论文标题
低能量定理，$γ\至3π$：$πa_1$ - 混合的表面术语
Low-energy theorem for $γ\to 3π$: surface terms against $πa_1$-mixing
论文作者
论文摘要
我们重新考虑$πa_1$ - 混合对异常的$γ\toπ^+π^0π^0π^ - $振幅从低能定理的角度来看，$ f^π= ef_π= ef_π^2 f^2 f^{3π} $，与电子$ f_ f _ f _ f _ f _ f _ f _ {f _ f _ {f _ f _ f _ f _ {3π} $相关，因子$ f_ {γ\toπ^+π^0π^ - } = f^{3π} $均在介子的消失时刻摄取。我们的方法基于最近提出的$πa_1$混合在标准有效QCD启发的梅森·拉格朗日（Nambu-Jona-Lasinio）框架中获得的$πa_1$混合的协变量对角线化。我们表明，该定理的唯一固定在异常的三角夸克图或AAA-type振幅的计算中出现的两个表面术语。结果，这两个形式因素$ f^π$和$ f^{3π} $不受$πa_1$ - 混合的影响，但是向量中梅森优势（VMD）的概念以$γ\toπ^+toπ^+ππ^0π^ - $而失败。
We reconsider the contribution due to $πa_1$-mixing to the anomalous $γ\toπ^+π^0π^-$ amplitude from the standpoint of the low-energy theorem $F^π=e f_π^2 F^{3π}$, which relates the electromagnetic form factor $F_{π^0\toγγ}=F^π$ with the form factor $F_{γ\toπ^+π^0π^-}=F^{3π}$ both taken at vanishing momenta of mesons. Our approach is based on a recently proposed covariant diagonalization of $πa_1$-mixing within a standard effective QCD-inspired meson Lagrangian obtained in the framework of the Nambu-Jona-Lasinio model. We show that the two surface terms appearing in the calculation of the anomalous triangle quark diagrams or AVV- and AAA-type amplitudes are uniquely fixed by this theorem. As a result, both form factors $F^π$ and $F^{3π}$ are not affected by the $πa_1$-mixing, but the concept of vector meson dominance (VMD) fails for $γ\toπ^+π^0π^-$.
