σ Meson Sum Rule

It is σconsensus that Quantum Chormodynamics is the fundamental theory for stronginteraction until now. This theory can describe very rich physical phenomena, such asscattering and decay of hadrons, the internal structure of nucleons. However, it is in essentialσnonperturbative theory. When one encounters hadronization, its application in practicebecomes difficult. Several methods have been developed to tackle this problem, QCD sumrules is one of them. It connects QCD correlation functions based on quark gluon degrees offreedom and phenomenalogical ones by assuming quark hadron duality. In QCD aspect,operator product expansion is used to contain perturbative effects and difficultnonperturbative effects, the nonperturbative part is represented by condensations withdifferent dimensions and can be regarded as inputs. Since the establishment of QCD sumrules, it is applied extensively to nuclear and particle physics, and became one of theimportant methods in dealing with nonperturbative problems.In the process of establishing quark gluon duality several sum rules arise. The mostfrequent used of them is Borel sum rules. In this sum rule scheme, the contribution rfomground state is enhanced, while that rfom excited states is suppressed strongly. However, aswe know, the excited states may produce background interference. Generally, thisinterference becomes stronger with increasing mass. In contrast, another sum rule——Gaussian sum rule which emphasizes the contribution rfom the hadron state in question, hasmore clean background. Therefore, in principle, Gaussian sum rule is more effective than theBorel one. At least, they should give almost the same results, since they base on the sameunderlying theory.In this thesis, we investigate the mass of the a-meson by using both Borel andGaussian sum rules. Although the scalars below1GeV are confirmed by experiments, theirquark structures are still in controversy. They have been assumed as quark-antiquark mesons,tetraquarks, or their mixing. For simplicity, we still assumed σmeson as an ordinaryquark-antiquark meson.We deduced its sum rules in detail, and investigate its mass by using the above sum rules.The results show that in both cases, the mass of ground state scalar with quark-antiquarkstructure is1-1.2GeV, which is in agreement with other research.