QCD中的非微扰方法：光锥求和规则与AdS/QCD
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摘要
本文主要研究强相互作用非微扰方面的某些问题，具体包括光锥求和规则和AdS／QCD两方面的内容。
首先，我们关注QCD光锥求和规则在重介子弱衰变中的应用。由于强子的光锥分布振幅还缺乏系统的理解，人们尝试在一些衰变过程中引入合适的手征流来消除一些目前尚不清楚的高扭度分布振幅，使得到的求和规则更加稳定。这使得相应的形状因子主要依赖于领头扭度的分布振幅，从而有助于从大量实验过程来研究和确定分布振幅的性质。我们将这种手征流光锥求和规则从衰变末态为赝标介子的半轻衰变过程推广到末态为矢量介子的情形，进而得到所有重到轻衰变过程形状因子之间的直接关系式。这些关系式与Stech早年在旁观者假定下得到的关系几乎完全相同，可以说是在光锥求和规则的基础上对Stech关系式的一种较严格的实现。接着我们尝试将光锥求和规则应用到衰变末态为含重味夸克的介子，如B→Dlv过程，以及B_c的所有半轻衰变过程。此时末态介子的分布振幅能用一些模型较好地描述，例如我们用BHL模型来描述J/ψ(η_c)时能得到与Belle和BaBar的实验吻合得较好的产生截面σ(e~+e~-→J/ψ+η_c)，克服了NRQCD解释实验结果的困难。
基于AdS／CFT对应的AdS／QCD方法近年来在研究强子谱及相互作用等方面取得一些引人注目的进展。我们对其中的一个唯象模型-soft wall模型做了一些感兴趣的讨论。首先指出，由于缺乏严格的红外截断，在一般的AdS／QCD模型中实现的ρ介子与任意强子态H的耦合常数g_(ρHH)的普适性在该模型中不再成立，而展现出一种随强子量子数线性增长的行为。基于强子的准经典近似，对这一行为做了简单的物理解释。与此同时，由于缺少红外边界条件，理论中的不可归一解不能完全确定下来。我们指出可以通过比较从不可归一解得到的关联函数与从色散关系得到的关联函数，反过来确定相应的解。而该模型中包含的严格的Regge行为则必然导致相应的关联函数展开中量纲为二的修正项的存在。这些工作有助于利用对偶理论进一步研究QCD的非微扰性质。
In this thesis I will present some results in studying strong interaction with some non-perturbative methods, namely light-cone sum rule and AdS/QCD.
First, we will focus on the application of light-cone sum rule in studying the weak decays of heavy mesons. To eliminate the contributions of the poorly known higher-twist distribution amplitudes, people introduce chiral current correlators to calculate the form factors of some semileptonic processes. We generalize this approach to more complicated case where the final state involves a vector meson. Moreover, we find simple relations between the form factors of all the semileptonic decays, which are almost identical to the ones found over ten years ago by Stech. Then we try to use these sum rules to study the decay process when the final state meson contains a heavy quark, such as B→Dlv, and all the semileptonic decays of the B_c meson. The meson containing a heavy quark can be well described by some models, for example, by employing the BHL model to describe the J/ψ(η_c) meson we can get the resultσ(e~+e~-→J/ψ+η_c) consistent with experiments of Belle and BaBar.
Recently the AdS/QCD approach, which is based on the famous AdS/CFT correspondence , has made remarkable achievements in studying hadron spectrum and strong dynamics. Here we just make some discussions on a phenomenological model, the socalled soft wall model. Due to the lack of an explicit infrared cutoff, theρcouplings with any hadron H in this model is not universal as in general AdS/QCD models, but expresses a linear increasing behavior with the exciting number of H. Based on quasi-classical approximation , we can give a simple explanation of this behavior. At the same time, we don't have an infrared boundary condition to constrain the non-normalized mode. However , we can use the correlation relation obtained from dispersion relation to determine the solution. In other words, we are actually determining the non-normalized mode for the corresponding normalized modes. Due to the explicit Regge trajectory in this model, the expansion of the correlation function necessarily contains a dimension-two term.
首先，我们关注QCD光锥求和规则在重介子弱衰变中的应用。由于强子的光锥分布振幅还缺乏系统的理解，人们尝试在一些衰变过程中引入合适的手征流来消除一些目前尚不清楚的高扭度分布振幅，使得到的求和规则更加稳定。这使得相应的形状因子主要依赖于领头扭度的分布振幅，从而有助于从大量实验过程来研究和确定分布振幅的性质。我们将这种手征流光锥求和规则从衰变末态为赝标介子的半轻衰变过程推广到末态为矢量介子的情形，进而得到所有重到轻衰变过程形状因子之间的直接关系式。这些关系式与Stech早年在旁观者假定下得到的关系几乎完全相同，可以说是在光锥求和规则的基础上对Stech关系式的一种较严格的实现。接着我们尝试将光锥求和规则应用到衰变末态为含重味夸克的介子，如B→Dlv过程，以及B_c的所有半轻衰变过程。此时末态介子的分布振幅能用一些模型较好地描述，例如我们用BHL模型来描述J/ψ(η_c)时能得到与Belle和BaBar的实验吻合得较好的产生截面σ(e~+e~-→J/ψ+η_c)，克服了NRQCD解释实验结果的困难。
基于AdS／CFT对应的AdS／QCD方法近年来在研究强子谱及相互作用等方面取得一些引人注目的进展。我们对其中的一个唯象模型-soft wall模型做了一些感兴趣的讨论。首先指出，由于缺乏严格的红外截断，在一般的AdS／QCD模型中实现的ρ介子与任意强子态H的耦合常数g_(ρHH)的普适性在该模型中不再成立，而展现出一种随强子量子数线性增长的行为。基于强子的准经典近似，对这一行为做了简单的物理解释。与此同时，由于缺少红外边界条件，理论中的不可归一解不能完全确定下来。我们指出可以通过比较从不可归一解得到的关联函数与从色散关系得到的关联函数，反过来确定相应的解。而该模型中包含的严格的Regge行为则必然导致相应的关联函数展开中量纲为二的修正项的存在。这些工作有助于利用对偶理论进一步研究QCD的非微扰性质。
In this thesis I will present some results in studying strong interaction with some non-perturbative methods, namely light-cone sum rule and AdS/QCD.
First, we will focus on the application of light-cone sum rule in studying the weak decays of heavy mesons. To eliminate the contributions of the poorly known higher-twist distribution amplitudes, people introduce chiral current correlators to calculate the form factors of some semileptonic processes. We generalize this approach to more complicated case where the final state involves a vector meson. Moreover, we find simple relations between the form factors of all the semileptonic decays, which are almost identical to the ones found over ten years ago by Stech. Then we try to use these sum rules to study the decay process when the final state meson contains a heavy quark, such as B→Dlv, and all the semileptonic decays of the B_c meson. The meson containing a heavy quark can be well described by some models, for example, by employing the BHL model to describe the J/ψ(η_c) meson we can get the resultσ(e~+e~-→J/ψ+η_c) consistent with experiments of Belle and BaBar.
Recently the AdS/QCD approach, which is based on the famous AdS/CFT correspondence , has made remarkable achievements in studying hadron spectrum and strong dynamics. Here we just make some discussions on a phenomenological model, the socalled soft wall model. Due to the lack of an explicit infrared cutoff, theρcouplings with any hadron H in this model is not universal as in general AdS/QCD models, but expresses a linear increasing behavior with the exciting number of H. Based on quasi-classical approximation , we can give a simple explanation of this behavior. At the same time, we don't have an infrared boundary condition to constrain the non-normalized mode. However , we can use the correlation relation obtained from dispersion relation to determine the solution. In other words, we are actually determining the non-normalized mode for the corresponding normalized modes. Due to the explicit Regge trajectory in this model, the expansion of the correlation function necessarily contains a dimension-two term.
引文
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