发表机构
Istanbul Aydin University（伊斯坦布尔阿ydin大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究采用光锥QCD求和规则计算核子的手征奇数形状因子，对不同味夸克进行张量多极矩的味分解，得到新的张量四极矩等结果，验证了相关平均场关系，还分析了味分布的横向位移与极化轴伸长特性。
AI 中文摘要
我们采用光锥QCD求和规则，分别针对$u$夸克和$d$夸克，计算核子的手征奇数形状因子$H_T$、$E_T$和$\hT$，并将其整理为张量单极矩、偶极矩和四极矩$g_T$、$\kappa_T$和$Q_T$。该框架的新颖之处在于：四极矩在领头扭度下无手征偶数对应项，而其同位标量道的求和规则已推导但从未被计算。形状因子仅在狄拉克串的正则排序后，才能从洛伦兹基中读取；8个幸存结构中的3个分别给出3个形状因子，而通常用于张量荷的结构不在这8个之中。分析得到两个精确解析结果：在手征极限下，$d$夸克对$E_T$和$\hT$的贡献大小相等、符号相反，其破坏与夸克质量及扭度6振幅$\mathcal{V}_6$成正比，因此$d$夸克 sector 仅携带一个独立函数；同位标量张量荷无领头扭度贡献，其扭度3项在各味间抵消，若不分辨味则无法观测到这两种结果。在$\mu^2=1$~GeV$^2$处，两组分布振幅给出$g_T^{u-d}=1.27(7)$、$1.08(6)$、$\kappa_T^{u-d}=1.35(62)$、$1.58(59)$、$Q_T^{u-d}=-4.40(83)$、$-4.20(73)$以及$g_T^{u+d}=0.39(7)$、$0.38(6)$、$\kappa_T^{u+d}=4.47(62)$、$4.32(59)$、$Q_T^{u+d}=2.41(53)$、$1.56(30)$。无需任何大$N_c$假设即可检验的平均场关系$2\hT^{u-d}=-E_T^{u-d}$，其符号和量级均成立，与预测的1相比，比值为$0.64(16)$和$0.67(15)$。在 impact-parameter 平面内，这些矩使两种味分布沿相反横向方向位移，位移量几乎相等，分别为$\langle b_y\rangle=0.37$和$-0.37$~fm，且使两者沿极化轴伸长，其中$d$夸克的伸长强度约为五到六倍
英文摘要
We compute the chiral-odd form factors $H_T$, $E_T$ and $\hT$ of the nucleon in light-cone QCD sum rules, separately for the $u$ and $d$ quarks, and organise them into the tensor monopole, dipole and quadrupole moments $g_T$, $κ_T$ and $Q_T$. The quadrupole moment, with no chiral-even counterpart at leading twist, and the isoscalar channel, whose sum rules were derived but never evaluated, are new in this framework. The form factors are read from a Lorentz basis independent only after canonical ordering of the Dirac strings; three of the eight surviving structures give the three form factors separately, and the one usually used for the tensor charge is not among the eight. Two exact results follow analytically. The $d$-quark contributions to $E_T$ and $\hT$ are equal and opposite in the chiral limit, broken in proportion to the quark mass and the twist-six amplitude $\mathcal{V}_6$, so the $d$-quark sector carries a single independent function; and the isoscalar tensor charge receives no leading-twist contribution, its twist-three terms cancelling between the flavours. Neither is visible without resolving the flavours. At $μ^2=1$~GeV$^2$ the two distribution-amplitude sets give $g_T^{u-d}=1.27(7)$, $1.08(6)$, $κ_T^{u-d}=1.35(62)$, $1.58(59)$, $Q_T^{u-d}=-4.40(83)$, $-4.20(73)$ and $g_T^{u+d}=0.39(7)$, $0.38(6)$, $κ_T^{u+d}=4.47(62)$, $4.32(59)$, $Q_T^{u+d}=2.41(53)$, $1.56(30)$. The mean-field relation $2\hT^{u-d}=-E_T^{u-d}$, tested without any large-$N_c$ assumption, holds in sign and order of magnitude, with ratio $0.64(16)$ and $0.67(15)$ against the predicted unity. In the impact-parameter plane the moments displace the two flavour distributions in opposite transverse directions by nearly equal amounts, $\langle b_y\rangle=0.37$ and $-0.37$~fm, and elongate both across the polarisation axis, the $d$ quark some five to six times more strongly
Comments19 pages, 4 figures, 4 tables
