I am not understanding what the advantage of using only two specific decay channels in combined measurement of the Higgs boson mass. This is how it is stated in a published paper titled "Combined Measurement of the Higgs Boson Mass in pp Collisions at sqrt(s) = 7 and 8 TeV with the ATLAS and CMS Experiments":
"The combination is performed using only the H → γγ and H → ZZ → 4l decay channels, because these two channels offer the best mass resolution. Interference between the Higgs boson signal and the continuum background is expected to produce a downward shift of the signal peak relative to the true value of mH. The overall effect in the H → γγ channel [18–20] is expected to be a few tens of MeV for a Higgs boson with a width near the SM value, which is small compared to the current precision. The effect in the H → ZZ → 4l channel is expected to be much smaller . The effects of the interference on the mass spectra are neglected in this Letter"