论文标题
超过$β_0$近似的无肾上腺扰动预测的配方
Formulation for renormalon-free perturbative predictions beyond large-$β_0$ approximation
论文作者
论文摘要
我们提出了一种表述，以始终如一地通过固定顺序扰动结果给出无肾上腺龙的预测。该公式与Lee的方法具有相似之处，因为无肾上腺的部分由两个部分组成：一个部分由不包含肾结足的串联扩展给出，而另一部分是单数骨变换的Borel积分的实际部分。主要的新颖方面是使用分散关系技术评估后一种对象，仅在$ $β_0$ $近似中才有可能。在这里，我们引入了“歧义函数”，该功能是由奇异骨变换的近蛋白转换来定义的。借助歧义函数，我们可以在替代公式中重写Borel积分，这使我们能够使用分析技术与大$β_0$近似相似。我们还提出了对配方重新归一化组特性的详细研究。例如，我们将公式应用于静态QCD电势的固定顺序结果，静态QCD电位的固定顺序结果已经可见。
We present a formulation to give renormalon-free predictions consistently with fixed order perturbative results. The formulation has a similarity to Lee's method in that the renormalon-free part consists of two parts: one is given by a series expansion which does not contain renormalons and the other is the real part of the Borel integral of a singular Borel transform. The main novel aspect is to evaluate the latter object using a dispersion relation technique, which was possible only in the large-$β_0$ approximation. Here, we introduce an "ambiguity function," which is defined by inverse Mellin transform of the singular Borel transform. With the ambiguity function, we can rewrite the Borel integral in an alternative formula, which allows us to obtain the real part using analytic techniques similarly to the case of the large-$β_0$ approximation. We also present detailed studies of renormalization group properties of the formulation. As an example, we apply our formulation to the fixed-order result of the static QCD potential, whose closest renormalon is already visible.
