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arXiv 0709.3150hep-lathep-ph
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淬灭格点量子色动力学的核子形状因子

Nucleon form factors from quenched lattice QCD with domain wall fermions

Shoichi Sasaki, Takeshi Yamazaki

摘要:

本文给出了弱核子形状因子:矢量(F_V(q^2))、诱导张量(F_T(q^2))、轴矢量(F_A(q^2))和诱导赝标(F_P(q^2))形状因子的猝灭格点计算。我们的模拟是在三种不同的晶格尺寸L^3 x T=24^3 x 32、16^3 x 32和12^3 x 32上进行的,晶格截止值为1/a = 1.3 GeV,轻夸克质量下降到奇异夸克质量的1/4(m_{pi} = 390 MeV),使用DBW 2规范作用量和畴壁费米子的组合。我们最大晶格的物理体积约为(3.6 fm)^3,在这里,有限体积对形状因子的影响可以忽略不计,并且可以获得较低的动量传递(q ^2 = 0.1 GeV ^2)。研究了低q^2区域中形状因子的q^2依赖性。结果表明,矢量、诱导张量、轴矢量形状因子都可以用偶极子形式很好地描述,而诱导赝标量形状因子则与π-极优势相一致.我们得到轴向与矢量耦合比g_A/g_V=F_A(0)/F_V(0)=1.219(38)和赝标耦合比g_P= m_{mu} F_P(0.88 m_{mu} ^2)=8.15(54),其中误差仅为统计误差。这些值与中子β衰变和μ子俘获质子的实验值一致。然而,均方根半径的矢量,诱导张量和轴矢量低估了约20%的已知实验值。我们还计算了核子的赝标矩阵元,以验证轴向Ward-Takahashi恒等式的核子矩阵元,这可称为广义Goldberger-Treiman关系.

英文摘要:

We present a quenched lattice calculation of the weak nucleon form factors: vector (F_V(q^2)), induced tensor (F_T(q^2)), axial-vector (F_A(q^2)) and induced pseudo-scalar (F_P(q^2)) form factors. Our simulations are performed on three different lattice sizes L^3 x T=24^3 x 32, 16^3 x 32 and 12^3 x 32 with a lattice cutoff of 1/a = 1.3 GeV and light quark masses down to about 1/4 the strange quark mass (m_{pi} = 390 MeV) using a combination of the DBW2 gauge action and domain wall fermions. The physical volume of our largest lattice is about (3.6 fm)^3, where the finite volume effects on form factors become negligible and the lower momentum transfers (q^2 = 0.1 GeV^2) are accessible. The q^2-dependences of form factors in the low q^2 region are examined. It is found that the vector, induced tensor, axial-vector form factors are well described by the dipole form, while the induced pseudo-scalar form factor is consistent with pion-pole dominance. We obtain the ratio of axial to vector coupling g_A/g_V=F_A(0)/F_V(0)=1.219(38) and the pseudo-scalar coupling g_P=m_{mu}F_P(0.88m_{mu}^2)=8.15(54), where the errors are statistical erros only. These values agree with experimental values from neutron beta decay and muon capture on the proton. However, the root mean squared radii of the vector, induced tensor and axial-vector underestimate the known experimental values by about 20%. We also calculate the pseudo-scalar nucleon matrix element in order to verify the axial Ward-Takahashi identity in terms of the nucleon matrix elements, which may be called as the generalized Goldberger-Treiman relation.

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