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arXiv 0705.1896hep-ph
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重子内插场的手征性质

Chiral Properties of Baryon Interpolating Fields

Keitaro Nagata, Atsushi Hosaka, V. Dmitrašinovi\' c

摘要:

本文研究了具有两种味的三夸克重子在良好的同位旋对称性条件下所有可能的局域(非导数)内插场算符的手征变换性质。我们推导和使用的重子运营商之间的关系/身份相同的量子数,遵循从合并的颜色,狄拉克和同位旋Fierz变换。这些关系减少了具有任意给定自旋和同位旋的独立重子算符的数目。Fierz恒等式也有效地限制了重子手征多重态。结果表明,重子的手征多重态等价于它们的洛伦兹表示。对于两个独立的核子算符,唯一允许的手征多重态是基本手征多重态$(\frac12,0)\oplus(0,\frac12)$。对于$Δ$,容许的洛伦兹表示是$(1,\frac12)\oplus (\frac12,1)$和$(\frac32,0)\oplus(0,\frac32)$。在$(1,\frac12)\oplus (\frac12,1)$手性多重峰的情况下,$I(J)=\frac32(\frac32)$ $Δ$字段具有一个$I(J)=\frac12(\frac32)$手性配偶体;否则它没有。我们还考虑了场的阿贝尔手征变换性质,并证明了每个重子都有两种类型:1)轴荷为+3的阿贝尔重子; 2)轴荷为-1的阿贝尔重子。在核子的情况下,这是两个约菲场;在$Δ$的情况下,$(1,\frac12)\oplus (\frac12,1)$多重态具有阿贝尔轴向电荷-1,而$(\frac32,0)\oplus(0,\frac32)$多重态具有阿贝尔轴向电荷+3。

英文摘要:

We study the chiral transformation properties of all possible local (non-derivative) interpolating field operators for baryons consisting of three quarks with two flavors, assuming good isospin symmetry. We derive and use the relations/identities among the baryon operators with identical quantum numbers that follow from the combined colour, Dirac and isospin Fierz transformations. These relations reduce the number of independent baryon operators with any given spin and isospin. The Fierz identities also effectively restrict allowed baryon chiral multiplets. It turns out that the chiral multiplets of the baryons are equivalent to their Lorentz representation. For the two independent nucleon operators the only permissible chiral multiplet is the fundamental one $(\frac12,0)\oplus(0,\frac12)$. For the $Δ$, admissible Lorentz representations are $(1,\frac12)\oplus (\frac12,1)$ and $(\frac32,0)\oplus(0,\frac32)$. In the case of the $(1,\frac12)\oplus (\frac12,1)$ chiral multiplet the $I(J)=\frac32(\frac32)$ $Δ$ field has one $I(J)=\frac12(\frac32)$ chiral partner; otherwise it has none. We also consider the Abelian ($U_A(1)$) chiral transformation properties of fields and show that each baryon comes in two varieties: 1) with Abelian axial charge +3; and 2) with Abelian axial charge -1. In case of the nucleon these are the two Ioffe's fields; in case of the $Δ$, the $(1,\frac12)\oplus (\frac12,1)$ multiplet has Abelian axial charge -1 and the $(\frac32,0)\oplus(0,\frac32)$ multiplet has Abelian axial charge +3.

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