Neutrinoless double beta decay: Theoretical challenges

The recent progress in theoretical description of the neutrinoless double beta decay (0νββ-decay) is briefly reviewed. A possible effect of nuclear medium on exchange of three light neutrinos is addressed. It is shown that non-standard neutrino interaction generates in-medium Majorana neutrino masses, which influences the 0νββ-decay rate. A subject of interest is also a problem of reliable calculation of the 0νββ-decay nuclear matrix elements. An impact of the quenching of the axial-vector coupling constant on double beta decay processes is discussed. A connection between two-neutrino and neutrinoless double beta decay nuclear matrix elements is analyzed.