论文标题
Mellin矩$ \ langle x \ rangle $和$ \ langle x^2 \ rangle $ for pion for the pion和lattice qcd的kaon
The Mellin moments $\langle x \rangle$ and $\langle x^2 \rangle$ for the pion and kaon from lattice QCD
论文作者
论文摘要
我们提出了Pion Quark动量分数的计算，$ \ langle X \ rangle $及其第三个Mellin Moment $ \ langle x^2 \ rangle $。我们还首次使用本地操作员直接获得$ \ langle x \ rangle $和$ \ langle x^2 \ rangle $。我们使用两个堕落的光的合奏，一个奇怪的和一个魅力夸克（$ n_f = 2+1+1 $）的最大扭曲的质量费米子，并改善了三叶草。选择了夸克群体，以便它们重现约260 meV的pion质量，而Kaon质量为530 MeV。集合的晶格间距为0.093 FM，晶格的空间范围为3 fm。我们分析了在$ 1.12-2.23 $ FM范围内的源 - 链时间分离的几个值，以研究和消除激发态贡献。必要的重归其化功能是在Ri $'$方案中非扰动的，并以2 GEV的比例转换为$ \ overline {\ rm MS} $方案。动量分数的最终值为$ \ langle x \ rangle^π_{u^+} = 0.261（3）_ {\ rm Stat}（6）_ {\ rm syst} $，$ \ langle x \ langle x \ rangle x \ rangle^k_^k_ { stat}（2）_ {\ rm syst} $，$ \ langle x \ rangle^k_ {s^+} = 0.317（2）_ {\ rm Stat}（\ rm Stat}（1）_ {\ rm syst} $。对于第三次梅林矩，我们发现$ \ langle x^2 \ rangle^π_{u^+} = 0.082（21）_ {\ rm Stat}（17）_ {\ rm syst} $，$ \ langle x^2 \ rangle x^2 \ rangle^rangle^rangle^k_ { stat}（3）_ {\ rm syst} $，$ \ langle x^2 \ rangle^k_ {s^+} = 0.134（5）_ {\ rm Stat}（\ rm Stat}（2）_ {\ rm syst} $。报告的系统不确定性是由于激发态污染。我们还给出了比率$ \ langle x^2 \ rangle/\ langle x \ rangle $，这表明PDF在$ x $上损失了支持的速度。
We present a calculation of the pion quark momentum fraction, $\langle x \rangle$, and its third Mellin moment $\langle x^2 \rangle$. We also obtain directly, for the first time, $\langle x \rangle$ and $\langle x^2 \rangle$ for the kaon using local operators. We use an ensemble of two degenerate light, a strange and a charm quark ($N_f=2+1+1$) of maximally twisted mass fermions with clover improvement. The quark masses are chosen so that they reproduce a pion mass of about 260 MeV, and a kaon mass of 530 MeV. The lattice spacing of the ensemble is 0.093 fm and the lattice has a spatial extent of 3 fm. We analyze several values of the source-sink time separation within the range of $1.12-2.23$ fm to study and eliminate excited-states contributions. The necessary renormalization functions are calculated non-perturbatively in the RI$'$ scheme, and are converted to the $\overline{\rm MS}$ scheme at a scale of 2 GeV. The final values for the momentum fraction are $\langle x \rangle^π_{u^+}=0.261(3)_{\rm stat}(6)_{\rm syst}$, $\langle x \rangle^K_{u^+}=0.246(2)_{\rm stat}(2)_{\rm syst}$, and $\langle x \rangle^K_{s^+}=0.317(2)_{\rm stat}(1)_{\rm syst}$. For the third Mellin moments we find $\langle x^2 \rangle^π_{u^+}=0.082(21)_{\rm stat}(17)_{\rm syst}$, $\langle x^2 \rangle^K_{u^+}=0.093(5)_{\rm stat}(3)_{\rm syst}$, and $\langle x^2 \rangle^K_{s^+}=0.134(5)_{\rm stat}(2)_{\rm syst}$. The reported systematic uncertainties are due to excited-state contamination. We also give the ratio $\langle x^2 \rangle/\langle x \rangle$ which is an indication of how quickly the PDFs lose support at large $x$.
