Nucleon Axial Form Factors from Clover Fermion on 2+1+1-flavor HISQ Lattice

Yong-Chull Jang, Rajan Gupta, Tanmoy Bhattacharya, Sungwoo Park, B. Yoon, Huey-Wen Lin
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引用次数: 2

Abstract

The nucleon axial form factors -- axial $G_A$, induced pseudoscalar $\widetilde{G}_P$ and pseudoscalar $G_P$ -- have displayed large systematics in lattice QCD calculations. The major symptoms were the violation of the partially conserved axial current (PCAC) relation between the three form factors, and the underestimation of the induced pseudoscalar coupling $g_P^\ast$ and the axial charge radius $r_A$ compared to phenomenological estimates. The small $g_P^\ast$ was a consequence of the failure of the pion-pole dominance (PPD) hypothesis, especially at low $M_\pi^2$. The small charge radius $r_A$ and the underestimate of $g_A$ were related. The dominant systematic responsible is the lack of inclusion of low-energy ($N \pi$) states that are not manifest in the multiexponential fit to the nucleon two-point correlator. We show that this low-energy state can be determined from the three-point correlator $\langle N A_4 N \rangle $ with the insertion of the temporal component of the axial current $A_4$ within the nucleon state, ie, the strategy labeled $S_{A4}$ [1]. Including this low-energy state in fits to control excited-state contamination (ESC) gives results for $g_A$, $r_A$, and $g_P^\ast$ that are consistent with experimental/phenomenological values. However, the systematic uncertainties, especially in data at small $Q^2$, are now much larger.
三叶草费米子在2+1+1味HISQ晶格上的核子轴向形状因子
核子轴向形因子——轴向$G_A$、诱导伪标量$\ widdetilde {G}_P$和伪标量$G_P$在晶格QCD计算中显示出较大的系统性。主要症状是三个形状因子之间的部分守恒轴向电流(PCAC)关系的违反,以及与现象学估计相比,诱导伪标量耦合$g_P^\ast$和轴向电荷半径$r_A$的低估。较小的$g_P^\ast$是介子-极优势(PPD)假设失败的结果,特别是在低$M_\pi^2$时。电荷半径$r_A$与电荷半径$g_A$的低估有关。主要的系统原因是缺少低能($N \pi$)态,这些态在核子两点相关器的多指数拟合中没有表现出来。我们证明了这个低能态可以通过三点相关器在核子态内插入轴向电流的时间分量来确定,即标记为S_{A4}$的策略[1]。在控制激发态污染(ESC)的拟合中加入这个低能态,可以得到$g_A$、$r_A$和$g_P^\ast$与实验/现象学值一致的结果。然而,系统的不确定性,特别是在小$Q^2$的数据中,现在要大得多。
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