Extended Goldberger-Treiman relation in a three-flavor parity doublet model
Extended Goldberger-Treiman relation in a three-flavor parity doublet model
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DOI：
10.1103/physrevd.92.054022
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发表时间：
2015-06
影响因子：
5
通讯作者：
Hiroki Nishihara;M. Harada
中科院分区：
文献类型：
--
作者：
Hiroki Nishihara;M. Harada
用三味宇称二重态模型研究了正负宇称核子的质量和衰变宽度。在该模型中，我们引入了三个表象：$\Left[({\bf3}，\bar{{\bf3}})\Oplus(\bar{{\bf3}}，{\bf3})\Right]$，$\Left[({\bf3}，{\bf6})\Oplus({\bf6}，{\bf3})\Right]$，和$\Left[({\bf8}，手性U$(3)_{\rM L}\次$U$(3)_{\rM R}$对称性的加性({\bf1}，{\bf8})$。我们在介子跃迁的质量差和耦合常数之间找到了Goldberger-Treiman关系的一个扩展版本。这一关系导致了衰变宽度的上界：$N(1440)\右目标N(939)+\pi$，与模型参数无关。我们对模型参数进行了数值拟合，并得出了几个预测，这些预测可以在未来的实验或晶格QCD分析中得到验证。此外，当我们使用晶格QCD分析得到的激发核子的轴向耦合作为输入时，我们发现基态核子$N(939)$由大约80%的$\Left[({\bf3}，{\bf6})\Oplus({\bf6}，{\bf3})\右]$组分组成，手征不变质量约为$500$-$800$MeV。
We study masses and decay widths of positive and negative parity nucleons using a three-flavor parity doublet model, in which we introduce three representations, $\left[({\bf 3} , \bar{{\bf 3}})\oplus (\bar{{\bf 3}} , {\bf 3})\right]$, $\left[({\bf 3} , {\bf 6}) \oplus ({\bf 6}, {\bf 3})\right]$, and $\left[({\bf 8} , {\bf 1}) \oplus ({\bf 1} , {\bf 8})\right]$ of the chiral U$(3)_{\rm L}\times$U$(3)_{\rm R}$ symmetry. We find an extended version of the Goldberger-Treiman relation among the mass differences and the coupling constants for pionic transitions. This relation leads to an upper bound for the decay width of $N(1440) \rightarrow N(939) + \pi$ independently of the model parameters. We perform the numerical fitting of the model parameters and derive several predictions, which can be tested in future experiments or lattice QCD analysis. Furthermore, when we use the axial coupling of the excited nucleons obtained from lattice QCD analyses as inputs, we find that the ground state nucleon $N(939)$ consists of about 80% of $\left[({\bf 3} , {\bf 6}) \oplus ({\bf 6}, {\bf 3})\right]$ component, and that the chiral invariant mass of $N(939)$ is roughly $500$ -- $800$MeV.