TeV Neutrinos from SuperNova Remnants embedded in Giant Molecular Clouds

The recent detection of $\gamma$-rays with energy up to 10 TeV from dense regions surrounding some Supernova Remnants (SNR) provides strong, though still not conclusive, evidence that the nucleonic component of galactic Cosmic Rays is accelerated in the supernova outflows. Neutrino telescopes could further support the validity of such scenario by detecting neutrinos coming from the same regions. We re-evaluate the TeV range neutrino-photon flux ratio to be expected from pion decay, finding small differences respect to previous derivations. We apply our results and the recent HESS measurements of the very high energy $\gamma$-ray flux from the molecular cloud complex in the Galactic Centre, to estimate the neutrino flux from that region discussing the detectability perspectives for Mediterranean Neutrino Telescopes. We also discuss under which conditions neutron decay may give rise to a significant TeV antineutrino flux from a SNR embedded in Molecular Cloud complexes.