We present a calculation of the pion and kaon Mellin moment $\langle x^3 \rangle$ extracted directly in lattice QCD using a three-derivative local operator. We use one ensemble of gauge configurations with two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with clover improvement. The ensemble reproduces a pion mass $\sim260$ MeV, and a kaon mass $\sim530$ MeV. Excited-states contamination is evaluated using four values of the source-sink time separation within the range of $1.12-1.67$ fm. We use an operator that is free of mixing, and apply a multiplicative renormalization function calculated non-perturbatively. Our results are converted to the $\overline{\rm MS}$ scheme and evolved at a scale of 2 GeV, using three-loop expressions in perturbation theory. The final values are $\langle x^3 \rangle_π^{u^+}=0.024(18)_{\rm stat}(2)_{\rm syst}$, $\langle x^3 \rangle_K^{u^+}=0.035(6)_{\rm stat}(3)_{\rm syst}$, and $\langle x^3 \rangle_K^{s^+}=0.075(5)_{\rm stat}(1)_{\rm syst}$, where the systematic error is the uncertainty due to excited state contamination.
We combine $\langle x^3 \rangle$ with the two lower moments to obtain the ratios $\langle x^3 \rangle/\langle x \rangle$ and $\langle x^3 \rangle/\langle x^2 \rangle$, as well as ratios between the pion and kaon moments. In addition, we reconstruct the $x$-dependence of the pion and kaon PDFs via 2- and 3-parameter fits to our results. We find that the reconstruction is feasible and that our lattice data favor a large $x$-dependence that falls as $(1-x)^2$ for both the pion and kaon PDFs. We integrate the reconstructed PDFs to extract the higher moments with $4\leq n\leq 6$. Finally, we compare the pion and kaon PDFs, as well as the ratios of their moments, to address the effect of SU(3) flavor symmetry breaking.
Parton physics from a heavy-quark operator product expansion: Dynamical lattice QCD calculation of moments of the pion and kaon light-cone distribution amplitudes
Institute of Physics, National Yang Ming Chiao Tung University（国立阳明交通大学物理研究所）；Center for Theoretical Physics - A Leinweber Institute, Massachusetts Institute of Technology（麻省理工学院理论物理中心-莱纳伯研究所）；University of Maryland（马里兰大学）；RIKEN Center for Computational Science（理化学研究所计算科学中心）；Chung-Yuan Christian University（中原大学）；Argonne National Laboratory（阿贡国家实验室）
Charting the coming synergy between lattice QCD and high-energy phenomenology
在参考文献[1]中开发的PDFSense框架的基础上，我们对当前和未来的高能数据对格点规范理论中通常评估的一些量的敏感性进行了全面分析，特别关注核子部分子分布函数（PDF）的积分梅林矩，例如$\langle x \rangle_{u^+ - d^+}$和$\langle x \rangle_{g}$，以及$x$依赖的夸克准分布--特别是等矢量组合的夸克准分布。我们的研究结果表明，晶格计算和唯象夸克分布通知高能实验数据，以合作改善核子的共线结构的图片的潜力。随着格点计算的计算资源进一步扩大，QCD全球分析的复杂性继续增长，这种情况将越来越多。我们的敏感性分析表明，未来的轻子强子对撞机将特别有助于提供唯象约束的晶格观测。
Quasi-distribution amplitudes for pion and kaon via the nonlocal chiral-quark model
本文研究了赝标介子（$π$和$K$）的准分布振幅（QDA），它被认为是在非微扰区大纵向赝标介子动量极限下的介子分布振幅（DA）$ϕ_{π,K}(x)$的渐近模拟，即$p_3\to\infty$.为此，我们采用非定域手征夸克模型（NLChQM）的光阵面形式与最小的Fock态的介子$\sim q\bar{q}$在模型$Λ\sim1$ GeV的低能标度参数。作为一种尝试，我们从模型中的波前波函数中提取横向动量分布振幅（TMDA），并借助于虚分布振幅将其转换为QDA。通过这样做，我们得到了一个解析表达式的非微扰QDA与夸克的电流质量校正高达$\mathcal{O}(Δm_q)$。在数值上，我们证实，得到的TMDA再现的光子-π跃迁形状因子$F_{γγ^*π^0}(Q^2)$在低$Q^2$定性好的实验数据。我们还观察到，所获得的QDA DA DA DA的$p_3$增加，显示对称和不对称曲线相对于$x$的π介子和K介子，分别由于电流夸克质量差$m_{u,d}\ll m_s$。在$ξ\equiv2x-1$中，利用π介子和K介子量子分布计算了矩$\langleξ^n\rangle_{π,K}$，与直接由量子分布计算的值相比，$p_3\gtrsim30Λ$的矩只有百分之几的偏差。事实证明，较高的时刻对$p_3$的变化更敏感，而较低的时刻对它的依赖性较小。
