[论文解读] Nucleon form factors and structure functions with N_f=2+1 dynamical domain wall fermions

Rbc-Ukqcd Collaborations, Takeshi Yamazaki+1 more|arXiv (Cornell University)|Oct 2, 2007

Particle physics theoretical and experimental studies参考文献 13被引用 4

一句话总结

本格子QCD研究使用Nf=2+1动力域壁费米子在(2.7 fm)³体积上计算了核子电磁和弱形因子及结构函数，π介子质量范围为330–670 MeV。研究发现，轴向电荷gA在最小夸克质量下因有限体积效应（以mπL为标度）而减少约15%；形因子半径比实验值小20–30%。⟨x⟩u−d/⟨x⟩∆u−d的比值与实验一致，未重整化的结构函数趋势在最小质量点处趋近实验值，表明在完成非微扰重整化后有望收敛至物理结果。

ABSTRACT

We report isovector form factors and low moments of structure functions of nucleon in numerical lattice quantum chromodynamics (QCD) from the on-going calculations by the RIKEN-BNL-Columbia (RBC) and UKQCD Collaborations with (2+1) dynamical flavors of domain-wall fermion (DWF) quarks. We calculate the matrix elements with four light quark masses, corresponding to pion mass values of m_\pi = 330-670 MeV, while the dynamical strange mass is fixed at a value close to physical, on (2.7 fm)^3 spatial volume. We found that our axial charge, g_A, at the lightest mass exhibits a large deviation from the heavier mass results. This deviation seems to be a finite-size effect as the g_A value scales with a single parameter, m_\pi L, the product of pion mass and linear spatial lattice size. The scaling is also seen in earlier 2-flavor dynamical DWF and Wilson quark calculations. Without this lightest point, the three heavier mass results show only very mild mass dependence and linearly extrapolate to g_A=1.16(6). We determined the four form factors, the vector (Dirac), induced tensor (Pauli), axial vector and induced pseudoscalar, at a few finite momentum transfer values as well. At the physical pion mass the form-factors root mean square radii determined from the momentum-transfer dependence %of the form factors are 20-30% smaller than the corresonding experiments. The ratio of the isovector quark momentum to helicity fractions, < x>_{u-d}/< x>_{\Delta u - \Delta d} is in agreement with experiment without much mass dependence including the lightest point. We obtain an estimate, 0.81(2), by a constant fit. Although the individual momentum and helicity fractions are yet to be renormalized, they show encouraging trend toward experiment.

研究动机与目标

• 使用Nf=2+1动力域壁费米子在格点上研究核子电磁和弱形因子及结构函数的低矩，
• 利用mπL标度参数评估有限体积效应对轴向电荷gA及其他可观测量的影响。
• 将格点结果与实验数据对比，特别关注动量和自旋分数。
• 通过多个夸克质量外推至物理点，并评估轴向电荷和形因子半径的一致性。
• 为实现与深度非弹性散射实验的直接比较，准备结构函数的非微扰重整化。

提出的方法

• 在β=2.13、域壁高度1.8的24³×64格点上使用(2+1)味动力域壁费米子，模拟π介子质量范围为330至670 MeV。
• 通过三线性相关函数与两线性相关函数的比值计算矩阵元，采用规范不变的高斯抽样以改善信噪比。
• 从零动量转移的比值中提取形因子（F1, F2, GA, GP）和结构函数矩（⟨x⟩u−d, ⟨x⟩∆u−∆d, ⟨1⟩δu−δd, d1）。
• 采用比值方法GA,P5z(t)/GV,Pt(t)获得重整化的轴向电荷gA，利用域壁费米子的规范对称性。
• 使用mπL标度识别有限体积效应，特别是在最小质量点处的轴向电荷。
• 排除最轻质量点进行线性外推，估算得到gA = 1.16(6)。

实验结果

研究问题

• RQ1 核子轴向电荷gA在不同π介子质量下的行为如何？是否存在有限体积效应？
• RQ2 格点QCD计算的核子形因子均方根半径与实验值相比如何？
• RQ3 随着夸克质量减小，未重整化的结构函数矩⟨x⟩u−d、⟨x⟩∆u−∆d和⟨1⟩δu−δd在多大程度上趋近于实验值？
• RQ4 扭曲-3的d1矩是否与Wandzura-Wilczek关系一致？在最小夸克质量下其行为如何？
• RQ5 核子动量分数与自旋分数之比⟨x⟩u−d/⟨x⟩∆u−d是否可在格点上准确预测？是否与实验一致？

主要发现

• 在最小夸克质量（mπ ≈ 330 MeV）下，轴向电荷gA比重质量下的值小约15%，表明其受mπL标度的有限体积效应影响。
• 排除最轻质量点后，三个较重质量点的线性外推给出物理点处gA = 1.16(6)。
• 在物理π介子质量下，矢量、泡利和轴向形因子的均方根半径比实验值小20–30%。
• 同位旋二重态夸克动量分数与自旋分数之比⟨x⟩u−d/⟨x⟩∆u−d为0.81(2)，与实验一致，且无显著质量依赖性。
• 未重整化的结构函数矩如⟨x⟩u−d和⟨x⟩∆u−∆d在最小夸克质量下呈现向实验值下降的趋势，表明通过手征外推有望实现收敛。
• 扭曲-3的d1矩较小，与Wandzura-Wilczek关系一致，且在最小质量点处表现出与线性外推的偏离。