  We analyse exotic tetraquark mesons - bound states formed by two quarks and
two antiquarks - for the specific case of four different quark flavours within
the framework of a well-defined limit of quantum chromodynamics characterized
by the correlated growth without bound of the number of colour degrees of
freedom and approach to zero of the coupling constant of the strong
interactions. On the one hand, the assumption that the tetraquarks of the kind
defined above show up, as poles in the amplitudes for the scattering of two
ordinary mesons with flavour quantum numbers that match those of these
tetraquarks, already at lowest possible order in an expansion in inverse powers
of the number of colours implies the existence of two types of flavour-exotic
tetraquarks, distinguishable by their dominant transitions to two ordinary
mesons. On the other hand, we are aware of merely a single, unique
colour-singlet arrangement of two quarks and two antiquarks capable of
tolerating a compact flavour-exotic tetraquark, a bound state of
colour-antisymmetric diquark and antidiquark. In view of these two clearly
contradictory observations, we are led to the plausible conclusion that, within
the considered limiting case of quantum chromodynamics, a conceivable
explanation of the riddle might consist in the non-existence of any
flavour-exotic tetraquarks in form of narrow states.
