π介子和K介子广义部分子分布的偏度依赖性
Skewness dependence of the pion and kaon generalized parton distributions
AI总结：
本研究在协变NJL模型下探究π、K介子广义部分子分布的偏度与动量转移依赖性，经DGLAP演化验证结果与实验、JAM分析及格点QCD结果一致，明确了价夸克与胶子分布对参数的依赖差异。
AI中文摘要：
我们在协变Nambu-Jona-Lasinio（NJL）模型框架下，研究了不同动量转移$-t$下π介子广义部分子分布（GPD）的偏度依赖性，采用Schwinger固有时正则化方案处理紫外发散，并实现了夸克禁闭的有效描述。我们将不同$-t$和$ξ$取值下的π介子GPD演化到$μ^2=4$和$27\textrm{ GeV}^2$的标度。我们发现，价夸克分布随$-t$和$ξ$的增大而受到抑制，且在更低标度$μ^2=4\textrm{ GeV}^2$下，这种抑制效应更为显著。在向前极限（$ξ=0$且$-t=0$）下，$μ^2=27\textrm{ GeV}^2$标度下预测的π介子价夸克分布与现有实验数据及JAM全局分析结果吻合良好。通过次领头阶（NLO）DGLAP演化得到的$μ^2=4\textrm{ GeV}^2$标度下的对应π介子胶子分布，也与JAM分析结果一致。我们进一步发现，π介子和K介子的价夸克分布对$-t$有强依赖性，但对$ξ$的依赖性较弱，而对应的胶子分布对$-t$和$ξ$的依赖性都很弱。$μ^2=4\textrm{ GeV}^2$标度下π介子和K介子的广义形状因子与对应的格点QCD结果吻合良好。
英文摘要：
We investigate the skewness dependence of the pion generalized parton distribution (GPD) at different momentum transfers $-t$ within the covariant Nambu-Jona-Lasinio (NJL) model, employing the Schwinger proper-time regularization scheme to regulate ultraviolet divergences and implement an effective description of quark confinement. We evolve the pion GPDs for various values of $-t$ and $ξ$ to the scales $μ^2=4$ and $27~\mathrm{GeV}^2$. We find that the valence-quark distributions are suppressed with increasing $-t$ and $ξ$, with the suppression becoming more pronounced at the lower scale, $μ^2=4~\mathrm{GeV}^2$. In the forward limit, $ξ=0$ and $-t=0$, the predicted pion valence-quark distribution at $μ^2=27~\mathrm{GeV}^2$ is in good agreement with the available experimental data and the global JAM analysis. The corresponding pion gluon distribution at $μ^2=4~\mathrm{GeV}^2$, obtained through next-to-leading-order (NLO) DGLAP evolution, is also consistent with the JAM analysis. We further find that the pion and kaon valence-quark distributions exhibit a strong dependence on $-t$ but only a weak dependence on $ξ$, whereas the corresponding gluon distributions show weak dependence on both $-t$ and $ξ$. The generalized form factors of the pion and kaon at $μ^2=4~\mathrm{GeV}^2$ are in good agreement with the corresponding lattice-QCD results.
