  This article considers the bound states of two heavy and two light bosons,
when a short-range force attracts the bosons of different mass, and a
short-range force repel the light bosons. The existence of such four-body bound
states results from the competition between these two forces. For a given
strength of the attraction, the critical strength of the repulsion necessary to
unbind the four particles is calculated. This study is motivated by the
experimental realisation of impurity atoms immersed in an atomic Bose-Einstein
condensate, and aims at determining in which regime only one boson contributes
to binding two impurities.
