  Because of the absence of indistinguishability constraint, interparticle
interactions between nonidentical particles have in general much more variety
than those between identical particles. In particular, it is known that there
exists a $U(2)$ family of two-body contact interactions between nonidentical
particles in one spatial dimension. This paper studies breakdown of continuous
scale invariance to discrete scale invariance under this $U(2)$ family of
two-body contact interactions in two-body problems of nonidentical particles on
the half line. We show that, in contrast to the corresponding
identical-particle problem, there exist two distinct channels that admit
geometric sequences of two-body bound states.
