"Decoupling" constraints on massless composite particles

It is pointed out that the use of the "decoupling" constraints on the spectrum of composite massless particles is not justified without further assumptions. There is an alternative condition, whose use would not be subject to the same criticisms, which would lead to the same constraints as the decoupling condition, and which would lead to other results as well, for instance that the nonchiral global symmetries in quantum chromodynamics (QCD) with $n$ massless flavors can not be spontaneously broken. However, this condition is found to be violated in a specific model. It is still an open possibility that the chiral symmetries of QCD are unbroken for $n$ not a multiple of 3.