More on infrared renormalon in $SU(N)$ QCD(adj.) on $\mathbb{R}^3\times S^1$

  • Masahiro Ashie
  • ,
  • Okuto Morikawa
  • ,
  • Hiroshi Suzuki
  • ,
  • Hiromasa Takaura

We present additional observations to previous studies on 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 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 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 resumed 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.

Arxiv Url
Arxiv Url
http://arxiv.org/pdf/2005.07407v1 本文へのリンクあり