  The neutron-neutron fusion process, $nn\to de\nu$, at very low neutron
energies is studied in the framework of pionless effective field theory that
incorporates dibaryon fields. The cross section and electron energy spectrum
for this process are calculated up to next-to-leading order. We include the
radiative corrections of ${\cal O}(\alpha)$ calculated for the one-body
transition amplitude. The precision of our theoretical estimates is found to be
governed essentially by the accuracy with which the empirical values of the
neutron-neutron scattering length and effective range are currently known. Also
discussed is the precision of theoretical estimates of the transition rates of
related electroweak processes in few-nucleon systems.
