标题： 瞬时Bethe-Salpeter方程的稳定性分析及其对介子光谱的影响 显示英文标题

标题： Stability Analysis of the Instantaneous Bethe-Salpeter Equation and the Consequences for Meson Spectroscopy

摘要： 我们研究在Bethe-Salpeter方程的瞬时近似（Salpeter方程）框架下的轻介子和重介子谱。 我们使用一个由单胶子交换部分和束缚贡献组成的静态核。 已知Salpeter方程在形式上等价于一种随机相位近似方程；因此，它可能会产生虚数本征值。 因此，在不首先讨论Salpeter方程的稳定性的情况下，我们的研究是不完整的。 稳定性分析限制了核的形式，并表明与通常的假设相反，束缚部分不能作为洛伦兹标量变换；它必须作为矢量的类时分量变换。 此外，稳定性分析对单胶子交换部分的大小设定了上限；临界耦合的值通过求解“半相对论”库仑问题确定。 这些限制对相互作用施加了重要的约束，并表明需要一个更复杂的模型来描述轻夸克和重夸克环状物。 显示英文摘要

摘要： We investigate the light and heavy meson spectra in the context of the instantaneous approximation to the Bethe-Salpeter equation (Salpeter's equation). We use a static kernel consisting of a one-gluon-exchange component and a confining contribution. Salpeter's equation is known to be formally equivalent to a random-phase-approximation equation; as such, it can develop imaginary eigenvalues. Thus, our study can not be complete without first discussing the stability of Salpeter's equation. The stability analysis limits the form of the kernel and reveals that, contrary to the usual assumption, the confining component can not transform as a Lorentz scalar; it must transform as the timelike component of a vector. Moreover, the stability analysis sets an upper limit on the size of the one-gluon-exchange component; the value for the critical coupling is determined through a solution of the ``semirelativistic'' Coulomb problem. These limits place important constraints on the interaction and suggest that a more sophisticated model is needed to describe the light and heavy quarkonia.