arXiv 1702.043842017-02-14hep-lathep-ph

核子矩阵元在物理π介子质量和代价上的比较

Nucleon Matrix Elements at Physical Pion Mass and Cost Comparison

Keh-Fei Liu, Jian Liang, Yi-Bo Yang

备注：: Talk at 34th International Symposium on Lattice Field Theory - LATTICE 2016, University of Southampton, UK

摘要：

本文报道了在物理π介子质量和5.5 μ m空间尺度下，在$48^3 \times 96$晶格上核子前向矩阵元的晶格计算。用畴壁费米子生成$2+1$味动力学费米子组态，价夸克采用重叠费米子。报道了三种源-库分离的等载体$g_A^3$和$g_S^3$，以及$g_S^0$的连接插入部分。在局域电流的情况下，我们通过两态拟合得到了$g_A^3 = 1.18(4)$。对于夸克动量分数$\langle x \rangle_{u-d}$，我们已经包括了较小的晶格（即$24^3 \times 64$和$32^3 \times 64$晶格，其介子质量分别为330和290 MeV），用于包括部分淬灭情况以及有限体积和连续修正的拟合。微扰重整化的全局拟合给出了$\langle x \rangle_{u-d} (\overline{MS},\, μ= 2\, {\rm GeV}) = 0.170(14)$。比较了在物理π介子点上用相似大小的晶格上的扭曲质量费米子和用相同的π晶格上的畴壁费米子计算核子矩阵元的代价。我们还比较了成本与三叶草费米子计算类似大小的晶格在大约相同的夸克质量。结果表明，通过采用网格源的多对多相关器、在连接插入中引入低模替换和在夸克环中引入低模平均等改进措施，可以使重叠计算与扭曲质量和三叶草费米子计算三点函数一样有效。它的效率比电灯泡高。当调用多质量特征时，重叠可以比迄今为止进行的单质量比较更有效地达到相同的精度。

英文摘要：

We report a lattice calculation of nucleon forward matrix elements on a $48^3 \times 96$ lattice at the physical pion mass and a spatial size of 5.5 fm. The $2+1$ flavor dynamical fermion configurations are generated with domain-wall fermions (DWF) and the overlap fermions are adopted for the valence quarks. The isovector $g_A^3$ and $g_S^3$, and the connected insertion part of $g_S^0$ are reported for three source-sink separations. With local current, we obtain $g_A^3 = 1.18(4)$ from a two-state fit. For the quark momentum fraction $\langle x \rangle_{u-d}$, we have included smaller lattices (i.e. $24^3 \times 64$ and $32^3 \times 64$ lattice with pion mass at 330 and 290 MeV respectively) for a fit which includes partially quenched cases as well as finite volume and continuum corrections. A global fit with perturbative renormalization gives $\langle x \rangle_{u-d} (\overline{MS},\, μ= 2\, {\rm GeV}) = 0.170(14)$. We made a cost comparison of calculating the nucleon matrix elements with those from the twisted mass fermion on similar sized lattice at the physical pion point and the domain-wall fermion calculation on the same DWF lattice. We also compare cost with the clover fermion calculation on similar sized lattice at about the same quark mass. The comparison shows that with several improvements, such as many-to-all correlator with grid source and low-mode substitution in the connected insertion and low-mode average in the quark loop can make the overlap as efficient as the twisted-mass and clover fermions in calculating the three-point functions. It is more efficient than the DWF. When the multi-mass feature is invoked, the overlap can be more efficient in reaching the same precision than the single mass comparison made so far.

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英文摘要：

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