  In $\mu$-hybrid inflation a nonzero inflaton vacuum expectation value induced
by supersymmetry breaking is proportional to the gravitino mass $m_{3/2}$,
which can be exploited to resolve the minimal supersymmetric standard model
$\mu$ problem. We show how this scenario can be successfully implemented with
$m_{3/2} \sim 1-100$ TeV and reheat temperature as low as $10^6$ GeV by
employing a minimal renormalizable superpotential coupled with a well defined
non-minimal K\"ahler potential. The tensor-to-scalar ratio $r$, a canonical
measure of primordial gravity waves in most cases is less than or of the order
of $10^{-6}-10^{-3}$.
