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arXiv 0806.0467hep-phhep-lat
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从有限能量QCD和规则到五个循环的上和down quark质量

Up and down quark masses from Finite Energy QCD sum rules to five loops

C. A. Dominguez, N. F. Nasrallah, R. H. Röntsch, K. Schilcher

备注：
Additional references to lattice QCD results have been added
发表信息：
Phys.Rev.D79:014009,2009
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摘要：

从优化的QCD有限能量和规则（FESR）中确定上下夸克的质量，该规则包括轴矢量发散的相关项，微扰QCD（PQCD）中的五圈阶，并包括领先的非微扰QCD和高阶夸克质量修正。这个FESR的目的是大大减少系统的不确定性所产生的（未测量的）强子共振部门，在这个框架中，贡献不到3-4%的夸克质量。这是通过引入二次多项式形式的积分核来实现的，该积分核被限制为在两个最低共振的峰值处消失。驱动强子的贡献是π介子极，其参数从实验中已知。该确定是在轮廓改进扰动理论（CIPT）的框架中进行的，其表现出非常好的收敛性，导致在异常宽的窗口$s_0 = 1.0 - 4.0 {GeV}^2$中的非常稳定的结果，其中$s_0$是复能量（平方）平面中的积分轮廓的半径。结果为：$m_u(Q= 2 {GeV}) = 2.9 \pm 0.2 $ MeV、$m_d(Q= 2 {GeV}) = 5.3 \pm 0.4$ MeV和$(m_u + m_d)/2 = 4.1 \pm 0.2$ MeV（在Q=2 GeV的标度下）。

英文摘要：

The up and down quark masses are determined from an optimized QCD Finite Energy Sum Rule (FESR) involving the correlator of axial-vector divergences, to five loop order in Perturbative QCD (PQCD), and including leading non-perturbative QCD and higher order quark mass corrections. This FESR is designed to reduce considerably the systematic uncertainties arising from the (unmeasured) hadronic resonance sector, which in this framework contributes less than 3-4% to the quark mass. This is achieved by introducing an integration kernel in the form of a second degree polynomial, restricted to vanish at the peak of the two lowest lying resonances. The driving hadronic contribution is then the pion pole, with parameters well known from experiment. The determination is done in the framework of Contour Improved Perturbation Theory (CIPT), which exhibits a very good convergence, leading to a remarkably stable result in the unusually wide window $s_0 = 1.0 - 4.0 {GeV}^2$, where $s_0$ is the radius of the integration contour in the complex energy (squared) plane. The results are: $m_u(Q= 2 {GeV}) = 2.9 \pm 0.2 $ MeV, $m_d(Q= 2 {GeV}) = 5.3 \pm 0.4$ MeV, and $(m_u + m_d)/2 = 4.1 \pm 0.2$ Mev (at a scale Q=2 GeV).

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