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arXiv · 2311.10345

Nucleon form factors in $N_f=2+1$ lattice QCD at the physical point : finite lattice spacing effect on the root-mean-square radii

Ryutaro Tsuji·Yasumichi Aoki·Ken-Ichi Ishikawa·Yoshinobu Kuramashi·Shoichi Sasaki·Kohei Sato·Eigo Shintani·Hiromasa Watanabe·Takeshi Yamazaki
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Abstract

We present results for the nucleon form factors: electric ($G_E$), magnetic ($G_M$), axial ($F_A$), induced pseudoscalar ($F_P$) and pseudoscalar ($G_P$) form factors, using the second PACS10 ensemble that is one of three sets of $2+1$ flavor lattice QCD configurations at physical quark masses in large spatial volumes (exceeding $(10\ \mathrm{fm})^3$). The second PACS10 gauge configurations are generated by the PACS Collaboration with the six stout-smeared $O(a)$ improved Wilson quark action and Iwasaki gauge action at the second gauge coupling $\beta=2.00$ corresponding to the lattice spacing of $a=0.063$ fm. We determine the isovector electric, magnetic and axial radii and magnetic moment from the corresponding form factors, as well as the axial-vector coupling $g_A$. Combining our previous results for the coarser lattice spacing [E. Shintani et al., Phys. Rev. D99 (2019) 014510; Phys. Rev. D102 (2020) 019902 (erattum)], the finite lattice spacing effects on the isovector radii, magnetic moment and axial-vector coupling are investigated using the difference between the two results. It was found that the effect on $g_A$ is kept smaller than the statistical error of 2% while the effect on the isovector radii was observed as a possible discretization error of about 10%, regardless of the channel. We also report the partially conserved axial vector current (PCAC) relation using a set of nucleon three-point correlation functions in order to verify the effect by $O(a)$-improvement of the axial-vector current.

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Ryutaro Tsuji, Yasumichi Aoki, Ken-Ichi Ishikawa, Yoshinobu Kuramashi, Shoichi Sasaki, Kohei Sato, Eigo Shintani, Hiromasa Watanabe, Takeshi Yamazaki. 2023-11-17. Nucleon form factors in $N_f=2+1$ lattice QCD at the physical point : finite lattice spacing effect on the root-mean-square radii. https://arxiv.org/abs/2311.10345

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