  In previews works, joint with N. Gurevitch, a family of Rankin-Selberg
integrals were shown to represent the twisted standard $\mathcal{L}$-function
$\mathcal{L}\left(s,\pi,\chi,\mathfrak{st}\right)$ of a cuspidal representation
$ \pi$ of the exceptional group of type $G_2$. This integral representation
binds the analytic behavior of this $\mathcal{L}$-functions with that of a
degenerate Eisenstein series defined over the family of quasi-split forms of
$Spin_8$ associated to an induction from a character on the Heisenberg
parabolic subgroup.
  This paper is divided into two parts. In part 1 we study the poles of this
degenerate Eisenstein series in the right half plane $\mathfrak{Re}(s)>0$. In
part 2 we use the results of part 1 to give a criterion for $\pi$ to be a {\bf
CAP} representation with respect to the Borel subgroup in terms of poles of
$\mathcal{L}\left(s,\pi,\chi,\mathfrak{st}\right)$. We also settle a conjecture
of J. Hundley and D. Ginzburg and prove a few results relating the analytic
behavior of $\mathcal{L}\left(s,\pi,\chi,\mathfrak{st}\right)$ and the set of
Fourier coefficients supported by $\pi$.
