论文标题
$ \ mathbb {r}^3 \ times s^1 $ on $ su（n）$ qcd（adj。）中的红外renormalon有关更多信息
More on the infrared renormalon in $SU(N)$ QCD(adj.) on $\mathbb{R}^3\times S^1$
论文作者
论文摘要
我们向先前关于红外（ir）肾上腺素的研究介绍了其他观察，$ su（n）$ qcd（adj。），$ su（n）$ gauge理论，具有$ n_w $ -flavor-flavory auspoint auspoint weyl weyl fermions on〜 $ \ $ \ mathbb {r}^3 \ times s^1 $ a $ \ mathbbbbbb {z Mathbbbb {z} $ twistect n $首先，我们表明，对于任意有限〜$ n $，“光子”真空极化（与〜$ su（n）$相关的量规玻色子的真空极化）的对数因素在$ s^1 $〜紧凑型下消失了。由于IR Renormalon归因于这种对数因素的存在，因此可以得出结论，该系统中没有IR renormalon，具有有限的〜$ n $。该结果概括了Anber和〜sulejmanpasic [J.高能物理学\ \ textbf {1501}，139（2015）]，$ n = 2 $和〜$ 3 $，以任意有限〜$ n $。接下来，我们指出，尽管肾上腺含量的歧义不是通过该系统中的Borel程序出现的，但在替代的重新召集程序中出现了歧义，在该程序中，通过一种动量整合给出了重新定量的数量，在该过程中，真空极化的倒数被包含为积分。这种歧义是由真空极化的非零动量下的简单零引起的。在分解〜$ r \至\ infty $的情况下，$ r $是$ s^1 $的半径，这种动量集成中的歧义可以平稳地减少到〜$ \ $ \ mathbb {r}^4 $中的ir renormalon歧义。我们将这种歧义性称为“肾上腺前体”的动量整合。 〜$ \ mathbb {r}^4 $在分解中的含义歧义的出现可以自然地通过此概念理解。
We present additional observations to previous studies on the infrared (IR) renormalon in $SU(N)$ QCD(adj.), the $SU(N)$ gauge theory with $n_W$-flavor adjoint Weyl fermions on~$\mathbb{R}^3\times S^1$ with the $\mathbb{Z}_N$ twisted boundary condition. First, we show that, for arbitrary finite~$N$, a logarithmic factor in the vacuum polarization of the "photon" (the gauge boson associated with the Cartan generators of~$SU(N)$) disappears under the $S^1$~compactification. Since the IR renormalon is attributed to the presence of this logarithmic factor, it is concluded that there is no IR renormalon in this system with finite~$N$. This result generalizes the observation made by Anber and~Sulejmanpasic [J. High Energy Phys.\ \textbf{1501}, 139 (2015)] for $N=2$ and~$3$ to arbitrary finite~$N$. Next, we point out that, although renormalon ambiguities do not appear through the Borel procedure in this system, an ambiguity appears in an alternative resummation procedure in which a resummed quantity is given by a momentum integration where the inverse of the vacuum polarization is included as the integrand. Such an ambiguity is caused by a simple zero at non-zero momentum of the vacuum polarization. Under the decompactification~$R\to\infty$, where $R$ is the radius of the $S^1$, this ambiguity in the momentum integration smoothly reduces to the IR renormalon ambiguity in~$\mathbb{R}^4$. We term this ambiguity in the momentum integration "renormalon precursor". The emergence of the IR renormalon ambiguity in~$\mathbb{R}^4$ under the decompactification can be naturally understood with this notion.
