  Bound electron pairs formed due to the peculiarities of the band dispersion
of electrons in crystals attract much interest because they can carry charge
and spin even in the absence of band conductivity. However, such an important
parameter of bound pairs as the effective mass is still poorly understood. We
carry out this study for materials described by the Bernevig-Hughes-Zhang model
in the electron-hole symmetric case and find a clear relationship between the
effective mass and the energy of a bound pair at rest. The dependence of mass
on energy has a specific form for each of different types of pairs, but a
common feature is the change of the mass sign when energy passes through the
middle of the band gap. The sign is negative when the energy is in the lower
half of the gap, and positive in the upper half.
