Digamma, what next?

If the 750 GeV resonance in the diphoton channel is confirmed, what are the measurements necessary to infer the properties of the new particle and understand its nature? We address this question in the framework of a single new scalar particle, called digamma ($\digamma$). We describe it by an effective field theory, which allows us to obtain general and model-independent results, and to identify the most useful observables, whose relevance will remain also in model-by-model analyses. We derive full expressions for the leading-order processes and compute rates for higher-order decays, digamma production in association with jets, gauge or Higgs bosons, and digamma pair production. We illustrate how measurements of these higher-order processes can be used to extract couplings, quantum numbers, and properties of the new particle.