层子和轻子的质量公式

Quark and Lepton Mass Formula

层子谱和轻子谱是当代粒子物理中最令人困惑的基本问题之一。eμτ的系列似乎是一种粒子的重复再现,u（d）c（s）,t（b）的系列也是如此,我们曾经指出,这种重复再现可能是基本粒子相互作用可重正性的一个必然结果,并给出了重层子的质量关系,本文对此作进一步的讨论。定理1 如轻子或层子的相互作用是可重正的,则在归一化质量参数μ→∞时,轻子或层子有质量公式 mk（μ→∞）=ms+λkma （1） k=0,1,2…代表可能存在的轻子态或层子态。证:由于相互作用的可重正性,任何顶角的重正化Green函数Γ（R）（μ,g,m,pi）当μ→μ′时,必有耦合常数g→g′,质量参数m→m′来与之补偿,使Γ（R）（μ,g,m。

It is point out that the recurrence of lepton (e—μ—τ) and quark (u(d)—c(s)—t(b)) chains may be a result of renormalizability of particle interactions. Some theorems are proved in this note. Theorem I. If the lepton (quark) interactions are renormalizable, then the masses of leptons (quarks) obey the relation m_k(μ→∞)=m_s+λ~km_α (1) as normalization mass approaches to infinity where k=0,1,2... denotes the possiblly occurring lepton (quark) states. Theorem Ⅱ. If the paticle interations are renormalizable, and γ_m, β_g, refer the coefficients of renormalization group equations, then the necessary condition of mass relation (1) being nontrivial (λ≠1, 0) is n>-1, where n is defined by γ_m/β_g～α(g-g_∞)~n(as μ→∞). Theorem Ⅲ. If mass relation (1) is nontrivial, then the particles in a chain possess the observed mass which includes m_(k+1)/m_k^((0)) λ for heavy quarks and suggests m_(k+1)/m_k^((0)) (1+(λ^(k+1)-1)/bα)/ (1+(λ~k-1)/bα)(λ=4~2=16, b=10) for charged leptons.