  A very plausible explanation for the recently observed diphoton excess at the
13 TeV LHC is a (pseudo)scalar with mass around 750 GeV, which couples to a
gluon pair and to a photon pair through loops involving vector-like quarks
(VLQs). To accommodate the observed rate, the required Yukawa couplings tend to
be large. A large Yukawa coupling would rapidly run up with the scale and
quickly reach the perturbativity bound, indicating that new physics, possibly
with a strong dynamics origin, is near by. The case becomes stronger especially
if the ATLAS observation of a large width persists. In this paper we study the
implication on the scale of new physics from the 750 GeV diphoton excess using
the method of renormalization group running with careful treatment of different
contributions and perturbativity criterion. Our results suggest that the scale
of new physics is generically not much larger than the TeV scale, in particular
if the width of the hinted (pseudo)scalar is large. Introducing multiple copies
of VLQs, lowing the VLQ masses and enlarging VLQ electric charges help reduce
the required Yukawa couplings and can push the cutoff scale to higher values.
Nevertheless, if the width of the 750 GeV resonance turns out to be larger than
about 1 GeV, it is very hard to increase the cutoff scale beyond a few TeVs.
This is a strong hint that new particles in addition to the 750 GeV resonance
and the vector-like quarks should be around the TeV scale.
