  Assuming a heavy electroweak singlet scalar, which couples to the Standard
Model gauge bosons only through loop-induced couplings, SU(2)_L x U(1)_Y gauge
invariance imposes interesting patterns on its decays into electroweak gauge
bosons, which are dictated by only two free parameters. Therefore experimental
measurements on any two of the four possible electroweak channels would
determine the remaining two decay channels completely. Furthermore, searches in
the WW/ZZ channels probe a complimentary region of parameter space from
searches in the gamma-gamma/Z-gamma channels. We derive a model-independent
upper bound on the branching fraction in each decay channel, which for the
diphoton channel turns out to be about 61%. Including the coupling to gluons,
the upper bound on the diphoton branching fraction implies an upper bound on
the mass scale of additional colored particles mediating the gluon-fusion
production. Using an event rate of about 5 fb for the reported 750 GeV diphoton
excess, we find the new colored particle must be lighter than O(1.7 TeV) and
O(2.6 TeV) for a pure CP-even and a pure CP-odd singlet scalar, respectively.
