How do we know that the 2012 LHC discovery is SM Higgs Boson and not a pseudo-dilaton? To be more clear, are there any measurements or analysis done on the new particle to verify if it is SM Higgs boson and not a pseudo-dilaton.
 A: Interpreting pseudo-dilaton with its usual meaning in this context, I can add some information to what John Rennie rightly stated. John Ellis wrote a very nice summary [1] which dates a bit (2013) but already back then, the pseudo-dilaton model was strongly disfavoured, as detailed in section 2.2.3, based on a previous work of his [2]. His conclusion is that the pseudo-dilaton is compatible with experimental data if and only if it is fine-tuned to mimic the Standard Model exactly, i.e. the dilaton v.e.v $V$ which breaks scale invariance has to be nearly equal to the v.e.v. $v$ of the Higgs: see the two plots on Fig. 19, showing that $v/V$ has to be peaked near 1. He concludes with humour that

Clearly, there is no evidence for any significant deviation from the Standard Model, and Peter Higgs may continue to smile!

[1] Ellis, John, Higgs Physics, arXiv:1312.5672
[2] J. Ellis and T. You, JHEP 1306 (2013) 103 arXiv:1303.3879.
A: With any new particle we look at the things we can measure, e.g. spin, charge and decay channels, and compare them to the properties predicted for the particle from the Standard Model.
In this case we find the measurements all match the properties the Standard Model predicts for the Higgs boson. That doesn't prove it's really the Higgs boson since there could be another particle with identical values for the properties we have measured but different values for properties we can't measure yet. But we already have enough data that would make this one hell of a coincidence, so it seems pretty unlikely.
