I'm sure this sounds like a daft question but I can't find anything all that helpful online to answer this, not even on the CMS website. Is the LHC measuring the actual mass of the Higgs boson or is it recording the masses of the Higgs' decay products? That's basically all I want to know.
The LHC records with various detectors the momenta and/or energies of charged and neutral particles for each proton proton interaction. From these hard numbers four vectors are created and thus any combination of two (or more) observed particle four vectors, gives the invariant mass of the pairs (or set of particles). That is what is the mass in special relativity.
Then simulation programs, called Monte Carlo, generate background events with the known physics, without the Higgs. The comparison between measured masses and the computed background shows an enhancement at what is now known as the mass of the Higgs.
A plot of the four vector invariant mass of two gamma in the data.
The final background estimation fits the data except for the bump, which is the four vector invariant mass of two gamma. This is one of the ways the mass of the Higgs has been measured.All the decays establish that it is the expected from the SU(3)xSU(2)xU(1) standard model of particle physics.
Since the life time of the Higgs boson is far too short, the ATLAS and CMS experiments (the LHC is just the collider) measure the mass of the decay products.