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arXiv 2405.08856hep-phhep-exnucl-th
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核子插值流的手征性质与$\theta$依赖的可观测量

Chiral properties of the nucleon interpolating current and $θ$-dependent observables

Yohei Ema, Ting Gao, Maxim Pospelov, Adam Ritz

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10 pages
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AI总结：

该研究重新分析核子插值流的手征性质，指出仅$j_1\pm j_2$两种线性组合满足反常$U(1)_A$协变性，并用QCD求和规则验证了协变流计算的$\theta$诱导核子电偶极矩与磁矩比值的物理自洽性。

摘要：

我们重新研究了核子插值流的手征性质，结果表明在两个领头阶流$j_1$和$j_2$中，仅有两个线性组合$j_1\pm j_2$在反常$U(1)_A$对称性下协变变换。因此，若使用不同的流线性组合计算在手征极限下因对称性而趋于零的物理量，可能会得到非物理结果，这类可观测量包括由QCD参数$\theta$诱导的电偶极矩，以及核子质量的$\theta$依赖项。为完整起见，我们还展示了针对两种协变的核子插值流选择，使用QCD求和规则计算得到的、由$\theta$诱导的核子电偶极矩（$d_{n,p}$）以及核子磁矩（$\mu_{n,p}$）的领头阶结果。各道中以比值$d_{n,p}/\mu_{n,p}$形式给出的结果在数值上是自洽的，且反映了所需的$\theta$物理依赖关系。

英文摘要：

We revisit the chiral properties of nucleon interpolating currents, and show that of the two leading order currents $j_1$ and $j_2$, only two linear combinations $j_1\pm j_2$ transform covariantly under the anomalous $U(1)_A$ symmetry. As a result, calculations of quantities which vanish by symmetry in the chiral limit may produce unphysical results if carried out with different linear combinations of the currents. This includes observables such as electric dipole moments, induced by the QCD parameter $θ$, and the $θ$-dependence of the nucleon mass. For completeness, we also exhibit the leading order results for nucleon electric dipole moments ($d_{n,p}$) induced by $θ$, and the nucleon magnetic moments ($μ_{n,p}$), when calculated using QCD sum rules for both the covariant choices of the nucleon interpolating current. The results in each channel, conveniently expressed as the ratios, $d_{n,p}/μ_{n,p}$, are numerically consistent, and reflect the required physical dependence on $θ$.

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