical predictions so far. It provides important theoretical foundation in hunting for supersymmetry particles and is essential for further study in the MSSM.
· The complex-mass scheme(CMS) is adopted in the precision study on g→ttχ10. It can solve multi-supersymmetry-particle resonance problem. We present firstly the corresponding counter-terms of the scalar top sector and their deduction in the CMS. In dealing with unstable particles, approaches like narrow-width approxi-mation and effective theory violate gauge invariance of theory. On the contrary, the CMS not only solves multi-particle resonance problem, but also guarantees gauge invariance.
作为标准模型中最重的费米子,顶夸克的质量最接近电弱对称性破缺能标,研究与顶夸克相关的性质被认为最可能发现电弱对称性破缺机制的秘密。强子对撞机会产生大量的顶夸克事例,其中对撞能量最高的LHC被称为顶夸克工厂,在强子对撞机上ttγ的强产生仅对t-t-γ的耦合敏感,不会引入t-t-Z耦合的信息,所以在强子对撞机上对ttγ伴随产生过程的精确研究能为我们精确检验顶夸克与光子的规范耦合提供更好的理论支撑。在论文第三章,我们研究了强子对撞机上顶夸克(top-quark)对伴随光子产生过程(pp/pp→ttγ+X)的次领头阶(NLO)QCD修正。给出了该过程领头阶(LO)和NLO QCD修正后的顶夸克和光子的横动量分布,并且计算了Tevatron上pp→ttγ+X过程的顶夸克电荷前后不对称性(AFB)。研究结果表明,包含了NLO QCD修正后,散射截面对非物理能标μ的依赖比LO有了很大的改善；当取μ=mt时,LHC上ttγ伴随产生过程的NLO QCD修正超过了50%,如此显著的效应在LHC的实验上是必须考虑的。我们的文章发表后,被Tevatron上的CDF实验组引用,同时也得到了LHC上ATLAS实验组的重视,根据ATLAS实验组的需要,我们将pp→ttγ+X过程的精确研究拓展到LHC当前对撞能量7TeV下,同时深入研究了低光子横动量截断(pT,cut(γ))以及奇异顶夸克(qt=-4e/3)所带来的影响,研究结果表明pp→ttγ+X过程的K-因子[K≡σ-NLO/σ-LO]对pT,cut(γ)以及顶夸克带电量(qt)都不敏感。当我们将qt从2e/3变为-4e/3时,K-因子仅变化了约3%,但是总的散射截面却强烈依赖pY,cut(γ)和qt的取值。
为了解决标准模型的一些根本不足,物理学家提出了各种新的理论模型,比如Little Higgs模型,大额外维模型(LED)和最小超对称模型(MSSM)等,其中最小超对称模型(MSSM)不仅拥有优美的对称性而且具有丰富的物理内涵,被认为是最有希望的新物理模型。根据MSSM,所有SM粒子都有其超对称伴随子。在R宇称守恒的MSSM中,通常认为χ10(最轻的neutralino)是最轻的超对称粒子(LSP),除LSP外的超对称粒子都不稳定,在对撞机上产生后,它们会迅速衰变到更轻的粒子。顶夸克的超对称伴随子标量顶夸克t1被认为是最轻的标量夸克(squarks)。χ10和t1都很可能在实验上被发现。做为带色的超对称粒子,标量夸克和g会在强子对撞机上大量产生,而这些粒子一旦产生就会衰变。根据参数选取的不同,g会有很多衰变道,就像人们期待t1是最轻的标量夸克一样,衰变道g→ttχ102是g最主要的衰变道,因此精确计算该衰变道的NLO修正就非常必要。在本论文第四章,我们给出了超对称粒子g(gluino)的三体衰变过程(g→ttχ10)的包括QCD修正在内的精确计算。关于超对称参数的选取,我们紧贴实验选择了由SPA方案给出的SPS6参数基准点,关于共振粒子的处理方法,我们选择了能保证规范不变性的复质量方案(CMS),并且首次给出了在复质量方案下标量顶夸克部分的抵消项的表达式和推导过程。在上述选择下,我们精确计算了该过程在参数基准点SPS6处的LO和NLO QCD修正后的衰变宽度,并且研究了它们对真空期望值(VEVs)tanβ、g的质量mg、标量顶夸克的质量(mt1、mt2)以及χ10的质量mχ10的依赖关系,同时给出了该过程LO和NLO QCD修正后的宽度随tt不变质量Mtt和χ10的能量Emiss (missing energy)的微分分布((?)和(?))。我们的研究结果表明,在某些参数空间,NLO QCD修正的绝对值超过了30%,这个效应是相当可观的,为实验上寻找相关超对称粒子提供了很好的理论依据。
本论文中创新之处主要在如下几点：
·本论文首次对强子对撞机上pp/pp→ttγ+x过程进行了系统的研究,准确计算了该过程的NLO QCD修正,给出了该产生过程目前最精确的理论预言,为LHC和Tevatron上精确研究ttγ的产生信号提供了理论依据,对于检验顶夸克与光子的耦合性质有着非常重要的意义。并且我们的计算结果被美国费米实验室的CDF实验组采用。
·我们发表的文章"Phys. Rev. D80(2009)014022",在本领域得到了广泛的重视,截止目前他引已达十余次。根据ATLAS实验组的需要,我们对LHC上ttγ伴随产生过程进行了更加深入的研究,给出了该过程在7TeV对撞能量下的目前最精确的理论预言,同时我们还研究了低光子横动量截断以及奇异顶夸克对该过程的影响。我们的计算结果得到了ATLAS实验组的认可,并被ATLAS实验组采用。
·本论文首次对g→ttχ10过程进行了精确的研究,准确计算了该过程的NLO QCD修正,给出了该衰变过程目前最精确的理论预言,这为实验上寻找超对称粒子提供了重要的理论依据,对我们更加深入的研究MSSM具有重要的意义。
·本论文在g→ttχ10过程的精确计算中引入了复质量方案(CMS)来解决遇到的有多个超对称粒子共振的问题。同时我们还首次给出了在复质量方案下标量顶夸克部分的抵消项的表达式和推导过程。对待不稳定粒子的共振,直接使用窄宽度近似、有效拉氏量方法无法保证理论的规范不变性,而复质量方案不仅解决了多粒子的共振问题,而且能保证规范不变性。
Although the standard model(SM) is considered as the most successful model of particle physics, the Higgs boson from Higgs Mechanism which is one of the SM corner-stones, has not been discovered yet. Thus probing the origin of electroweak symmetry breaking(EWSB) and searching for new physics are the most important goals in modern particle physics. Fortunately, the Tevatron at Fermilab and the Large Hardon Collider (LHC) at CERN provide us good plats to test the SM precisely and probe new physics. The topic of this thesis follows the trends in both theoretical and experimental particle physics. We study precisely the t-t-γ coupling and gluino Decay.
The top-quark is the heaviest elementary fermion in SM whose mass is close to the scale of EWSB. It is natural to assume that the top-quark is most sensitive to EWSB. Hadron colliders can produce copious top events, and the LHC is called a top facto-ry, ttγ hadronic production is sensitive only to t-t-γ coupling and free from t-t-Z coupling at Hadron colliders. Thus precision study on ttγ associated production can support precision test on t-t-γ coupling in theoretical aspect. In chapter3, we present the precision study on associated production of ttγ at hadron colliders including the next-to-leading order(NLO) QCD corrections. We provide the leading order(LO) and NLO cross sections, distributions of the transverse momenta of top-quark and photon. We also study the LO and NLO top-quark charge forward-backward asymmetry(AFB) at the Tevatron. We find that the NLO corrections improve obviously the indepen-dence of the LO cross sections on the unphy sical scale μ. Our numerical results show that the NLO QCD corrections can surpass50%assuming μ=mt at the LHC. Such a remarkable effect must be taken into account for the precise experimental measure-ment at the LHC. Our first published paper was cited by the Tevatron CDF experi-mental group and drew great attentions of the LHC ATLAS experimental group. Ac-cording to the needs of the LHC ATLAS experimental group, we extend the study on ttγ associated production to the7TeV LHC, and probe the impacts from the lower PT,cut(γ) and the exotic top-quark(qt=-4e/3). Our further studies turn out that the K-factor[K≡σNLO/σLO] varies only slightly with the variation of either the PT,cut(γ) or the top-quark electric charge(qt)(about3%for the latter). However the LO and NLO cross sections strongly depend on the pT,cut(γ) and qt.
Various new models, such as the Little Higgs Models (LH), the Large Extra Di-mension Model (LED) and the Minimal Supersymmetiy Standard Model (MSSM), are raised to solve the fundamental problems in the SM. Among these new models, the MSSM was regarded as the most promising candidate due to its elegant symmetry and rich physics meaning. According to the MSSM, all the SM particles have their su-persymmetric partners. In the R-conserving MSSM, the lightest neutralino is usually thought to be the lightest supersymmetry particle (LSP). The supersymmetric particles are unstable and decay into lighter particles immediately after productions except L-SP. The supersymmetry partner t1of top quark is regarded as the lightest scalar quark (squark). Thus x10and t1can be probably discovered in experiments. Colored supersym-metry scalar quarks and gluinos can be copiously produced at hardon colliders and de-cay immediately. Depending on the mass spectrum of supersymmetry particles, gluinos may have many decay modes. As one expects that t1is the lightest squark, the decay mode g→ttχ10could have major contribution to the total decay width of gluino. Therefore, the accurate calculations including the NLO corrections to this decay mode are necessary. In chapter4, we present the precision study on the decay of the super-symmetry particle gluino (g→ttχ10) including the NLO QCD corrections. We select the scenario SPS6point as proposed in the SPA project as the supersymmetry parame-ters. In dealing with resonant propagators, we adopt the complex-mass scheme (CMS) which can guarantee gauge invariance. And also we present firstly the corresponding counter-terms in the scalar top sector and their deduction in the CMS. Then, using the SPS6reference point and CMS, we present the LO and NLO QCD width of the decay g→ttχ10. Meanwhile, we study their dependence on the vacuum expectation val-ue(VEVs)(tan β), the mass of gluino(mg), the masses of scalar top quarks (mt1, mt2) and the mass of χ10(mχ1o). We present the LO and NLO width distributions of the tt invariant mass (Mtt) and the missing energy (Emiss). Our numerical results show that, in some parameter space, the absolute relative correction can exceed30%. Such con-siderable effect can provide excellent theoretical foundation for supersymmetry particle hunting.
The innovative points in this thesis are mainly listed below:
· This is the first systematic study of pp/pp→ttγ+X, including the NLO QCD corrections and the most precise theoretical predictions until now. It provides theoretical foundation for studying ttγ events at the Tevatron and the LHC, espe-cially for the precise measurement of top-photon coupling. Our results have been adopted by Tevatron CDF experiment group at Fermilab.
· Our publication "Phys. Rev. D80(2009)014022" has drawn attention in the field of particle physics and has been cited more than10times by others until now. According to the needs of the Atlas experimental group at the LHC, we studied further on this topic and gave the most precise theoretical predictions at the7TeV LHC so far. We also explored the impacts from the exotic top-quark and lower PT,cut(γ) Our results have been adopted by the LHC ATLAS experimental group at CERN.
· This is the first precision study on g→ttχ10, including the NLO QCD correc-tions and the most precise theoretical predictions so far. It provides important theoretical foundation in hunting for supersymmetry particles and is essential for further study in the MSSM.
· The complex-mass scheme(CMS) is adopted in the precision study on g→ttχ10. It can solve multi-supersymmetry-particle resonance problem. We present firstly the corresponding counter-terms of the scalar top sector and their deduction in the CMS. In dealing with unstable particles, approaches like narrow-width approxi-mation and effective theory violate gauge invariance of theory. On the contrary, the CMS not only solves multi-particle resonance problem, but also guarantees gauge invariance.
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