Correlation functions can be described by the corresponding equations, $viz.$, gap equation for quark propagator and the inhomogeneous Bethe-Salpeter equation for vector dressed-fermion-Abelian-gauge-boson vertex in which specific truncations have to be implemented. The general vector and axial-vector Ward-Green-Takahashi identities require these correlation functions to be interconnected, in consequence of this, truncations made must be controlled consistently. It turns out that if the rainbow approximation is assumed in gap equation, the scattering kernel in Bethe-Salpeter equation can adopt the ladder approximation, which is one of the most basic attempts to truncate the scattering kernel. Additionally, a modified-ladder approximation is also found to be a possible symmetry-preserving truncation scheme. As an illustration of this approximation for application a treatment of pion is included. Pion mass and decay constant are found to be degenerate in ladder and modified-ladder approximations, even though the Bethe-Salpeter amplitude are with apparent distinction. The justification for the modified-ladder approximation is examined with the help of the Gell-Mann-Oakes-Renner (GMOR) relation.
Calculation of tensor susceptibility beyond rainbow-ladder approximation of Dyson-Schwinger equations approach
本文推广了[Y. M. Shi，K. P. Wu，W. M. Sun，H. S. Zong，J. L. Ping，Phys. Lett. B $\bf{639}$，248（2006）]的方法与采用Ball-Chiu（BC）顶点的方法相比。研究了夸克胶子顶点的修饰效应对张量真空磁化率的影响。结果表明，与彩虹梯近似值相比，在BC顶点近似下得到的张量真空磁化率降低了约10%。这说明在DS方法中计算张量真空磁化率时，夸克胶子顶点的修饰效应并不大。
We suggest a framework based on the rainbow approximation to the Dyson-Schwinger and Bethe-Salpeter equations with effective parameters adjusted to lattice QCD data to calculate the masses of the ground and excited states of pseudo-scalar glueballs. The structure of the truncated Bethe-Salpeter equation with the gluon and ghost propagators as solutions of the truncated Dyson-Schwinger equations is analysed in Landau gauge. Both, the Bete-Salpeter and Dyson-Schwinger equations, are solved numerically within the same rainbow-ladder truncation with the same effective parameters which ensure consi…
总结了基于截断到阶梯彩虹水平的Dyson-Schwinger方程组的软QCD建模的最新进展。这种强子物理学的协变方法可以容纳夸克禁闭并实现QCD单圈重整化群行为。我们比较了缀饰夸克传播子，赝标和矢量介子质量作为夸克质量的函数，以及rho -> pi pi耦合到最近的晶格QCD数据。盖尔曼-奥克斯-伦纳关系与夸克质量增加的错误进行量化比较，在梯形彩虹戴森Schwinger模型内评估的精确的赝标质量关系。
We provide a novel approach to calculate the gravitational form factor of pion under the ladder approximation of the Bethe-Salpeter equation, with contact interactions. Central to this approach is a symmetry-preserving treatment of the dressed $ππ$ amplitude, which shows explicitly the contributions from intrinsic quarks and bound states, the latter being necessary to produce the $D$-term of pion in the soft-pion limit. The approach we provide in this work can be applied to many processes of physical significance.
Spectra of light and heavy mesons with $J \le 5$ in a relativistic Bethe-Salpeter approach
Institut für Theoretische Physik, Justus-Liebig-Universität Giessen（吉森大学理论物理研究所）；Helmholtz Forschungsakademie Hessen für FAIR (HFHF), GSI Helmholtzzentrum für Schwerionenforschung（黑森亥姆霍兹FAIR研究学院，GSI重离子研究中心）
The electromagnetic form factor of the pion is calculated within the use of functional formalism. We develop integral representation for the minimal set of Standard Model Green's functions and derive the dispersion relation for the form factor in the two flavor QCD isospin limit $m_u=m_d$. We use the dressed quark propagator as obtained form the gap equation in Minkowski space and within the Dyson-Schwinger equations formalism to derive the approximate dispersion relation for the form factor for the first time. We evaluate the form factor for the spacelike as well as for the timelike momentum …
Analysis of a quenched lattice-QCD dressed-quark propagator
淬熄的格点量子色动力学关于缀饰夸克施温格函数的数据可以通过彩虹隙方程与缀饰胶子数据相关联，只要该方程的核在红外动量处具有比单独胶子所表现出的增强。所需的增强可以归因于夸克-胶子顶点的修饰。彩虹带隙方程的解表现出动力学手征对称性破缺，与禁闭相一致。能隙方程和相关的、保序的阶梯贝特-萨尔彼得方程给出了手征和物理π介子观测量的估计，表明这些量在猝灭理论中被严重低估了：|<bar-q q>| by a factor of two and f_pi by 30%.
In this work, I studied the spectrum of scalar mesons and axial-vector mesons via Dyson-Schwinger equation and Bethe-Salpeter equation approach in the rainbow-ladder approximation. An interaction model with a repulsive term added to the one used for the pseudoscalar and vector mesons is proposed. My results are consistent with the experiment data and other model results, which shows that this interaction model is effective for all the heavy, heavy-light, and light scalar and axial-vector mesons.
The combined Dyson-Schwinger and Bethe-Salpeter equations in rainbow-ladder approximation are used to search for Regge trajectories of mesons in the pseudo-scalar and vector channels. We focus on the often employed Alkofer-Watson-Weigel kernel which is known to deliver good results for the ground state meson spectra; it provides linear Regge trajectories in the $J^P= 0^-$ channel.
The in-medium behavior of ground-state $q\bar{q}$ mesons, where $q \in \{u,d,s,c\}$, in vector and axial-vector channels is studied based on the spectral analysis for mesonic correlators at finite temperature and zero chemical potential. We first compute the correlators by solving the quark gap equations and the inhomogeneous Bethe-Salpeter equations in the rainbow-ladder approximation. Using a phenomenological ansatz, the spectral functions are extracted by fitting the correlators. By analyzing the evolution of the spectral functions with the temperature, we obtain the dissociation temperatur…
