arXiv 0705.04702007-05hep-ph

用QCD求和规则计算强子参数的系统不确定性

Systematic uncertainties of hadron parameters obtained with QCD sum rules

Wolfgang Lucha, Dmitri Melikhov, Silvano Simula

备注：: Revtex 9 pages, typoes corrected, version to be published in Phys. Rev. D
发表信息：: Phys.Rev.D76:036002,2007
DOI：: 10.1103/PhysRevD.76.036002

摘要：

本文以谐振子势模型为例，研究了由Shifman-Vainshtein-Zakharov（SVZ）求和规则确定基态参数的不确定性。在这种情况下，人们知道偏振算子$Π(μ)$的精确解，这使得人们可以获得任何阶的OPE和态谱。我们从$Π(μ)$的OPE开始，分析了从SVZ求和规则中提取基态波函数$R\propto|Ψ_0(\vec r=0)|^2$的平方，将基态$E_0$的质量设置为等于其已知值，并将有效连续阈值作为拟合参数。我们表明，在一个有限的“信托”范围内的Borel参数存在一个解决方案的有效阈值，精确地再现了精确的$Π(μ)$的范围内的任何值的$R$ $0.7 \le R/R_0 \le 1.15$（$R_0$是已知的精确值）。因此，从求和规则中提取的$R$的值在很大程度上取决于强子连续统的贡献。我们的主要发现是，在强子连续不知道的情况下，是由一个有效的连续阈值建模，系统的不确定性的总和规则程序无法控制。

英文摘要：

We study the uncertainties of the determination of the ground-state parameters from Shifman-Vainshtein-Zakharov (SVZ) sum rules, making use of the harmonic-oscillator potential model as an example. In this case, one knows the exact solution for the polarization operator $Π(μ)$, which allows one to obtain both the OPE to any order and the spectrum of states. We start with the OPE for $Π(μ)$ and analyze the extraction of the square of the ground-state wave function, $R\propto|Ψ_0(\vec r=0)|^2$, from an SVZ sum rule, setting the mass of the ground state $E_0$ equal to its known value and treating the effective continuum threshold as a fit parameter. We show that in a limited ``fiducial'' range of the Borel parameter there exists a solution for the effective threshold which precisely reproduces the exact $Π(μ)$ for any value of $R$ within the range $0.7 \le R/R_0 \le 1.15$ ($R_0$ is the known exact value). Thus, the value of $R$ extracted from the sum rule is determined to a great extent by the contribution of the hadron continuum. Our main finding is that in the cases where the hadron continuum is not known and is modeled by an effective continuum threshold, the systematic uncertainties of the sum-rule procedure cannot be controlled.

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