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4.9 with Run 2 alone.

The linked summary slides claim 5.9 sigma in a combination of Run 1 and Run 2 (slide 7), but I don't see that combination in a CMS talk.
 
Oh, I hadn't checked the first link... As far as I understood in slide 7 they mention the combined ATLAS+CMS significance (5.5)? Although I might be wrong right now (tired and the slides are not very clear).

For me, an interesting approach is how they estimated the Ztautau background (by replacing the muons of Zmumu with taus)... Similar approaches I've seen by SUSY guys when they want to estimate the Znunu+jets background (by adding the muons' pT of a Zmumu region to missing momentum)
 
Well, independent of the exact combinations we have available: ##H \to \tau \tau## has been observed clearly. ##H \to bb## has some notable evidence already, and it will probably follow as soon as CMS gives an update with 2016 data.
Then we will see the Higgs decays in more production modes and more accurate measurements, but no new decay channels until the HL-LHC runs.

The decay to gluons is completely indistinguishable from background. The decay to charm is impossible to see as well - a factor 10 smaller branching fraction and a factor 10 higher background than bottom.
##H\to Z \gamma## will go from upper limits to measured branching fractions after Run 2 (2018), but with an expected significance of something like 1.3 sigma. Here is an ATLAS study, predicting 2.3 sigma with 300/fb (2023) and 3.9 with 3000/fb (~2035).
##H \to \mu \mu## looks a bit better, with the HL-LHC dataset it is expected that both ATLAS and CMS get a bit over 5 sigma.
There are also more exotic decays to specific hadrons, but they are rare to be found even with the HL-LHC (assuming Standard Model branching fractions).
 
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European Physical Society. The first sentence has a link already where you can find this. It doesn’t really matter because it is an international conference anyway.