Ground state energy in a wormhole space-time

The ground state energy of the massive scalar field with nonconformal coupling $\xi$ on a short-throat flat-space wormhole background is calculated by using the zeta renormalization approach. We discuss the renormalization and relevant heat kernel coefficients in detail. We show that a stable configuration of wormholes can exist for $\xi >0.123\mathrm{}$. In the particular case of a massive conformal scalar field with $\xi =1/6\mathrm{}$, the radius of the throat of a stable wormhole $a\approx 0.16/m$. The self-consistent wormhole has the radius of throat $a\approx {0.0141l}_p$ and the mass of the scalar boson $m\approx {11.35m}_p{(l}_p$ and $m_p$ are the Planck length and mass, respectively).