  In some extensions of the Standard Model (SM), two neutrons are allowed to
decay into two sterile anti-neutrinos ($nn \rightarrow \bar{\chi}\bar{\chi}$)
via new scalar bosons. This process violates both the baryon number
($\mathcal{B}$) and the lepton number ($\mathcal{L}$) by two units but
conserves their difference $(\mathcal{B}-\mathcal{L})$. Neutron stars contain a
large number of neutrons and thus the $nn \rightarrow \bar{\chi}\bar{\chi}$
process can be greatly enhanced inside a neutron star. This process could
result in non-trivial effects that are different from the SM predictions and
can be explored through astrophysical and laboratory observations. Furthermore,
a large number of sterile antineutrinos, which may be dark matter candidates,
can be emitted from the interior of the neutron star. The properties of the
emitted particles show a particular pattern that can be uniquely determined by
the mass and radius of the neutron star. In addition, the dineutron decay may
contribute to the orbital-period change of the binary systems containing
neutron stars. We analyze the possibility to constrain the mass of the new
scalar bosons using the observations of the binary's orbital-period changes. It
is found that the mass of the new scalar bosons is roughly restricted in the
range from 1 TeV to several TeV, which is possibly within the reach of direct
searches at the LHC or future high-energy experiments. The joint analysis which
combines the astrophysics and particle phenomenology could provide an excellent
opportunity for the study of the new physical effects beyond the SM.
