The neutron-neutron fusion process, nn→ deν, 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 O(α) 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

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... s 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.