arXiv 0704.31892007-04-24hep-phhep-th

II。QCD中夸克禁闭问题的质量隙和解

II. The mass gap and solution of the quark confinement problem in QCD

V. Gogokhia

备注：: No tables and figures, 15 pages

摘要：

我们研究了夸克传播子的封闭方程组，该方程组是在低能QCD的一般方法中早期获得的。这意味着夸克禁闭（夸克传播子确实没有极点），以及手征对称性的动力学破坏（不允许有保持手征对称性的解）。该方程组可以在手征极限下精确求解。我们建立了光滑测试函数空间（由夸克传播子的格林函数和相应的夸克胶子顶点组成），在这个空间中，我们的广义函数（约束胶子传播子）成为连续的线性泛函。它是无限可微函数的线性拓扑空间$K(c)$（相对于无量纲动量变量$x$），在区域$x \leq c$中具有紧支撑。我们开发了一个分析的形式主义，所谓的手征微扰理论的基本夸克水平，它允许一个找到明确的解决方案的夸克传播轻夸克质量的权力。我们还开发了一个分析的形式主义，它允许一个找到的解决方案的夸克传播的重夸克质量的逆幂。它证明了使用重夸克传播子及其自由对应物直到$1/m_Q^3$阶项的合理性，其中$m_Q$是重夸克质量。所以这个解自动具有重夸克自旋味对称性。

英文摘要：

We have investigated a closed system of equations for the quark propagator, obtained earlier within our general approach to QCD at low energies. It implies quark confinement (the quark propagator has no pole, indeed), as well as the dynamical breakdown of chiral symmetry (a chiral symmetry preserving solution is forbidded). This system can be solved exactly in the chiral limit. We have established the space of the smooth test functions (consisting of the Green's functions for the quark propagator and the corresponding quark-gluon vertex) in which our generalized function (the confining gluon propagator) becomes a continuous linear functional. It is a linear topological space $K(c)$ of the infinitely differentiable functions (with respect to the dimensionless momentum variable $x$), having compact support in the region $x \leq c$. We develop an analytical formalism, the so-called chiral perturbtion theory at the fundamental quark level, which allows one to find explicit solution for the quark propagator in powers of the light quark masses. We also develop an analytical formalism, which allows one to find the solution for the quark propagator in the inverse powers of the heavy quark masses. It justifies the use for the heavy quark propagator its free counterpart up to terms of the order $1/m_Q^3$, where $m_Q$ is the heavy quark mass. So this solution automatically possesses the heavy quark spin-flavor symmetry.

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摘要：

英文摘要：

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