We present a comprehensive analysis of the deuteron charge and quadrupole form factors based on the latest two-nucleon potentials and charge-density operators derived in chiral effective field theory. The single- and two-nucleon contributions to the charge density are expressed in terms of the proton and neutron form factors, for which the most up to date empirical parametrizations are employed. By adjusting the fifth-order short-range terms in the two-nucleon charge-density operator to reproduce the world data on the momentum-transfer dependence of the deuteron charge and quadrupole form factors, we predict the values of the structure radius and the quadrupole moment of the deuteron: $r_{\mathrm{str}}=1.{9729}_{-0.0012}^{+0.0015}\mathrm{fm},Q_d=0.{2854}_{-0.0017}^{+0.0038}{\mathrm{fm}}^2.$ A comprehensive and systematic analysis of various sources of uncertainty in our predictions is performed. Following the strategy advocated in our recent publication [Filin, Baru, Epelbaum, Krebs, Möller, and Reinert, Phys. Rev. Lett. 124, 082501 (2020)], we employ the extracted structure radius together with the accurate atomic data for the deuteron-proton mean-square charge radii difference to update the determination of the neutron charge radius, for which we find $r_n^2=-0.{105}_{-0.006}^{+0.005}{\text{fm}}^2$. Given the observed rapid convergence of the deuteron form factors in the momentum-transfer range of $Q\simeq 1–2.5{\mathrm{fm}}^{-1}$, we argue that this intermediate energy domain is particularly sensitive to the details of the nucleon form factors and can be used to test different parametrizations.

中文翻译：

---

手性有效场理论中氘代电荷和四极子形状因子的高精度计算

我们基于手性有效场理论中得出的最新的两个核子势和电荷密度算符，对氘核电荷和四极子形状因子进行了全面分析。单核子和二核子对电荷密度的贡献以质子和中子形状因子表示，为此使用了最新的经验参数。通过在双核子电荷密度算符中调整五阶短程项以重现氘核电荷和四极子形状因子的动量转移相关性的世界数据，我们可以预测结构半径和四极子的值氘核的时刻：${\mathrm{[R}}_{\mathrm{力量}}=\mathrm{1个}。{9729}_{-0.0012}^{+0.0015}\mathrm{调频}，{问}_d=0。{2854}_{-0.0017}^{+0.0038}{\mathrm{调频}}^2。$对我们的预测中各种不确定性来源进行了全面而系统的分析。遵循我们最近的出版物中提倡的策略[Filin，Baru，Epelbaum，Krebs，Möller和Reinert，Phys。牧师 124，082501（2020）]，我们采用所提取的结构半径连同用于氘核-质子均方半径的电荷差的精确的原子数据来更新所述中子电荷半径的确定，为此我们找到${\mathrm{[R}}_{ñ}^2=-0。{105}_{-0.006}^{+0.005}{\text{调频}}^2$。鉴于氘核形态因子在动量传递范围内的快速收敛$问\simeq \mathrm{1个}–2.5{\mathrm{调频}}^{-\mathrm{1个}}$，我们认为这个中间能域对核子形状因子的细节特别敏感，可用于测试不同的参数化。