Neutrinoless double-beta decay with Majoron emission

The neutrinoless ββ decay with Majoron emission is examined in detail for the 0+→0+ and 0+→2+ transitions. Especially, the quantitative analysis is made on the correction term which was not dealt with properly before. We found that the correction term does not change the fundamental characters of the energy spectra of emitted electrons and the angular correlation obtained from the main term. The dominant contribution comes from the main term through two light neutrino propagations, except some special cases which have the large mixings between light and heavy neutrinos. Also it is shown that the 0+→2+ transition occurs only through the correction term, and it is by at least ∼10-7 smaller than the 0+→0+ transition