QCD求和规则方法概论及其在轻强子态研究中的应用

发布时间：2018-04-30 19:48

本文选题：非微扰QCD + QCD求和规则　；参考：《浙江大学》2017年博士论文

【摘要】：QCD求和规则是一种半理论半唯象的非微扰方法。其核心要素——QCD关联函数通过色散关系连接了夸克层次的理论和强子层次的唯象,而非微扰效应被吸收到一系列可以唯象地确定的真空凝聚值中。因此QCD求和规则可以看成三个方面(层次)的有机结合:QCD理论(?)求和规则具体方法(?)强子唯象。本文中,我们围绕以上三个方面,系统地研究了 1-+轻混杂态、0--/1+-轻四夸克态和ρ介子的求和规则。在QCD理论计算方面,我们将(1-+,0++)关联函数的算符乘积展开拓展到完整的8维夸克和胶子算符凝聚项(考虑算符混合),并考察了这些高维凝聚项对OPE收敛性(或求和规则窗口)以及求和规则质量预言的影响。此外,我们还检验了矢量流关联函数中αsG2和mqqq的次领头项的计算,并主要考察了这些项在Holder不等式决定的求和规则窗口中的作用。在求和规则方法方面,我们使用不同的求和规则来进行分析并尝试改进这些求和规则。我们使用的求和规则包括Laplace/Borel求和规则、有限能量求和规则、蒙特卡洛求和规则等。首先,我们将传统求和规则中的稳定原则引入到了光锥求和规则的分析中。更重要的是,我们改进了蒙特卡洛求和规则(或加权最小二乘法拟合):我们通过引入一种Breit-Wigner型的谱密度(包含强子宽度)和由Holder不等式严格决定的求和规则窗口,去掉了求和规则中关于窗口的假设,并成功应用于ρ介子。在强子唯象方面,我们获得了 1-+轻混杂态、0--及1+-轻四夸克态的质量预言,我们也计算了 1-+轻混杂态的b1π和ρπ衰变道的衰变宽度并对0--轻四夸克态的衰变模式进行了分析。我们关于1-+轻混杂态的结果显示π(2015)是比π(1400)和π1(1600)更好的混杂态候选者,并且ρπ衰变道可能是鉴别混杂态的一个重要衰变道。我们关于0--四夸克态的研究显示D0衰变中的ρπ主导可能是一个四夸克态,而a0π是唯一可能的S波衰变模式,值得实验上特别关注。此外,我们给出的1+-轻四夸克态的质量预言显示这个态的质量应在具有同样量子数的普通介子h1(1170)质量之上的270MeV的范围内。
[Abstract]:QCD summation rule is a semi-theoretical semi-phenomenological non-perturbation method. Its core element, QCD correlation function, connects the theory of quark level and the phenomenology of Hadron level by dispersion relation, and the non-perturbation effect is absorbed into a series of phenomenological vacuum condensate values. Therefore, the summation rule of QCD can be regarded as an organic combination of three aspects (hierarchy). Specific methods of summation rules) Hadron phenomenology. In this paper, we systematically study the summation rules of 1-light hybrid state 0--r 1-light four-quark state and 蟻 meson around the above three aspects. In terms of QCD theory, In this paper, the operator product expansion of the correlation function is extended to the complete 8-dimensional quark and gluon operator condensate (considering the operator mixing), and the convergence of these high-dimensional condensations to OPE (or summation rule window) is investigated. And the influence of summation rule quality prediction. In addition, we also examine the calculation of subleading terms of 伪 sG2 and mqqq in vector flow correlation function, and mainly investigate the function of these terms in the summation rule window determined by Holder inequality. In the summation rule method, we use different summation rules to analyze and try to improve these summation rules. The summation rules we use include Laplace/Borel summation rules, finite energy summation rules, Monte Carlo summation rules and so on. Firstly, we introduce the stability principle of traditional summation rules into the analysis of optical cone summation rules. More importantly, we improve the Monte Carlo summation rule (or weighted least square fitting) by introducing a Breit-Wigner type spectral density (including Hadron width) and a sum rule window strictly determined by the Holder inequality. The hypothesis of window in summation rule is removed and successfully applied to 蟻 meson. In terms of Hadron phenomenology, we have obtained the mass predictions of 1-light hybrid state 0- and 1-light four-quark state. We have also calculated the decay widths of b1 蟺 and 蟻蟺 decay channels of 1-light hybrid state and analyzed the decay mode of 0-light four-quark state. Our results on 1- light hybrid state show that 蟺 -N _ (2015) is a better candidate for hybrid state than 蟺 _ (1400) and 蟺 _ (11) 1600), and 蟻蟺 decay channel may be an important decay channel for discriminating hybrid states. Our study of 0-4 quark states shows that the 蟻蟺 dominant in D 0 decay may be a four quark state, and a 0 蟺 is the only possible S wave decay mode, which deserves special attention in experiments. In addition, the mass prediction of the 1-light four-quark state shows that the mass of this state should be within the range of 270MeV above the mass of the ordinary meson H1C1170) with the same quantum number.
【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O572.243

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