  Gauge invariance dictates that a resonance produced from initial state gluons
must be produced through a non-renormalizable operator or a loop process.
Should such a resonance be discovered, uncovering the dynamics that give rise
to its couplings to gluons will be crucial to understanding the nature of the
new state. Here we study how the production of this resonance at high
transverse momentum in association with one (or more) jets can be used to
directly measure the scale of the operator or the mass of the particles in the
loop. We use a 750 GeV diphoton resonance as an example application, and we
study how the non-renormalizable operator case can be described by a slowly
converging effective field theory (EFT) expansion with operators of dimension
five and seven. We show that with O(100) events, one can put strong constraints
on the scale of the EFT, particularly in theories with strong coupling. We also
compare the EFT analysis to that of a UV completion with vector-like quarks,
and outline how the mass of said quarks could be measured.
