  The Join-the-Shortest Queue (JSQ) policy is a classical benchmark for the
performance of many-server queueing systems due to its strong optimality
properties. While the exact analysis of the JSQ policy is an open question to
date, even under Markovian assumption on the service requirements, recently,
there has been a significant progress in understanding its many-server
asymptotic behavior since the work of Eschenfeldt and Gamarnik
(Math.~Oper.~Res.~43 (2018) 867--886).
  In this paper, we analyze the many-server limits of the JSQ policy in the
\emph{super-Halfin-Whitt} scaling window when load per server $\lambda_N$
scales with the system size $N$ as
$\lim_{N\rightarrow\infty}N^{\alpha}(1-\lambda_N)=\beta$ for $\alpha\in (1/2,
1)$ and $\beta>0$. We establish that the centered and scaled total queue length
process converges to a certain Bessel process with negative drift and the
associated centered and scaled steady-state total queue length, indexed by $N$,
converges to a $\mathrm{Gamma}(2,\beta)$ distribution. Both the transient and
steady-state limit laws are universal in the sense that they do not depend on
the value of the scaling parameter $\alpha$, and exhibit fundamentally
different qualitative behavior from both the Halfin-Whitt regime ($\alpha =
1/2$) and the Non-degenerate Slowdown (NDS) regime ($\alpha=1$).
