核子中夸克纵自旋结构和色力的晶格结果
Lattice results for the longitudinal spin structure and color forces on quarks in a nucleon
摘要：
用格点QCD方法计算了核子中自旋结构函数$g_1$和$g_2$的扭转2贡献$a_2$对三阶Mellin矩的贡献。此外，我们评估扭转3的贡献$d_2$。我们的计算利用协调晶格模拟（CLS）的努力产生的$N_f=2+1$规范场系综。忽略夸克线不连通的贡献，我们得到作为我们的最佳估计$a_2^{(p)}= 0.069(17)$，$d_2^{(p)}= 0.0105(68)$和$a_2^{(n)}= 0.0068(88)$，$d_2^{(n)}= -0.0009(70)$分别为质子和中子，其中我们使用方程中给出的归一化。(58)和（59）。虽然$a_2$的结果已经被转换为使用三回路微扰理论的$\overline{\mathrm{MS}}$方案，但是$d_2$的数字在正则化独立动量减法（RI $^\prime$ -RIO）方案中给出，即，该转换仅在三级微扰理论中进行。$d_2$的结果可以解释为对应的横向色洛伦兹力的夸克在一个横向极化质子的大小为$F^{(u)} = 116(61)$ MeV/fm和$F^{(d)} = -38(66)$ MeV/fm的$u$和$d$夸克，分别。引用的误差估计包括在正交中添加的统计和系统不确定性。
英文摘要：
Using lattice QCD, we calculate the twist-2 contribution $a_2$ to the third Mellin moment of the spin structure functions $g_1$ and $g_2$ in the nucleon. In addition we evaluate the twist-3 contribution $d_2$. Our computations make use of $N_f=2+1$ gauge field ensembles generated by the Coordinated Lattice Simulations (CLS) effort. Neglecting quark-line disconnected contributions we obtain as our best estimates $a_2^{(p)}= 0.069(17)$, $d_2^{(p)}= 0.0105(68)$ and $a_2^{(n)}= 0.0068(88)$, $d_2^{(n)}= -0.0009(70)$ for the proton and the neutron, respectively, where we use the normalizations given in Eqs. (58) and (59). While the $a_2$ results have been converted to the $\overline{\mathrm{MS}}$ scheme using three-loop perturbation theory, the numbers for $d_2$ are given in the regularization independent momentum subtraction (RI$^\prime$-MOM) scheme, i.e., the conversion has been performed only in tree-level perturbation theory. The $d_2$ results can be interpreted as corresponding to a transverse color Lorentz force on a quark in a transversely polarized proton of size $F^{(u)} = 116(61)$ MeV/fm and $F^{(d)} = -38(66)$ MeV/fm for $u$ and $d$ quarks, respectively. The error estimates quoted include statistical and systematic uncertainties added in quadrature.
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