Spectra Of Heavy Exotic Hadrons And Studies Of Rare Decay Within NMSSM

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 A01of 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.