重味奇特强子质量谱和NMSSM模型中稀有衰变的研究
摘要
在粒子物理学中，描述粒子之间强相互作用、弱相互作用和电磁相互作用的基本理论是标准模型。标准模型是建立在场论、规范对称性和希格斯（Higgs）机制上的理论，它的理论预言与实验数据在合理的误差范围内表现出惊人的一致。标准模型在各方面取得的成功足以使我们相信其正确性。
然而，标准模型中仍然存在一些基本问题没有解决，例如，如何处理和计算非微扰效应、长程相互作用、高圈图的贡献等等。在朴素夸克模型中，介子是由一对正反夸克构成的（qqˉ），重子是由三个夸克构成的（qqq）。然而，为解释实验中新观测到的强子态谱和及其某些不寻常的特性（产生，衰变），奇特强子态得到了广泛的研究。夸克模型和量子色动力学并未排除奇特强子态的存在，如：胶球、混杂子、多夸克态和Diquark态等。格点计算和大多数的唯象模型确认低能胶球的质量位于charm-tau能区，然而在BES等实验上并未发现纯态胶球的存在。目前的理论倾向于混合的观点。由于在charm-tau能区，强子谱很丰富，可能有很多本征质量和纯胶球本征质量很接近的纯夸克态存在，因而具有相同量子数的胶球和介子间会发生混合，所以理论上倾向于认为可观测的物理态应为胶球和介子的混合态。混杂子是由一对正反夸克（qqˉ）（或三个夸克（qqq））和一个或多个胶子组成的混合体。多夸克态是指四夸克态和五夸克态等。此外要特别指出的是，Diquark概念在夸克模型诞生后不久就被Gell-Mann等人提出，并在理论方面得到了广泛的研究。
量子色动力学（QCD）已被毫无争议地证实是描述强相互作用的合理理论。渐近自由作为量子色动力学的重要结论已经得到了实验上的广泛验证。由于有渐近自由的存在，我们可知微扰理论只有在高能情况下才能得到合理的结果。因此，在强子物理问题中，微扰理论在什么情况下适用是必须要考虑的问题。在一般的强子问题中，我们可以把物理过程因子化为微扰部分和非微扰部分。对于微扰部分，我们可以借助量子色动力学得到合理准确的计算；对于非微扰部分，我们必须借助于处理非微扰效应的理论方法。目前，在粒子物理中得到广泛应用的处理非微扰效应的理论方法有:格点QCD、口袋模型、有效场论、势模型、QCD求和规则等。
在这些处理非微扰效应的方法里，QCD求和规则是计算强子性质的有力工具，并且在过去的三十年时间内已取得了显著的成功。在QCD求和规则中，强子的性质由插入的夸克流（或夸克-胶子流）来表示。基于夸克流（或夸克-胶子流），我们可以构造出理论计算所需要的关联函数。应用算符乘积展开（OPE），我们可以把关联函数在QCD层面上展开。算符乘积展开（OPE）可以把夸克-胶子相互作用中的短程相互作用（short-distance）和长程相互作用（long-distance）分离开。其中短程相互作用可以通过微扰QCD来计算，长程相互作用则被参数化成普适的真空凝聚，如夸克凝聚、胶子凝聚等等。
另一方面，关联函数又可以通过色散关系表示成对强子态的求和。联立QCD层面的关联函数和强子层面的关联函数，或者说基于夸克-强子二重性（quark-hadron duality），我们就可以得到QCD求和规则的主方程。
在标准模型中，Higgs机制是十分重要的部分，而且也是十分值得研究的部分。Higgs场和它非零的真空期望值（VEV）是产生自发对称性破缺（SSB）的基本因素。自发对称性破缺使得拉氏量中无质量的费米子获得质量，从而成为有质量的物理费米子。然而，Higgs粒子迄今为止仍未被实验观测到。此外，Higgs机制的非自然性问题目前仍未得到令人信服的解决。为了解决这些问题，新物理（NP）的引入是十分必要的。
在涉及强相互作用的物理过程中，由于强相互作用占有主导地位，新物理的效应被完全湮灭掉了。然而，在弱相互作用过程中，由于相互作用的能标较高，新物理的效应得以显现出来。例如，基于次最小超对称标准模型（NMSSM）中的赝标Higgs粒子A0
1，何小刚等人解释了HyperCP实验组在弱相互作用过程Σ+→pμ+μ中观测到的实验现象。因而，我们应该探索Higgs粒子在弱相互作用物理过程中产生的效应。
本博士论文主要研究强子物理的质量谱和NMSSM中赝标介子的稀有衰变，涉及非微扰效应的合理估算以及在稀有衰变过程中探索新物理。
本论文的研究包括：
在QCD求和规则的框架下，我们计算了标量胶球0~(++)的质量在两圈水平上的费米子修正。结果表明，该修正改变算符乘积展开（OPE）的系数（Wilson系数），也因此轻微地改变了胶球的质量。
我们认为量子数为0~(++)的介子态f0(1370)、f0(1500)和f0(1710)是夸克态和胶球的混合态，两者之间的变换矩阵定义为V。应用QCD求和规则，我们计算了量子数为0~(++)的qqˉ、ssˉ、胶球以及夸克-胶球混合的关联函数。最后我们确定了混合矩阵V。具体地讲，我们的计算并确定了qqˉ、ssˉ和胶球在物理态f0(1370)、f0(1500)和f0(1710)中所占的比重，我们的结果和其它唯象研究的结果基本一致。
为了分析近期实验上新发现的共振态，我们应用QCD求和规则计算了量子数为1共振态的质量谱。我们假定该共振态为粲夸克偶素混杂子态（Hybrid），即由c、cˉ和G构成粲夸克偶素混杂子，然后计算了它的质量谱。同时，我们还计算了底夸克偶素混杂子（bˉbG）的质量谱。结果表明，粲夸克偶素混杂子的质量谱为：mHc=4.12～4.79GeV，底夸克偶素混杂子的质量谱为：mHb=10.24～11.15GeV。粲夸克偶素混杂子的质量既不等于粲夸克偶素的质量谱，也不等于实验中新观测到的共振态。我们得到如下结论：在实验上观测到的物理态并不是单纯的粲夸克偶素混杂子，而是它和胶球或一般的粲夸克偶素态的混合。然而，底夸克混杂子的质量谱与最近在BELLE上观测到的奇特强子态一致。
基于上述工作的理论方法，我们系统地研究了不同量子数的重夸克偶素混杂子的质量谱，如：1+、0~(++)、1~(++)、0+、1+、0、1和0+。值得指出的是，以上混杂子态在J.Govaerts等人的工作中曾被计算过，我们与他们不同之处是：我们不仅采用了不同于他们计算方法的“固定点规范”方法，而且首次加入了三胶子凝聚的贡献，并且发现三胶子凝聚贡献在质量谱的稳定性方面起到了很重要的作用。
通过应用QCD求和规则和Diquark点粒子的概念，我们计算了双重夸克重子的质量谱。重子关联函数的内插流由一个重Diquark场和一个轻夸克场组成。在算符乘积展开方面，我们计算到了量纲为六的算符。结果表明，在合理的误差范围内，我们的结果和其它理论方法预测的结果基本一致。这也说明了点粒子的Diquark图像不仅反映了物理事实，而且可以应用到双重夸克重子上。
为了分析由不同组分构成的Diquark态的稳定性，我们应用QCD求和规则计算了重-重Diquark的质量谱。在此基础上借助其他人在轻-轻和轻-重Diquark方面的工作，我们系统分析了三类Diquark的质量谱和稳定性。通过与基本的物理常识进行比较，我们发现我们得到的结果与文献中的结论不一致，因此我们得到了如下结论：由于QCD求和规则在理论方面的不确定性，我们用此方法得到的E（Diquark的质量与连续谱的距离）去分析Diquark的稳定性并不合理，我们要么对QCD的理论框架进行实质性的修正，要么借助于其它的理论方法。
为了解释Σ+→p+μ+μ的较大反常衰变率，何小刚等人提出了一个新的机制,该机制认为存在一个质量为214.3MeV的轻的赝标玻色子,并且认为它就是次最小超对称标准模型(NMSSM)中轻的CP为负的希格斯粒子A01。随后,杨亚东等人应用同样的机制研究了衰变π0→e+e-,他们的结果表明这个提议的质量不能拟合π0→e+e的实验数据。这个不符合之处可能是由∑+→p+μ+μ的实验误差造成的,因为该衰变的事例数很少。这个机制是否合理是我们在同一模型内研究赝标介子双轻衰变的动机,如：π0→e+e-、η(η')→μ+μ-→μ+μ和ηb→τ+-。值得注意的是,对于衰变模式π0→e+e,标准模型的理论值小于实验数据；而衰变η→μ+μ的标准模型理论值也低于实验数据的中心值。这意味着,在标准模型之外还存在其它有贡献的机制,何小刚的假设是一种可能的机制。通过对这些衰变进行理论计算,我们可以检验是否存在一个可以解释所有这些模式的普适的A01质量。不幸的是,我们发现对于相同的耦合常数|gl|,不可以得到这样一个A01的质量。因此,我们认为,即使仍然还存有一个很小的A01质量的窗口,但唯象学上不支持这样一个轻的A01。
本博士论文在对现有实验的测量结果进行解释的同时,通过加入可能的新物理模型计算了超越标准模型的理论结果,以期望在未来的更精确的高能物理实验中得到检验。通过与实验结果的比较,我们一方面可以得到更多的有关奇特强子的信息,另一方面又可以更加深入地理解低能QCD。通过本博士论文,我们得到如下结论：我们不仅要对QCD Sum Rules方法进行更加深入的研究,而且还要深入地研究新物理模型NMSSM在稀有衰变过程中所起的作用。
The Standard Model (SM) of particle physics is a fundamental theory for describ-ing the strong, weak and the electric-magnetic interaction, which mediate the dynam-ics of the known subatomic particles. The theoretical predictions of the SM, whosefoundations are field theory, gauge symmetry and Higgs mechanism, are remarkableconsistent with the experimental observations in a reasonable error range. The successof the SM in theory and experiment has made us to believe the validity for describingthe interaction of the subatomic particles.
However, there still exist some unsolved problems in the SM, such as the methodand calculation for dealing with the nonperturbative interaction, the long-distance ef-fect, and the contributions of the higher order perturbative Feynman diagrams and soon. In the naive quark model, meson is composed of a quark and an anti-quark (q qˉ),and baryon is made up of three quarks (qqq). Nevertheless, in order to explain thehadron spectra and some abnormal property concerning the emergency and decay of thehadron, which are observed in recent experiments, exotic hadron states have receivednumerous investigation. Theoretically, the quark model and Quantum chromodynamicsdo not exclude the existence of the exotic hadron states, such as the glueball, hybrid,multi-quark state and diqruak and so on. In Lattice and most of the phenomenologicalmodels, the mass of the low lying glueball is confirmed to reside in charm-tau energyscale, however, they have not been observed in the particle accelerator until now, suchas BES, KEKB and so on. Now, the tendency for describing the glueball is to rec-ognize them as the admixture. Since the hadron spectra are rich in charm-tau energyscale, there may be several pure quark states whose eigen masses are close to the pureglueball. So according to the quantum mechanics, they mix with each other, and thenthe observable physical states should be these mixtures. The hybrid is an admixturewhich is composed of a pair of quark and anti-quark (or three quarks qqq) and one ormore gluons. What is more, the multi-quark states include the tetraquark state and pen-taquark state. Especially, the concept of diquark was proposed in Gell-Mann’s originalpaper on the quark model, and was widely studied in the theoretical aspect.
Quantum chromodynamics (QCD) is soundly established as a valid theory fordescribing the strong interaction in particle physics. The asymptotic freedom is theimportant deduction of the QCD, and has received many confirmations. In light of theasymptotic freedom, we know that the perturbative theory is available only in the high energy processes. Hence, in the hadron sector, we must take into account a necessaryquestion that is when the perturbative theory hold true. In a general hadron problem,we parameterize the physical process to a perturbative part and a nonperturbative part.With the aid of QCD, we can calculate the perturbative part and obtain reasonableresults. But for the nonperturbative part, we must recur to the theoretical technics fordealing with them. Up to now, several nonperturbative theoretical technics have beenused widely in particle physics, such as the Lattice QCD, the bag model, the effectivefield theory, the potential model and the QCD Sum Rules and so on.
Among those theoretical methods in dealing with the non-perturbative effects,QCD Sum Rules innovated by Shifman et al. turns out to be a remarkably successfuland powerful technique for computation of hadronic properties. In QCD Sum Rules, theproperties of hadron are dominated by the interpolation currents, which are composedof quark fields (or gluon fields or mixture) and construct the correlation functions forthis method. By the operator product expansion (OPE), the correlation function can beexpanded as a series of terms which are composed of operators and their correspondingWilson coefficients. The OPE can separate the short-distance effect, which is calcu-lated with the pertrubative QCD, from the long-distance effect, which is parameterizedas the vacuum condensates, such as the quark-condensate, the gluon-condensate, themixture-condensate and so on. On the other hand, based on the dispersion relation, thiscorrelation function can also be represented as a summation of all possible hadronicstates created by the inserting current.
In light of the quark-hadron duality, we obtain the main function of QCD SumRules.
In SM, Higgs Mechanism is extremely important, and has been attracted muchattention to study. Spontaneous Symmetry Breaking (SSB), where the Higgs fieldsand its nonzero vacuum expectation value (VEV) are the basic ingredients, makes themassless fermions to attain their masses and then the fermions with mass emerge. How-ever, Higgs has not been detected in experiments. Moreover, the naturalness problemhas not been solved with a creditable way yet. In order to solve these questions, theconsideration of NP is necessary.
The effects of New Physics (NP) are buried in physical processes referred to thestrong interaction, since the strong interaction dominates in these processes. However,in the processes of the weak interaction, because of the higher energy scale, the ef-fects of NP emerge. For instance, based on the light CP-odd Higgs A0
1of the Next-to Minimal Supersymmetry Standard Model (NMSSM), Xiao-Gang He et al. interpretedthe HyperCP Collaboration’s experimental result, which is referred to explaining thesemileptonic decay of Σ+→pμ+μ. Hence, we’d better make more efforts to probethe NP effects in weak interaction.
This doctoral dissertation is mainly about the spectra and some rare decays ofthe pesudoscalar mesons within the NMSSM, and refers to the reasonable estimationsof the non-perturbative effects and the probing for NP in the rare decays of the pesu-doscalar mesons in the NMSSM.
The subjects of this thesis include:
In the framework of QCD Sum Rules, we calculate the contributions offermions to the mass of the scalar glueball0~(++)at two-loop level. It obviously changesthe coefficients in the OPE and shifts the mass of the glueball.
We calculate the correlation functions of0~(++), which include q qˉ, ssˉand glue-ball, in QCD Sum Rules and obtain the mass matrix where non-diagonal terms aredetermined by the cross correlations among the three states. Diagonalizing the massmatrix and identifying the eigenstates as the physical0~(++)scalar mesons, we can de-termine the mixing. Concretely, our calculations determine the fractions of q qˉ, ssˉandglueball in the physical states f0(1370), f0(1500) and f0(1710), the results are consis-tent with that gained by other phenomenological researches.
In order to analyze the new discovered resonances in experiments, we applyQCD Sum Rules to compute the mass spectra of1charmonium (ccˉG)and bot-tomonium (bˉbG) hybrids. We find that the ground state hybrid in charm sector liesin mHc=4.12～4.79GeV, while in bottom sector the hybrid may situated inmHb=10.24～11.15GeV. Since the numerical result on charmonium hybrid massis not compatible with the charmonium spectra, including structures newly observed inexperiment, we tempt to conclude that such a hybrid does not purely exist, but rather asan admixture with other states, like glueball and regular quarkonium, in experimentalobservation. However, our result on bottomonium hybrid coincides with the “exoticstructure” recently observed at BELLE.
In analogous to the above-mentioned work, we revisit the mass spectra of heavyhybrid quarkonia (QQˉG) with various quantum numbers, JP C=1+,0~(++),1~(++),0+,1+,0,1and0+, in the framework of QCD Sum Rules. In comparison withthe former study by Govaerts et al., we include the contribution of three-gluon con-densates, which are found small but non-negligible in getting more stable results for hybrid masses. After adding these new terms and considering the uncertainty of QCDSum Rules with different input parameters, we obtain the available ranges for eachhybrid.
We calculate the mass spectra of doubly heavy baryons with the diqurk modelin terms of the QCD Sum Rules. The interpolating currents are composed of a heavydiquark field and a light quark field. Contributions of the operators up to dimension sixare taken into account in the OPE. Within a reasonable error tolerance, our numericalresults are compatible with other theoretical predictions. This indicates that the diquarkpicture reflects the reality and is applicable to the study of doubly heavy baryons.
According to the number of the heavy quark in diquarks, we clarify them asthree kinds: H-H, H-L and L-L, where H represents c or b quark, and L represents u,d or s quark. In order to analyze the stability of each kind of diqurks, we apply QCDSum Rules to calculate the mass spectrum of H-H diquraks. Combined with the formerwork on H-L and L-L diqurks by other authors, we systematically analyze the spectraand stability of these three kind of diquarks. We suggest a criterion as the quantitativestandard for the stability of the diquark. It is the gap between the masses of the diquarkand√s0where√s0is the threshold of the excited states and continuity, namely thelarger the gap is, the more stable the diquark would be. As the criterion being taken, wefind that all the gaps for various diquarks are within a small range, especially the gap forthe diquark with two heavy quarks which is believed to be a stable structure, is slightlysmaller than that for other two types of diquarks, therefore we conclude that becauseof the large theoretical uncertainty, we cannot use the numerical results obtained withQCD Sum Rules to assess the stability of diqurks, but need to invoke other theoreticalframework.
To explain the anomalously large decay rate of Σ+→p+μ+μ, it was pro-posed that a new mechanism where a light CP-odd pseudoscalar boson of mA10=214.3MeV makes a crucial contribution. Later, some authors have studied the transi-tion π0→e+e in terms of the same mechanism and their result indicates thatwith the suggested mass one cannot fit the data. This discrepancy might be causedby experimental error of Σ+→p+μ+μ because there were only a few events.Whether the mechanism is a reasonable one motivates us to investigate the transitionsπ0→e+e; η(η)→μ+μ; ηc→μ+μ; ηb→τ+τ within the same framework.It is noted that for π0→e+e, the standard model (SM) prediction is smaller thanthe data, whereas the experimental central value of η→μ+μ is also above the SM prediction. It means that there should be extra contributions from other mechanisms and the contribution of A10may be a possible one. Theoretically calculating the branch-ing ratios of the concerned modes, we would check if we can obtain an universal mass for A10which reconcile the theoretical predictions and data for all the modes. Unfor-tunately, we find that it is impossible to have such a mass with the same coupling|ge|. Therefore we conclude that the phenomenology does not favor such a light A10, even though a small window is still open.
In this doctoral thesis, one aspect is to explain the existing experimental data, and the other is to employ the NP models to compute the theoretical results which are sensitive to the beyond SM and will be search in the future experiments. When we compare our results with the experimental data, we not only receive more information on heavy exotic hadrons, but also extend our understanding for the low energy QCD. In a word, through the study of this thesis, we obtain the conclusions as follows:we should make more efforts to analyze and apply QCD Sum Rules, as well as pay more attention to the effects in rare decay mode induced by New Physics model, such as NMSSM.
然而，标准模型中仍然存在一些基本问题没有解决，例如，如何处理和计算非微扰效应、长程相互作用、高圈图的贡献等等。在朴素夸克模型中，介子是由一对正反夸克构成的（qqˉ），重子是由三个夸克构成的（qqq）。然而，为解释实验中新观测到的强子态谱和及其某些不寻常的特性（产生，衰变），奇特强子态得到了广泛的研究。夸克模型和量子色动力学并未排除奇特强子态的存在，如：胶球、混杂子、多夸克态和Diquark态等。格点计算和大多数的唯象模型确认低能胶球的质量位于charm-tau能区，然而在BES等实验上并未发现纯态胶球的存在。目前的理论倾向于混合的观点。由于在charm-tau能区，强子谱很丰富，可能有很多本征质量和纯胶球本征质量很接近的纯夸克态存在，因而具有相同量子数的胶球和介子间会发生混合，所以理论上倾向于认为可观测的物理态应为胶球和介子的混合态。混杂子是由一对正反夸克（qqˉ）（或三个夸克（qqq））和一个或多个胶子组成的混合体。多夸克态是指四夸克态和五夸克态等。此外要特别指出的是，Diquark概念在夸克模型诞生后不久就被Gell-Mann等人提出，并在理论方面得到了广泛的研究。
量子色动力学（QCD）已被毫无争议地证实是描述强相互作用的合理理论。渐近自由作为量子色动力学的重要结论已经得到了实验上的广泛验证。由于有渐近自由的存在，我们可知微扰理论只有在高能情况下才能得到合理的结果。因此，在强子物理问题中，微扰理论在什么情况下适用是必须要考虑的问题。在一般的强子问题中，我们可以把物理过程因子化为微扰部分和非微扰部分。对于微扰部分，我们可以借助量子色动力学得到合理准确的计算；对于非微扰部分，我们必须借助于处理非微扰效应的理论方法。目前，在粒子物理中得到广泛应用的处理非微扰效应的理论方法有:格点QCD、口袋模型、有效场论、势模型、QCD求和规则等。
在这些处理非微扰效应的方法里，QCD求和规则是计算强子性质的有力工具，并且在过去的三十年时间内已取得了显著的成功。在QCD求和规则中，强子的性质由插入的夸克流（或夸克-胶子流）来表示。基于夸克流（或夸克-胶子流），我们可以构造出理论计算所需要的关联函数。应用算符乘积展开（OPE），我们可以把关联函数在QCD层面上展开。算符乘积展开（OPE）可以把夸克-胶子相互作用中的短程相互作用（short-distance）和长程相互作用（long-distance）分离开。其中短程相互作用可以通过微扰QCD来计算，长程相互作用则被参数化成普适的真空凝聚，如夸克凝聚、胶子凝聚等等。
另一方面，关联函数又可以通过色散关系表示成对强子态的求和。联立QCD层面的关联函数和强子层面的关联函数，或者说基于夸克-强子二重性（quark-hadron duality），我们就可以得到QCD求和规则的主方程。
在标准模型中，Higgs机制是十分重要的部分，而且也是十分值得研究的部分。Higgs场和它非零的真空期望值（VEV）是产生自发对称性破缺（SSB）的基本因素。自发对称性破缺使得拉氏量中无质量的费米子获得质量，从而成为有质量的物理费米子。然而，Higgs粒子迄今为止仍未被实验观测到。此外，Higgs机制的非自然性问题目前仍未得到令人信服的解决。为了解决这些问题，新物理（NP）的引入是十分必要的。
在涉及强相互作用的物理过程中，由于强相互作用占有主导地位，新物理的效应被完全湮灭掉了。然而，在弱相互作用过程中，由于相互作用的能标较高，新物理的效应得以显现出来。例如，基于次最小超对称标准模型（NMSSM）中的赝标Higgs粒子A0
1，何小刚等人解释了HyperCP实验组在弱相互作用过程Σ+→pμ+μ中观测到的实验现象。因而，我们应该探索Higgs粒子在弱相互作用物理过程中产生的效应。
本博士论文主要研究强子物理的质量谱和NMSSM中赝标介子的稀有衰变，涉及非微扰效应的合理估算以及在稀有衰变过程中探索新物理。
本论文的研究包括：
在QCD求和规则的框架下，我们计算了标量胶球0~(++)的质量在两圈水平上的费米子修正。结果表明，该修正改变算符乘积展开（OPE）的系数（Wilson系数），也因此轻微地改变了胶球的质量。
我们认为量子数为0~(++)的介子态f0(1370)、f0(1500)和f0(1710)是夸克态和胶球的混合态，两者之间的变换矩阵定义为V。应用QCD求和规则，我们计算了量子数为0~(++)的qqˉ、ssˉ、胶球以及夸克-胶球混合的关联函数。最后我们确定了混合矩阵V。具体地讲，我们的计算并确定了qqˉ、ssˉ和胶球在物理态f0(1370)、f0(1500)和f0(1710)中所占的比重，我们的结果和其它唯象研究的结果基本一致。
为了分析近期实验上新发现的共振态，我们应用QCD求和规则计算了量子数为1共振态的质量谱。我们假定该共振态为粲夸克偶素混杂子态（Hybrid），即由c、cˉ和G构成粲夸克偶素混杂子，然后计算了它的质量谱。同时，我们还计算了底夸克偶素混杂子（bˉbG）的质量谱。结果表明，粲夸克偶素混杂子的质量谱为：mHc=4.12～4.79GeV，底夸克偶素混杂子的质量谱为：mHb=10.24～11.15GeV。粲夸克偶素混杂子的质量既不等于粲夸克偶素的质量谱，也不等于实验中新观测到的共振态。我们得到如下结论：在实验上观测到的物理态并不是单纯的粲夸克偶素混杂子，而是它和胶球或一般的粲夸克偶素态的混合。然而，底夸克混杂子的质量谱与最近在BELLE上观测到的奇特强子态一致。
基于上述工作的理论方法，我们系统地研究了不同量子数的重夸克偶素混杂子的质量谱，如：1+、0~(++)、1~(++)、0+、1+、0、1和0+。值得指出的是，以上混杂子态在J.Govaerts等人的工作中曾被计算过，我们与他们不同之处是：我们不仅采用了不同于他们计算方法的“固定点规范”方法，而且首次加入了三胶子凝聚的贡献，并且发现三胶子凝聚贡献在质量谱的稳定性方面起到了很重要的作用。
通过应用QCD求和规则和Diquark点粒子的概念，我们计算了双重夸克重子的质量谱。重子关联函数的内插流由一个重Diquark场和一个轻夸克场组成。在算符乘积展开方面，我们计算到了量纲为六的算符。结果表明，在合理的误差范围内，我们的结果和其它理论方法预测的结果基本一致。这也说明了点粒子的Diquark图像不仅反映了物理事实，而且可以应用到双重夸克重子上。
为了分析由不同组分构成的Diquark态的稳定性，我们应用QCD求和规则计算了重-重Diquark的质量谱。在此基础上借助其他人在轻-轻和轻-重Diquark方面的工作，我们系统分析了三类Diquark的质量谱和稳定性。通过与基本的物理常识进行比较，我们发现我们得到的结果与文献中的结论不一致，因此我们得到了如下结论：由于QCD求和规则在理论方面的不确定性，我们用此方法得到的E（Diquark的质量与连续谱的距离）去分析Diquark的稳定性并不合理，我们要么对QCD的理论框架进行实质性的修正，要么借助于其它的理论方法。
为了解释Σ+→p+μ+μ的较大反常衰变率，何小刚等人提出了一个新的机制,该机制认为存在一个质量为214.3MeV的轻的赝标玻色子,并且认为它就是次最小超对称标准模型(NMSSM)中轻的CP为负的希格斯粒子A01。随后,杨亚东等人应用同样的机制研究了衰变π0→e+e-,他们的结果表明这个提议的质量不能拟合π0→e+e的实验数据。这个不符合之处可能是由∑+→p+μ+μ的实验误差造成的,因为该衰变的事例数很少。这个机制是否合理是我们在同一模型内研究赝标介子双轻衰变的动机,如：π0→e+e-、η(η')→μ+μ-→μ+μ和ηb→τ+-。值得注意的是,对于衰变模式π0→e+e,标准模型的理论值小于实验数据；而衰变η→μ+μ的标准模型理论值也低于实验数据的中心值。这意味着,在标准模型之外还存在其它有贡献的机制,何小刚的假设是一种可能的机制。通过对这些衰变进行理论计算,我们可以检验是否存在一个可以解释所有这些模式的普适的A01质量。不幸的是,我们发现对于相同的耦合常数|gl|,不可以得到这样一个A01的质量。因此,我们认为,即使仍然还存有一个很小的A01质量的窗口,但唯象学上不支持这样一个轻的A01。
本博士论文在对现有实验的测量结果进行解释的同时,通过加入可能的新物理模型计算了超越标准模型的理论结果,以期望在未来的更精确的高能物理实验中得到检验。通过与实验结果的比较,我们一方面可以得到更多的有关奇特强子的信息,另一方面又可以更加深入地理解低能QCD。通过本博士论文,我们得到如下结论：我们不仅要对QCD Sum Rules方法进行更加深入的研究,而且还要深入地研究新物理模型NMSSM在稀有衰变过程中所起的作用。
The Standard Model (SM) of particle physics is a fundamental theory for describ-ing the strong, weak and the electric-magnetic interaction, which mediate the dynam-ics of the known subatomic particles. The theoretical predictions of the SM, whosefoundations are field theory, gauge symmetry and Higgs mechanism, are remarkableconsistent with the experimental observations in a reasonable error range. The successof the SM in theory and experiment has made us to believe the validity for describingthe interaction of the subatomic particles.
However, there still exist some unsolved problems in the SM, such as the methodand calculation for dealing with the nonperturbative interaction, the long-distance ef-fect, and the contributions of the higher order perturbative Feynman diagrams and soon. In the naive quark model, meson is composed of a quark and an anti-quark (q qˉ),and baryon is made up of three quarks (qqq). Nevertheless, in order to explain thehadron spectra and some abnormal property concerning the emergency and decay of thehadron, which are observed in recent experiments, exotic hadron states have receivednumerous investigation. Theoretically, the quark model and Quantum chromodynamicsdo not exclude the existence of the exotic hadron states, such as the glueball, hybrid,multi-quark state and diqruak and so on. In Lattice and most of the phenomenologicalmodels, the mass of the low lying glueball is confirmed to reside in charm-tau energyscale, however, they have not been observed in the particle accelerator until now, suchas BES, KEKB and so on. Now, the tendency for describing the glueball is to rec-ognize them as the admixture. Since the hadron spectra are rich in charm-tau energyscale, there may be several pure quark states whose eigen masses are close to the pureglueball. So according to the quantum mechanics, they mix with each other, and thenthe observable physical states should be these mixtures. The hybrid is an admixturewhich is composed of a pair of quark and anti-quark (or three quarks qqq) and one ormore gluons. What is more, the multi-quark states include the tetraquark state and pen-taquark state. Especially, the concept of diquark was proposed in Gell-Mann’s originalpaper on the quark model, and was widely studied in the theoretical aspect.
Quantum chromodynamics (QCD) is soundly established as a valid theory fordescribing the strong interaction in particle physics. The asymptotic freedom is theimportant deduction of the QCD, and has received many confirmations. In light of theasymptotic freedom, we know that the perturbative theory is available only in the high energy processes. Hence, in the hadron sector, we must take into account a necessaryquestion that is when the perturbative theory hold true. In a general hadron problem,we parameterize the physical process to a perturbative part and a nonperturbative part.With the aid of QCD, we can calculate the perturbative part and obtain reasonableresults. But for the nonperturbative part, we must recur to the theoretical technics fordealing with them. Up to now, several nonperturbative theoretical technics have beenused widely in particle physics, such as the Lattice QCD, the bag model, the effectivefield theory, the potential model and the QCD Sum Rules and so on.
Among those theoretical methods in dealing with the non-perturbative effects,QCD Sum Rules innovated by Shifman et al. turns out to be a remarkably successfuland powerful technique for computation of hadronic properties. In QCD Sum Rules, theproperties of hadron are dominated by the interpolation currents, which are composedof quark fields (or gluon fields or mixture) and construct the correlation functions forthis method. By the operator product expansion (OPE), the correlation function can beexpanded as a series of terms which are composed of operators and their correspondingWilson coefficients. The OPE can separate the short-distance effect, which is calcu-lated with the pertrubative QCD, from the long-distance effect, which is parameterizedas the vacuum condensates, such as the quark-condensate, the gluon-condensate, themixture-condensate and so on. On the other hand, based on the dispersion relation, thiscorrelation function can also be represented as a summation of all possible hadronicstates created by the inserting current.
In light of the quark-hadron duality, we obtain the main function of QCD SumRules.
In SM, Higgs Mechanism is extremely important, and has been attracted muchattention to study. Spontaneous Symmetry Breaking (SSB), where the Higgs fieldsand its nonzero vacuum expectation value (VEV) are the basic ingredients, makes themassless fermions to attain their masses and then the fermions with mass emerge. How-ever, Higgs has not been detected in experiments. Moreover, the naturalness problemhas not been solved with a creditable way yet. In order to solve these questions, theconsideration of NP is necessary.
The effects of New Physics (NP) are buried in physical processes referred to thestrong interaction, since the strong interaction dominates in these processes. However,in the processes of the weak interaction, because of the higher energy scale, the ef-fects of NP emerge. For instance, based on the light CP-odd Higgs A0
1of the Next-to Minimal Supersymmetry Standard Model (NMSSM), Xiao-Gang He et al. interpretedthe HyperCP Collaboration’s experimental result, which is referred to explaining thesemileptonic decay of Σ+→pμ+μ. Hence, we’d better make more efforts to probethe NP effects in weak interaction.
This doctoral dissertation is mainly about the spectra and some rare decays ofthe pesudoscalar mesons within the NMSSM, and refers to the reasonable estimationsof the non-perturbative effects and the probing for NP in the rare decays of the pesu-doscalar mesons in the NMSSM.
The subjects of this thesis include:
In the framework of QCD Sum Rules, we calculate the contributions offermions to the mass of the scalar glueball0~(++)at two-loop level. It obviously changesthe coefficients in the OPE and shifts the mass of the glueball.
We calculate the correlation functions of0~(++), which include q qˉ, ssˉand glue-ball, in QCD Sum Rules and obtain the mass matrix where non-diagonal terms aredetermined by the cross correlations among the three states. Diagonalizing the massmatrix and identifying the eigenstates as the physical0~(++)scalar mesons, we can de-termine the mixing. Concretely, our calculations determine the fractions of q qˉ, ssˉandglueball in the physical states f0(1370), f0(1500) and f0(1710), the results are consis-tent with that gained by other phenomenological researches.
In order to analyze the new discovered resonances in experiments, we applyQCD Sum Rules to compute the mass spectra of1charmonium (ccˉG)and bot-tomonium (bˉbG) hybrids. We find that the ground state hybrid in charm sector liesin mHc=4.12～4.79GeV, while in bottom sector the hybrid may situated inmHb=10.24～11.15GeV. Since the numerical result on charmonium hybrid massis not compatible with the charmonium spectra, including structures newly observed inexperiment, we tempt to conclude that such a hybrid does not purely exist, but rather asan admixture with other states, like glueball and regular quarkonium, in experimentalobservation. However, our result on bottomonium hybrid coincides with the “exoticstructure” recently observed at BELLE.
In analogous to the above-mentioned work, we revisit the mass spectra of heavyhybrid quarkonia (QQˉG) with various quantum numbers, JP C=1+,0~(++),1~(++),0+,1+,0,1and0+, in the framework of QCD Sum Rules. In comparison withthe former study by Govaerts et al., we include the contribution of three-gluon con-densates, which are found small but non-negligible in getting more stable results for hybrid masses. After adding these new terms and considering the uncertainty of QCDSum Rules with different input parameters, we obtain the available ranges for eachhybrid.
We calculate the mass spectra of doubly heavy baryons with the diqurk modelin terms of the QCD Sum Rules. The interpolating currents are composed of a heavydiquark field and a light quark field. Contributions of the operators up to dimension sixare taken into account in the OPE. Within a reasonable error tolerance, our numericalresults are compatible with other theoretical predictions. This indicates that the diquarkpicture reflects the reality and is applicable to the study of doubly heavy baryons.
According to the number of the heavy quark in diquarks, we clarify them asthree kinds: H-H, H-L and L-L, where H represents c or b quark, and L represents u,d or s quark. In order to analyze the stability of each kind of diqurks, we apply QCDSum Rules to calculate the mass spectrum of H-H diquraks. Combined with the formerwork on H-L and L-L diqurks by other authors, we systematically analyze the spectraand stability of these three kind of diquarks. We suggest a criterion as the quantitativestandard for the stability of the diquark. It is the gap between the masses of the diquarkand√s0where√s0is the threshold of the excited states and continuity, namely thelarger the gap is, the more stable the diquark would be. As the criterion being taken, wefind that all the gaps for various diquarks are within a small range, especially the gap forthe diquark with two heavy quarks which is believed to be a stable structure, is slightlysmaller than that for other two types of diquarks, therefore we conclude that becauseof the large theoretical uncertainty, we cannot use the numerical results obtained withQCD Sum Rules to assess the stability of diqurks, but need to invoke other theoreticalframework.
To explain the anomalously large decay rate of Σ+→p+μ+μ, it was pro-posed that a new mechanism where a light CP-odd pseudoscalar boson of mA10=214.3MeV makes a crucial contribution. Later, some authors have studied the transi-tion π0→e+e in terms of the same mechanism and their result indicates thatwith the suggested mass one cannot fit the data. This discrepancy might be causedby experimental error of Σ+→p+μ+μ because there were only a few events.Whether the mechanism is a reasonable one motivates us to investigate the transitionsπ0→e+e; η(η)→μ+μ; ηc→μ+μ; ηb→τ+τ within the same framework.It is noted that for π0→e+e, the standard model (SM) prediction is smaller thanthe data, whereas the experimental central value of η→μ+μ is also above the SM prediction. It means that there should be extra contributions from other mechanisms and the contribution of A10may be a possible one. Theoretically calculating the branch-ing ratios of the concerned modes, we would check if we can obtain an universal mass for A10which reconcile the theoretical predictions and data for all the modes. Unfor-tunately, we find that it is impossible to have such a mass with the same coupling|ge|. Therefore we conclude that the phenomenology does not favor such a light A10, even though a small window is still open.
In this doctoral thesis, one aspect is to explain the existing experimental data, and the other is to employ the NP models to compute the theoretical results which are sensitive to the beyond SM and will be search in the future experiments. When we compare our results with the experimental data, we not only receive more information on heavy exotic hadrons, but also extend our understanding for the low energy QCD. In a word, through the study of this thesis, we obtain the conclusions as follows:we should make more efforts to analyze and apply QCD Sum Rules, as well as pay more attention to the effects in rare decay mode induced by New Physics model, such as NMSSM.
引文
[1] Hai-Yang. Zheng Int. J. Mod. Phys. A24,3392(2009).
[2] G. S. Bali, et al.[UKQCD Collaboration], Phys. Lett. B309,378(1993).
[3] H. Chen, J. Sexton, A. Vaccarino and D. Weingarten, Nucl. Phys. Proc. Suppl.34,357(1994)[arXiv:hep-lat/9401020].
[4] C. J. Morningstar and M. J. Peardon, Phys. Rev. D60,034509(1999)[arXiv:hep-lat/9901004].
[5] A. Vaccarino and D. Weingarten, Phys. Rev. D60,114501(1999)[arXiv:hep-lat/9910007].
[6] C. Liu, Chin. Phys. Lett.18,187(2001)[arXiv:hep-lat/0004018].
[7] D. Q. Liu, J. M. Wu and Y. Chen, High Energy Phys. Nucl. Phys.26,222(2002).;
[8] N. Ishii, H. Suganuma and H. Matsufuru, Phys. Rev. D66,014507(2002).;
[9] M. Loan, X. Q. Luo and Z. H. Luo, Int. J. Mod. Phys. A21,2905(2006).;
[10] Y. Chen et al., Phys. Rev. D73,014516(2006).;
[11] V. A. Novikov, M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov Nucl. Phys. B165,67(1980).
[12] P. Pascual and R. Tarrach Phys. Lett. B113495(1982).
[13] S. Narison, Z. Phys. C,26209(1984).
[14] E. Bagan and T. G. Steele, Phys. Lett. B243,413(1990).
[15] T. Huang, H. Jin and A. Zhang, Phys. Rev. D.59034026(1999).
[16] K. Ishikawa, M. Teper and G. Schierholz, Phys. Lett. B110,399(1982).
[17] B. Berg and A. Billoire, Nucl. Phys. B221,109(1983).
[18] P. de Forcrand, G. Schierholz, H. Schneider and M. Teper, Phys. Lett. B152,107(1985).
[19] M. Teper, Phys. Lett. B183,345(1987).
[20] M. Albanese et al.[APE Collaboration], Phys. Lett. B192,163(1987).
[21] M. J. Teper, arXiv:hep-th/9812187.
[22] N. Ishii, H. Suganuma and H. Matsufuru, Phys. Rev. D66,094506(2002)[arXiv:hep-lat/0206020].
[23] H. B. Meyer and M. J. Teper, Phys. Lett. B605,344(2005)[arXiv:hep-ph/0409183].
[24] KNakamura et al.[Particle Data Group Collaboration], J. Phys. G G37,075021(2010).
[25] X. H. Yuan and L. Tang, Commun. Theor. Phys.54,495(2010)[arXiv:0911.0806[hep-ph]].
[26] L. J. Reinders, S. Yazaki and H. R. Rubinstein, Nucl. Phys. B196,125(1982).
[27] W. E. Burcham and M. Jobes, Harlow, UK: Longman (1995)752p.
[28] A. H. ROSENFELD et al., Rev. Mod. Phys.39,1(1967).
[29] A. V. Anisovich, V. V. Anisovich and A. V. Sarantsev, Phys. Lett. B395,123(1997)[arXiv:hep-ph/9611333].
[30] F. E. Close and A. Kirk, Phys. Lett. B483,345(2000)[arXiv:hep-ph/0004241].
[31] F. E. Close and A. Kirk, Eur. Phys. J. C21,531(2001)[arXiv:hep-ph/0103173].
[32] F. Giacosa, T. Gutsche, V. E. Lyubovitskij and A. Faessler, Phys. Rev. D72,094006(2005)[arXiv:hep-ph/0509247].
[33] X. G. He, X. Q. Li, X. Liu and X. Q. Zeng, Phys. Rev. D73,114026(2006)[arXiv:hep-ph/0604141].
[34] M. Shifman, Nucl. Phys. Proc. Suppl.207-208,298(2010)[arXiv:1101.1122[hep-ph]].
[35] S. Narison, Nucl. Phys. Proc. Suppl.64,210(1998)[arXiv:hep-ph/9710281].
[36] S. Narison, Nucl. Phys. B509,312(1998)[arXiv:hep-ph/9612457].
[37] D. Harnett, R. T. Kleiv, K. Moats and T. G. Steele, Nucl. Phys. A850,110(2011)[arXiv:0804.2195[hep-ph]].
[38] W. Buchmu¨ller and H. Tye, Phys. Rev. Lett.44,850(1980).
[39] N. Isgur and J. Paton, Phys. Rev. D31,2910(1985).
[40] E. Swanson and A. Seczepaniak, Phys. Rev. D59,014035(1999).
[41] T. Allen, M. Olsson and S. Veseli, Phys. Lett. B434,110(1998).
[42] Y. Kuang and T. Yan, Phys. Rev. D24,2874(1981).
[43] H.W. Ke, J. Tang, X.Q. Hao and X.Q. Li, Phys. Rev. D76,074035(2007).
[44] T. Barnes, F.E. Close and F. de Viron, Nucl. Phys. B、B224,241(1983); M.S. Chanowitz andS.R. Sharpe, Nucl. Phys. B222,211(1983).
[45] N. Isgur, R. Kokoski and J. Paton, Phys. Rev. Lett.54,869(1985); F.E. Close and P.R. Page,Nucl. Phys. B443,233(1995); F. E. Close and P.R. Page, Phys. Rev. D52,1706(1995).
[46] S. Perantonis and C. Michael, Nucl. Phys. B347,854(1990); N.A. Campbell, L.A. Griffiths,C. Michael and P.E.L. Rakow, Phys. Lett. B142,291(1984); L.A. Griffiths, C. Michael andP.E.L. Rakow, B129,351(1983).
[47] I.I. Balitsky, D.I. Diakonov and A.V. Yung, Phys. Lett. B112,71(1982); I. I. Balitsky, D.I.Diakonov and A.V. Yung, Z. Phys. C33,265(1986).
[48] J.I. Latorre, S. Narison, P. Pascual and R. Tarrach, Phys. Lett. B147,169(1984); J. I. Latorre,P. Pascual and S. Narison, Z. Phys. C34,347(1987).
[49] H. Y. Jin and J. G. Korner, Phys. Rev. D64,074002(2001); H. Y. Jin, J. G. Korner and T. G.Steele, Phys. Rev. D67,014025(2003).
[50] Tao Huang, H.Y. Jin and A.L. Zhang, Eur. Phys. J. C8,465(1999).
[51] F.K. Guo, P.N. Shen, Z.G. Wang, W.H. Liang and L.S. Kisslinger, hep-ph/0703062.
[52] Tao Huang, H.Y. Jin and A.L. Zhang, Phys. Rev. D60,114004(1999); Tao Huang, H.Y. Jinand A.L. Zhang, Phys. Rev. D61,034016(2000).
[53] J. Govaerts, L.J. Reinders, H.R. Rubinstein, and J. Weyers, Nucl. Phys. B258,215(1985); J.Govaerts, L.J. Reinders and J. Weyers, Nucl. Phys. B262,575(1985); J. Govaerts, L.J. Reinders,P. Franchen, X. Gonze and J. Weyers, Nucl. Phys. B284,674(1987).
[54] S.L. Zhu, Phys. Rev. D60,014008(1999); ibid, Rev. D60,031501(1999); ibid, Rev. D60,097502(1999).
[55] L.S. Kisslinger, D. Parno and S. Riordan, Adv. High Energy Phys.2008,982341(2008).
[56] J. Govaerts, F. de Viron, D. Gusbin and J. Weyers, Phys. Lett. B128,262(1983); J. Govaerts,F. de Viron, D. Gusbin and J. Weyers, Nucl. Phys. B248,1(1984).
[57] S. Narison, World Sci. Lect. Notes Phys.26,1(1989).
[58] S. Narison, Phys. Lett. B675,319(2009).
[59] K. G. Chetyrkin and S. Narison, Phys. Lett. B485,145(2000).
[60] F. Close and A. Kirk, Phys. Lett. B483,345(2000).
[61] X.G. He, X.Q. Li, X. Liu and X.Q. Zeng, Phys. Rev. D73,051502(2006); ibid, Phys. Rev.D73,114026(2006).
[62] B. Aubert, et al.,[BABAR Collaboration], Phys. Rev. Lett.98,212001(2007).
[63] B. Aubert, et al.,[BABAR Collaboration], Phys. Rev. Lett.95,142001(2005).
[64] X.L. Wang, et al.,[Belle Collaboration], Phys. Rev. Lett.99,142002(2007).
[65] G.J. Ding, J.J. Zhu and M.L. Yan, Phys. Rev. D77,014033(2008); B.Q. Li and K.T. Chao,Phys. Rev. D79,094004(2009); A.M. Badalian, B.L. G. Bakker and I.V. Danilkin, Phys. Atom.Nucl.72,638(2009).
[66] C.F. Qiao, J. Phys. G35,075008(2008).
[67] F.K. Guo, C. Hanhart and U.G. Meissner, Phys. Lett. B665,26(2008).
[68] R.M. Albuquerque and M. Nielsen, Nucl. Phys. A815,53(2009).
[69] M. Gell-Mann, Phys. Lett.8,214(1964).
[70] M. Ida and R. Kobayashi, Prog. Theor. Phys.36(1966)846.
[71] D. B. Lichtenberg, Nuovo Cim. A28,563(1975).
[72] D. B. Lichtenberg, W. Namgung, E. Predazzi and J. G. Wills, Phys. Rev. Lett.48,1653(1982).
[73] R. L. Jaffe, Phys. Rept.409,1(2005)[Nucl. Phys. Proc. Suppl.142,343(2005)].
[74] F. Wilczek, arXiv:hep-ph/0409168.
[75] H. W. Ke, X. Q. Li and Z. T. Wei, Phys. Rev. D77,014020(2008)[arXiv:0710.1927[hep-ph]].
[76] A. F. Falk, M. E. Luke, M. J. Savage and M. B. Wise, Phys. Rev. D49,555(1994)[arXiv:hep-ph/9305315].
[77] M. Mattson et al.[SELEX Collaboration], Phys. Rev. Lett.89,112001(2002)[arXiv:hep-ex/0208014].
[78] A. Ocherashvili et al.[SELEX Collaboration], Phys. Lett. B628,18(2005)[arXiv:hep-ex/0406033].
[79] B. Aubert et al.[BABAR Collaboration], Phys. Rev. D74,011103(2006).
[80] R. Chistov et al.[BELLE Collaboration], Phys. Rev. Lett.97,162001(2006).
[81] A. Majethiya, B. Patel, A. K. Rai and P. C. Vinodkumar, arXiv:0809.4910[hep-ph].
[82] S. P. Tong, Y. B. Ding, X. H. Guo, H. Y. Jin, X. Q. Li, P. N. Shen and R. Zhang, Phys. Rev. D62,054024(2000)[arXiv:hep-ph/9910259].
[83] D. Ebert, R. N. Faustov, V. O. Galkin and A. P. Martynenko, Phys. Rev. D66,014008(2002)[arXiv:hep-ph/0201217].
[84] D. H. He, K. Qian, Y. B. Ding, X. Q. Li and P. N. Shen, Phys. Rev. D70,094004(2004)[arXiv:hep-ph/0403301].
[85] V. V. Kiselev, A. K. Likhoded, O. N. Pakhomova, V. A. Saleev, Phys. Rev. D66,034030(2002).[hep-ph/0206140].
[86] M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Nucl. Phys. B147,385(1979).
[87] M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Nucl. Phys. B147,448(1979).
[88] Z. G. Wang and X. H. Zhang, Commun. Theor. Phys.54,323(2010)[arXiv:0905.3784[hep-ph]]; Z. G. Wang, Y. M. Xu and H. J. Wang, Commun. Theor. Phys.55,1049(2011)[arXiv:1004.0484[hep-ph]].
[89] J. R. Zhang and M. Q. Huang, Commun. Theor. Phys.54,1075(2010)[arXiv:0905.4672[hep-ph]].
[90] C. F. Qiao, L. Tang, G. Hao and X. Q. Li, J. Phys. G39,015005(2012) arXiv:1012.2614[hep-ph].
[91] V. V. Kiselev, A. K. Likhoded, Phys. Usp.45,455-506(2002)[hep-ph/0103169].
[92] E. Bagan, M. Chabab and S. Narison, Phys. Lett. B306,350(1993).
[93] J. R. Zhang and M. Q. Huang, Phys. Rev. D78,094007(2008)[arXiv:0810.5396[hep-ph]].
[94] R. M. Albuquerque and S. Narison, Nucl. Phys. Proc. Suppl.207-208,265(2010)[arXiv:1009.2428[hep-ph]].
[95] S. Narison and R. Albuquerque, Phys. Lett. B694,217(2010)[arXiv:1006.2091[hep-ph]].
[96] Maiani L, Piccinini F, Polosa A D et al. Phys. Rev. D,2005,71:014028.
[97] Nielsen M, Matheus R D’E, Navarra F S et al. Nucl. Phys. Proc. Suppl,2006,161:193-199.
[98] DING G J, YAN M L. Phys. Lett. B,2006,643:33-40.
[99] ZHANG A, HUANG T, Steele T G. Phys. Rev. D,2007,76:036004.
[100] Rehman A. arXiv:hepph/1109.1095.
[101] Kim K, Jido D, Lee S H. Phys. Rev. C,2011,84:025204.
[102] L. Tang, X. H. Yuan, C. F. Qiao and X. Q. Li, Commun. Theor. Phys.57,435(2012)[arXiv:1104.4934[hep-ph]].
[103] Ishii N, Bentz W, Yazaki K, Nucl. Phys. A,1995,587:617.
[104] Nicmorus D, Eichmann G, Krassnigg A et al. PoS C,2008, ONFINEMENT8:052.
[105] Dosch H G, Jamin M, Stech B. Z. Phys. C,1989,42:167. Jamin M, Neubert M. Phys. Lett.B,1990,238:387.
[106] WANG Z G. Eur. Phys. J. C,2011,71:1524.
[107] X. G. He, J. Tandean and G. Valencia, Phys. Rev. Lett.98,081802(2007)[arXiv:hep-ph/0610362].
[108] Q. Chang and Y. D. Yang, Phys. Lett. B676,88(2009)[arXiv:0808.2933[hep-ph]].
[109] S. Narison, Nucl. Phys. Proc. Suppl.207-208,315(2010)[arXiv:1010.1959[hep-ph]].
[110] G. F. Sterman, Cambridge, UK: Univ. Pr.(1993)572p.
[111] P. Colangelo and A. Khodjamirian, arXiv:hep-ph/0010175.
[112] S. Narison, arXiv:1105.5070[hep-ph].
[113] Reinders L J, Rubinstein H, Yazaki S, Phys. Rept,1985,127:1.
[114] D. S. Du, J. W. Li and M. Z. Yang, Phys. Lett. B619,105(2005)[arXiv:hep-ph/0409302].
[115] J. Govaerts, L. J. Reinders, P. Franchen, X. Gonze and J. Weyers, Nucl. Phys. B284,674(1987).
[116] R. Jakob, P. Kroll, M. Schurmann and W. Schweiger, Z. Phys. A347,109(1993)[arXiv:hep-ph/9310227].
[117] Ioffe B L. Prog. Part. Nucl. Phys,2006,56:232.
[118] F. Englert and R. Brout, Phys. Rev. Lett.13,321(1964).
[119] P. W. Higgs, Phys. Rev. Lett.13,508(1964).
[120] G. S. Guralnik, C. R. Hagen and T. W. B. Kibble, Phys. Rev. Lett.13,585(1964).
[121] S. Weinberg, Phys. Rev. Lett.19,1264(1967).
[122] M. E. Peskin and D. V. Schroeder, An Introduction To Quantum Field Theory, Reading, USA:Addison-Wesley (1995)842p.
[123] Yi. Liao, Quantum Field Theory Part II: Gauge Theories.
[124] S. R. Coleman and J. Mandula, Phys. Rev.159,1251(1967).
[125] R. Haag, J. T. Lopuszanski and M. Sohnius, Nucl. Phys. B88,257(1975).
[126] J. j. Cao, Z. h. Xiong and J. M. Yang, Nucl. Phys. B651,87(2003)[arXiv:hep-ph/0208035].
[127] J. Rosiek, Phys. Rev. D41,3464(1990).
[128] H. P. Nilles, M. Srednicki and D. Wyler, Phys. Lett. B120(1983)346; J. M. Frere, D. R. T.Jones and S. Raby, Nucl. Phys. B222,(1983)11; J. P. Derendinger and C. A. Savoy, Nucl. Phys.B237,(1984)307; J. R. Ellis, J. F. Gunion, H. E. Haber, L. Roszkowski and F. Zwirner, Phys.Rev. D39(1989)844; M. Drees, Int. J. Mod. Phys. A4(1989)3635.
[129] J. J. Cao, K. i. Hikasa, W. Wang, J. M. Yang, K. i. Hikasa, W. Y. Wang and J. M. Yang, Phys.Lett. B703,292(2011)[arXiv:1104.1754[hep-ph]].
[130] G. Hiller, Phys. Rev. D70,034018(2004)[arXiv:hep-ph/0404220].
[131] Z. Heng, R. J. Oakes, W. Wang, Z. Xiong and J. M. Yang, Phys. Rev. D77,095012(2008)[arXiv:0801.1169[hep-ph]].
[132] X. G. He, J. Tandean and G. Valencia, Phys. Rev. D74,115015(2006)[arXiv:hep-ph/0610274].
[133] E. Fullana and M. A. Sanchis-Lozano, Phys. Lett. B653,67(2007)[arXiv:hep-ph/0702190].
[134] X. G. He, J. Tandean and G. Valencia, Phys. Rev. D72,074003(2005)[arXiv:hep-ph/0506067].
[135] W. Love et al.[CLEO Collaboration], Phys. Rev. Lett.101,201601(2008)[arXiv:0807.2695[hep-ex]].
[136] B. Aubert et al.[BaBar Collaboration], arXiv:0808.0017[hep-ex].
[137] H. Park et al.[HyperCP Collaboration], Phys. Rev. Lett.94,021801(2005)[hep-ex/0501014].
[138] The ATLAS and CMS Collaborations, Combined Standard Model Higgs boson searches withup to2.3fb1of pp collision data at√s=7TeV at the LHC, ATLAS-CONF-2011-157, CMSPAS HIG-11-023(2011).
[139] F. Gianotti (the ATLAS Collaboration), Update on the Standard Model Higgs searches inATLAS, CERN Public Seminar,13December2011, CERN.
[140] G. Tonelli (the CMS Collaboration), Update on the Standard Model Higgs searches in CMS,CERN Public Seminar,13December2011, CERN.
[141] C. Kao, H.-Y. Cheng, W.-S. Hou and J. Sayre, arXiv:1112.1707[hep-ph].
[142] Z. K. Silagadze, Phys. Rev. D74,054003(2006)[hep-ph/0606284].
[143] M. Z. Yang, Phys. Rev. D79,074026(2009)[arXiv:0902.1295[hep-ph]].
[144] T. Feldmann, P. Kroll and B. Stech, Phys. Rev. D58,114006(1998)[hep-ph/9802409].
[145] T. N. Pham, Phys. Rev. D77,014024(2008)[Erratum-ibid. D77,019905(2008)][arXiv:0710.2412[hep-ph]].
[146] T. P. Cheng and L. F. Li, Oxford, Uk: Clarendon (1984)536P.(Oxford Science Publica-tions).
[147] D. S. Hwang and G. H. Kim, Z. Phys. C76,107(1997)[arXiv:hep-ph/9703364].
[148] B. Aubert et al.[BABAR Collaboration], Phys. Rev. Lett.103,161801(2009)[arXiv:0903.1124[hep-ex]].
[149] H. W. Ke, X. Q. Li and X. Liu, arXiv:1002.1187[hep-ph].
[150] H.-W. Ke, X.-H. Yuan and X.-Q. Li, Int. J. Mod. Phys. A26,4731(2011)[arXiv:1101.3407[hep-ph]].
[151] A. Rashed, M. Duraisamy and A. Datta, Phys. Rev. D82,054031(2010)[arXiv:1004.5419[hep-ph]].
[152] T. Huang, H.-Y. Jin, A.-L. Zhang, Phys. Rev. D59,034026(1999).[hep-ph/9807391].
[153] P. Pascual and R. Tarrach, Lect. Notes Phys.194,1(1984).
[154] M. Ablikim et al.[BES Collaboration], Phys. Lett. B607,243(2005)[arXiv:hep-ex/0411001].
[155] M. Ablikim et al.[BES Collaboration], Phys. Rev. Lett.96,162002(2006)[arXiv:hep-ex/0602031].
[156] X. G. He, X. Q. Li, X. Liu and X. Q. Zeng, Phys. Rev. D73,051502(2006)[arXiv:hep-ph/0602075].
[2] G. S. Bali, et al.[UKQCD Collaboration], Phys. Lett. B309,378(1993).
[3] H. Chen, J. Sexton, A. Vaccarino and D. Weingarten, Nucl. Phys. Proc. Suppl.34,357(1994)[arXiv:hep-lat/9401020].
[4] C. J. Morningstar and M. J. Peardon, Phys. Rev. D60,034509(1999)[arXiv:hep-lat/9901004].
[5] A. Vaccarino and D. Weingarten, Phys. Rev. D60,114501(1999)[arXiv:hep-lat/9910007].
[6] C. Liu, Chin. Phys. Lett.18,187(2001)[arXiv:hep-lat/0004018].
[7] D. Q. Liu, J. M. Wu and Y. Chen, High Energy Phys. Nucl. Phys.26,222(2002).;
[8] N. Ishii, H. Suganuma and H. Matsufuru, Phys. Rev. D66,014507(2002).;
[9] M. Loan, X. Q. Luo and Z. H. Luo, Int. J. Mod. Phys. A21,2905(2006).;
[10] Y. Chen et al., Phys. Rev. D73,014516(2006).;
[11] V. A. Novikov, M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov Nucl. Phys. B165,67(1980).
[12] P. Pascual and R. Tarrach Phys. Lett. B113495(1982).
[13] S. Narison, Z. Phys. C,26209(1984).
[14] E. Bagan and T. G. Steele, Phys. Lett. B243,413(1990).
[15] T. Huang, H. Jin and A. Zhang, Phys. Rev. D.59034026(1999).
[16] K. Ishikawa, M. Teper and G. Schierholz, Phys. Lett. B110,399(1982).
[17] B. Berg and A. Billoire, Nucl. Phys. B221,109(1983).
[18] P. de Forcrand, G. Schierholz, H. Schneider and M. Teper, Phys. Lett. B152,107(1985).
[19] M. Teper, Phys. Lett. B183,345(1987).
[20] M. Albanese et al.[APE Collaboration], Phys. Lett. B192,163(1987).
[21] M. J. Teper, arXiv:hep-th/9812187.
[22] N. Ishii, H. Suganuma and H. Matsufuru, Phys. Rev. D66,094506(2002)[arXiv:hep-lat/0206020].
[23] H. B. Meyer and M. J. Teper, Phys. Lett. B605,344(2005)[arXiv:hep-ph/0409183].
[24] KNakamura et al.[Particle Data Group Collaboration], J. Phys. G G37,075021(2010).
[25] X. H. Yuan and L. Tang, Commun. Theor. Phys.54,495(2010)[arXiv:0911.0806[hep-ph]].
[26] L. J. Reinders, S. Yazaki and H. R. Rubinstein, Nucl. Phys. B196,125(1982).
[27] W. E. Burcham and M. Jobes, Harlow, UK: Longman (1995)752p.
[28] A. H. ROSENFELD et al., Rev. Mod. Phys.39,1(1967).
[29] A. V. Anisovich, V. V. Anisovich and A. V. Sarantsev, Phys. Lett. B395,123(1997)[arXiv:hep-ph/9611333].
[30] F. E. Close and A. Kirk, Phys. Lett. B483,345(2000)[arXiv:hep-ph/0004241].
[31] F. E. Close and A. Kirk, Eur. Phys. J. C21,531(2001)[arXiv:hep-ph/0103173].
[32] F. Giacosa, T. Gutsche, V. E. Lyubovitskij and A. Faessler, Phys. Rev. D72,094006(2005)[arXiv:hep-ph/0509247].
[33] X. G. He, X. Q. Li, X. Liu and X. Q. Zeng, Phys. Rev. D73,114026(2006)[arXiv:hep-ph/0604141].
[34] M. Shifman, Nucl. Phys. Proc. Suppl.207-208,298(2010)[arXiv:1101.1122[hep-ph]].
[35] S. Narison, Nucl. Phys. Proc. Suppl.64,210(1998)[arXiv:hep-ph/9710281].
[36] S. Narison, Nucl. Phys. B509,312(1998)[arXiv:hep-ph/9612457].
[37] D. Harnett, R. T. Kleiv, K. Moats and T. G. Steele, Nucl. Phys. A850,110(2011)[arXiv:0804.2195[hep-ph]].
[38] W. Buchmu¨ller and H. Tye, Phys. Rev. Lett.44,850(1980).
[39] N. Isgur and J. Paton, Phys. Rev. D31,2910(1985).
[40] E. Swanson and A. Seczepaniak, Phys. Rev. D59,014035(1999).
[41] T. Allen, M. Olsson and S. Veseli, Phys. Lett. B434,110(1998).
[42] Y. Kuang and T. Yan, Phys. Rev. D24,2874(1981).
[43] H.W. Ke, J. Tang, X.Q. Hao and X.Q. Li, Phys. Rev. D76,074035(2007).
[44] T. Barnes, F.E. Close and F. de Viron, Nucl. Phys. B、B224,241(1983); M.S. Chanowitz andS.R. Sharpe, Nucl. Phys. B222,211(1983).
[45] N. Isgur, R. Kokoski and J. Paton, Phys. Rev. Lett.54,869(1985); F.E. Close and P.R. Page,Nucl. Phys. B443,233(1995); F. E. Close and P.R. Page, Phys. Rev. D52,1706(1995).
[46] S. Perantonis and C. Michael, Nucl. Phys. B347,854(1990); N.A. Campbell, L.A. Griffiths,C. Michael and P.E.L. Rakow, Phys. Lett. B142,291(1984); L.A. Griffiths, C. Michael andP.E.L. Rakow, B129,351(1983).
[47] I.I. Balitsky, D.I. Diakonov and A.V. Yung, Phys. Lett. B112,71(1982); I. I. Balitsky, D.I.Diakonov and A.V. Yung, Z. Phys. C33,265(1986).
[48] J.I. Latorre, S. Narison, P. Pascual and R. Tarrach, Phys. Lett. B147,169(1984); J. I. Latorre,P. Pascual and S. Narison, Z. Phys. C34,347(1987).
[49] H. Y. Jin and J. G. Korner, Phys. Rev. D64,074002(2001); H. Y. Jin, J. G. Korner and T. G.Steele, Phys. Rev. D67,014025(2003).
[50] Tao Huang, H.Y. Jin and A.L. Zhang, Eur. Phys. J. C8,465(1999).
[51] F.K. Guo, P.N. Shen, Z.G. Wang, W.H. Liang and L.S. Kisslinger, hep-ph/0703062.
[52] Tao Huang, H.Y. Jin and A.L. Zhang, Phys. Rev. D60,114004(1999); Tao Huang, H.Y. Jinand A.L. Zhang, Phys. Rev. D61,034016(2000).
[53] J. Govaerts, L.J. Reinders, H.R. Rubinstein, and J. Weyers, Nucl. Phys. B258,215(1985); J.Govaerts, L.J. Reinders and J. Weyers, Nucl. Phys. B262,575(1985); J. Govaerts, L.J. Reinders,P. Franchen, X. Gonze and J. Weyers, Nucl. Phys. B284,674(1987).
[54] S.L. Zhu, Phys. Rev. D60,014008(1999); ibid, Rev. D60,031501(1999); ibid, Rev. D60,097502(1999).
[55] L.S. Kisslinger, D. Parno and S. Riordan, Adv. High Energy Phys.2008,982341(2008).
[56] J. Govaerts, F. de Viron, D. Gusbin and J. Weyers, Phys. Lett. B128,262(1983); J. Govaerts,F. de Viron, D. Gusbin and J. Weyers, Nucl. Phys. B248,1(1984).
[57] S. Narison, World Sci. Lect. Notes Phys.26,1(1989).
[58] S. Narison, Phys. Lett. B675,319(2009).
[59] K. G. Chetyrkin and S. Narison, Phys. Lett. B485,145(2000).
[60] F. Close and A. Kirk, Phys. Lett. B483,345(2000).
[61] X.G. He, X.Q. Li, X. Liu and X.Q. Zeng, Phys. Rev. D73,051502(2006); ibid, Phys. Rev.D73,114026(2006).
[62] B. Aubert, et al.,[BABAR Collaboration], Phys. Rev. Lett.98,212001(2007).
[63] B. Aubert, et al.,[BABAR Collaboration], Phys. Rev. Lett.95,142001(2005).
[64] X.L. Wang, et al.,[Belle Collaboration], Phys. Rev. Lett.99,142002(2007).
[65] G.J. Ding, J.J. Zhu and M.L. Yan, Phys. Rev. D77,014033(2008); B.Q. Li and K.T. Chao,Phys. Rev. D79,094004(2009); A.M. Badalian, B.L. G. Bakker and I.V. Danilkin, Phys. Atom.Nucl.72,638(2009).
[66] C.F. Qiao, J. Phys. G35,075008(2008).
[67] F.K. Guo, C. Hanhart and U.G. Meissner, Phys. Lett. B665,26(2008).
[68] R.M. Albuquerque and M. Nielsen, Nucl. Phys. A815,53(2009).
[69] M. Gell-Mann, Phys. Lett.8,214(1964).
[70] M. Ida and R. Kobayashi, Prog. Theor. Phys.36(1966)846.
[71] D. B. Lichtenberg, Nuovo Cim. A28,563(1975).
[72] D. B. Lichtenberg, W. Namgung, E. Predazzi and J. G. Wills, Phys. Rev. Lett.48,1653(1982).
[73] R. L. Jaffe, Phys. Rept.409,1(2005)[Nucl. Phys. Proc. Suppl.142,343(2005)].
[74] F. Wilczek, arXiv:hep-ph/0409168.
[75] H. W. Ke, X. Q. Li and Z. T. Wei, Phys. Rev. D77,014020(2008)[arXiv:0710.1927[hep-ph]].
[76] A. F. Falk, M. E. Luke, M. J. Savage and M. B. Wise, Phys. Rev. D49,555(1994)[arXiv:hep-ph/9305315].
[77] M. Mattson et al.[SELEX Collaboration], Phys. Rev. Lett.89,112001(2002)[arXiv:hep-ex/0208014].
[78] A. Ocherashvili et al.[SELEX Collaboration], Phys. Lett. B628,18(2005)[arXiv:hep-ex/0406033].
[79] B. Aubert et al.[BABAR Collaboration], Phys. Rev. D74,011103(2006).
[80] R. Chistov et al.[BELLE Collaboration], Phys. Rev. Lett.97,162001(2006).
[81] A. Majethiya, B. Patel, A. K. Rai and P. C. Vinodkumar, arXiv:0809.4910[hep-ph].
[82] S. P. Tong, Y. B. Ding, X. H. Guo, H. Y. Jin, X. Q. Li, P. N. Shen and R. Zhang, Phys. Rev. D62,054024(2000)[arXiv:hep-ph/9910259].
[83] D. Ebert, R. N. Faustov, V. O. Galkin and A. P. Martynenko, Phys. Rev. D66,014008(2002)[arXiv:hep-ph/0201217].
[84] D. H. He, K. Qian, Y. B. Ding, X. Q. Li and P. N. Shen, Phys. Rev. D70,094004(2004)[arXiv:hep-ph/0403301].
[85] V. V. Kiselev, A. K. Likhoded, O. N. Pakhomova, V. A. Saleev, Phys. Rev. D66,034030(2002).[hep-ph/0206140].
[86] M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Nucl. Phys. B147,385(1979).
[87] M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Nucl. Phys. B147,448(1979).
[88] Z. G. Wang and X. H. Zhang, Commun. Theor. Phys.54,323(2010)[arXiv:0905.3784[hep-ph]]; Z. G. Wang, Y. M. Xu and H. J. Wang, Commun. Theor. Phys.55,1049(2011)[arXiv:1004.0484[hep-ph]].
[89] J. R. Zhang and M. Q. Huang, Commun. Theor. Phys.54,1075(2010)[arXiv:0905.4672[hep-ph]].
[90] C. F. Qiao, L. Tang, G. Hao and X. Q. Li, J. Phys. G39,015005(2012) arXiv:1012.2614[hep-ph].
[91] V. V. Kiselev, A. K. Likhoded, Phys. Usp.45,455-506(2002)[hep-ph/0103169].
[92] E. Bagan, M. Chabab and S. Narison, Phys. Lett. B306,350(1993).
[93] J. R. Zhang and M. Q. Huang, Phys. Rev. D78,094007(2008)[arXiv:0810.5396[hep-ph]].
[94] R. M. Albuquerque and S. Narison, Nucl. Phys. Proc. Suppl.207-208,265(2010)[arXiv:1009.2428[hep-ph]].
[95] S. Narison and R. Albuquerque, Phys. Lett. B694,217(2010)[arXiv:1006.2091[hep-ph]].
[96] Maiani L, Piccinini F, Polosa A D et al. Phys. Rev. D,2005,71:014028.
[97] Nielsen M, Matheus R D’E, Navarra F S et al. Nucl. Phys. Proc. Suppl,2006,161:193-199.
[98] DING G J, YAN M L. Phys. Lett. B,2006,643:33-40.
[99] ZHANG A, HUANG T, Steele T G. Phys. Rev. D,2007,76:036004.
[100] Rehman A. arXiv:hepph/1109.1095.
[101] Kim K, Jido D, Lee S H. Phys. Rev. C,2011,84:025204.
[102] L. Tang, X. H. Yuan, C. F. Qiao and X. Q. Li, Commun. Theor. Phys.57,435(2012)[arXiv:1104.4934[hep-ph]].
[103] Ishii N, Bentz W, Yazaki K, Nucl. Phys. A,1995,587:617.
[104] Nicmorus D, Eichmann G, Krassnigg A et al. PoS C,2008, ONFINEMENT8:052.
[105] Dosch H G, Jamin M, Stech B. Z. Phys. C,1989,42:167. Jamin M, Neubert M. Phys. Lett.B,1990,238:387.
[106] WANG Z G. Eur. Phys. J. C,2011,71:1524.
[107] X. G. He, J. Tandean and G. Valencia, Phys. Rev. Lett.98,081802(2007)[arXiv:hep-ph/0610362].
[108] Q. Chang and Y. D. Yang, Phys. Lett. B676,88(2009)[arXiv:0808.2933[hep-ph]].
[109] S. Narison, Nucl. Phys. Proc. Suppl.207-208,315(2010)[arXiv:1010.1959[hep-ph]].
[110] G. F. Sterman, Cambridge, UK: Univ. Pr.(1993)572p.
[111] P. Colangelo and A. Khodjamirian, arXiv:hep-ph/0010175.
[112] S. Narison, arXiv:1105.5070[hep-ph].
[113] Reinders L J, Rubinstein H, Yazaki S, Phys. Rept,1985,127:1.
[114] D. S. Du, J. W. Li and M. Z. Yang, Phys. Lett. B619,105(2005)[arXiv:hep-ph/0409302].
[115] J. Govaerts, L. J. Reinders, P. Franchen, X. Gonze and J. Weyers, Nucl. Phys. B284,674(1987).
[116] R. Jakob, P. Kroll, M. Schurmann and W. Schweiger, Z. Phys. A347,109(1993)[arXiv:hep-ph/9310227].
[117] Ioffe B L. Prog. Part. Nucl. Phys,2006,56:232.
[118] F. Englert and R. Brout, Phys. Rev. Lett.13,321(1964).
[119] P. W. Higgs, Phys. Rev. Lett.13,508(1964).
[120] G. S. Guralnik, C. R. Hagen and T. W. B. Kibble, Phys. Rev. Lett.13,585(1964).
[121] S. Weinberg, Phys. Rev. Lett.19,1264(1967).
[122] M. E. Peskin and D. V. Schroeder, An Introduction To Quantum Field Theory, Reading, USA:Addison-Wesley (1995)842p.
[123] Yi. Liao, Quantum Field Theory Part II: Gauge Theories.
[124] S. R. Coleman and J. Mandula, Phys. Rev.159,1251(1967).
[125] R. Haag, J. T. Lopuszanski and M. Sohnius, Nucl. Phys. B88,257(1975).
[126] J. j. Cao, Z. h. Xiong and J. M. Yang, Nucl. Phys. B651,87(2003)[arXiv:hep-ph/0208035].
[127] J. Rosiek, Phys. Rev. D41,3464(1990).
[128] H. P. Nilles, M. Srednicki and D. Wyler, Phys. Lett. B120(1983)346; J. M. Frere, D. R. T.Jones and S. Raby, Nucl. Phys. B222,(1983)11; J. P. Derendinger and C. A. Savoy, Nucl. Phys.B237,(1984)307; J. R. Ellis, J. F. Gunion, H. E. Haber, L. Roszkowski and F. Zwirner, Phys.Rev. D39(1989)844; M. Drees, Int. J. Mod. Phys. A4(1989)3635.
[129] J. J. Cao, K. i. Hikasa, W. Wang, J. M. Yang, K. i. Hikasa, W. Y. Wang and J. M. Yang, Phys.Lett. B703,292(2011)[arXiv:1104.1754[hep-ph]].
[130] G. Hiller, Phys. Rev. D70,034018(2004)[arXiv:hep-ph/0404220].
[131] Z. Heng, R. J. Oakes, W. Wang, Z. Xiong and J. M. Yang, Phys. Rev. D77,095012(2008)[arXiv:0801.1169[hep-ph]].
[132] X. G. He, J. Tandean and G. Valencia, Phys. Rev. D74,115015(2006)[arXiv:hep-ph/0610274].
[133] E. Fullana and M. A. Sanchis-Lozano, Phys. Lett. B653,67(2007)[arXiv:hep-ph/0702190].
[134] X. G. He, J. Tandean and G. Valencia, Phys. Rev. D72,074003(2005)[arXiv:hep-ph/0506067].
[135] W. Love et al.[CLEO Collaboration], Phys. Rev. Lett.101,201601(2008)[arXiv:0807.2695[hep-ex]].
[136] B. Aubert et al.[BaBar Collaboration], arXiv:0808.0017[hep-ex].
[137] H. Park et al.[HyperCP Collaboration], Phys. Rev. Lett.94,021801(2005)[hep-ex/0501014].
[138] The ATLAS and CMS Collaborations, Combined Standard Model Higgs boson searches withup to2.3fb1of pp collision data at√s=7TeV at the LHC, ATLAS-CONF-2011-157, CMSPAS HIG-11-023(2011).
[139] F. Gianotti (the ATLAS Collaboration), Update on the Standard Model Higgs searches inATLAS, CERN Public Seminar,13December2011, CERN.
[140] G. Tonelli (the CMS Collaboration), Update on the Standard Model Higgs searches in CMS,CERN Public Seminar,13December2011, CERN.
[141] C. Kao, H.-Y. Cheng, W.-S. Hou and J. Sayre, arXiv:1112.1707[hep-ph].
[142] Z. K. Silagadze, Phys. Rev. D74,054003(2006)[hep-ph/0606284].
[143] M. Z. Yang, Phys. Rev. D79,074026(2009)[arXiv:0902.1295[hep-ph]].
[144] T. Feldmann, P. Kroll and B. Stech, Phys. Rev. D58,114006(1998)[hep-ph/9802409].
[145] T. N. Pham, Phys. Rev. D77,014024(2008)[Erratum-ibid. D77,019905(2008)][arXiv:0710.2412[hep-ph]].
[146] T. P. Cheng and L. F. Li, Oxford, Uk: Clarendon (1984)536P.(Oxford Science Publica-tions).
[147] D. S. Hwang and G. H. Kim, Z. Phys. C76,107(1997)[arXiv:hep-ph/9703364].
[148] B. Aubert et al.[BABAR Collaboration], Phys. Rev. Lett.103,161801(2009)[arXiv:0903.1124[hep-ex]].
[149] H. W. Ke, X. Q. Li and X. Liu, arXiv:1002.1187[hep-ph].
[150] H.-W. Ke, X.-H. Yuan and X.-Q. Li, Int. J. Mod. Phys. A26,4731(2011)[arXiv:1101.3407[hep-ph]].
[151] A. Rashed, M. Duraisamy and A. Datta, Phys. Rev. D82,054031(2010)[arXiv:1004.5419[hep-ph]].
[152] T. Huang, H.-Y. Jin, A.-L. Zhang, Phys. Rev. D59,034026(1999).[hep-ph/9807391].
[153] P. Pascual and R. Tarrach, Lect. Notes Phys.194,1(1984).
[154] M. Ablikim et al.[BES Collaboration], Phys. Lett. B607,243(2005)[arXiv:hep-ex/0411001].
[155] M. Ablikim et al.[BES Collaboration], Phys. Rev. Lett.96,162002(2006)[arXiv:hep-ex/0602031].
[156] X. G. He, X. Q. Li, X. Liu and X. Q. Zeng, Phys. Rev. D73,051502(2006)[arXiv:hep-ph/0602075].
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |