瞬时相互作用近似下介子结构波函数的一些探讨(Ⅱ)——赝标介子和矢量介子的谐振子模型

本文在文献1]基础上讨论由一对正反层子组成的介子结构波函数。假定层子质量很重,相互作用是谐振子位阱,旋量耦合方式符合一定的要求,则可以普遍给出以下结果:(1)自动给出质量谱的平方等距关系,又可以避免通常谐振子基态能级过高的困难;(2)如果层子原始弱流为V-A型,层子原始电磁流无反常磁矩项,可以解决赝标介子二体轻子衰变Cabibbo角的不谐调和矢量介子衰变到e⁺e^-几率比的困难;(3)只要在相互作用中引入很小比例的SU(3)破坏项,就足以解释现有介子质量的SU(3)分裂。这就对为什么K-π质量差3.5倍却在许多情况下表现有相当好的SU(3)对称性给以一个合理解释;(4)方程的展开和波函数都有较好的近似性;(5)介子中层子反层子分布半径与现有关于介子电磁半径的实验量级是可以谐调的;(6)介子结构波函数的旋量结构和动量结构都是完全确定的。

SOME DISCUSSIONS OF THE STRUCTURE WAVE FUNCTIONS OF MESONS IN THE APPROXIMATION OF INSTANTANEOUS INTERACTION (Ⅱ)——THE HARMONIC OSCILLATOR MODEL OF PSEUDO-SCALAR AND VECTOR MESONS

On the basis of our previous report this paper discusses the structure wave functions of mesons formed from a straton and anti-straton pair. We assume that the straton is very heavy and that the interaction is the potential of a harmonic oscillator. Provided the spinor type coupling satisfies certain conditions then the following general results are obtained: (1) The equal spacing relation of the squared mass levels are obtained antomatically, and at the same time the usual difficulty of too high energy values for the ground states is avoided; (2) If the intrinsic weak current of the straton is of the V-A type, and also if its intrinsic electro-magnetic current contains no anomalous magnetic moment, then the inconsistency in the Cabibbo angle for the two body lepton decay of the pseudo-scalar meson and the difficulty in explaining the branching ratios of e⁺e^- decay of various vector mesons may be avoided; (3) A very small SU(3) violation term is sufficient to explain the observed SU(3) mass breaking of mesons. This gives a reasonable explanation why the mass of K is 3.5 times that of the pion while SU(3) symmetry is still manifested in many situations; (4) The expansion of the equation with respect to p²/M² gives fairly good approximation; (5) The radius of distribution of the straton and anti-straton is compatible in order of magnitude with the observed electro-magnetic radius of the meson; (6) The spinor and momentum structures of the structure wave functions are completely determined by the theory.