  We study the reactions $\gamma d\to\pi\gamma NN$ with the aim to search for
six-quark states, the decay of which into two nucleons is forbidden by the
Pauli exclusion principle. These states with the masses $M<2m_N+m_{\pi}$ should
mainly decay by emitting a photon. This is a new class of metastable six-quark
states with the decay widths $<< 1$keV. The recent experiment at Proton Linear
Accelerator of INR (Moscow) suggests a possibility of the existence of such
states with masses 1904, 1926, and 1942 MeV. The proposed experiment at MAMI-C
could provide an unique opportunity to observe such dibaryon states in mass
region up to 2000 MeV and determine their masses and quantum numbers.
