What can we learn from LHC Higgs combination

Recently, ATLAS and CMS released the first combination of their Higgs results. Of course, one should not expect any big news here: combination of two datasets that agree very well with the Standard Model predictions has to agree very well with the Standard Model predictions...  However, it is interesting to ask what the new results change at the quantitative level concerning our constraints on Higgs boson couplings to matter.

First, experiments quote the overall signal strength μ, which measures how many Higgs events were detected at the LHC in all possible production and decay channels compared to the expectations in the Standard Model. The latter, by definition, is μ=1.  Now, if you had been impatient to wait for the official combination, you could have made a naive one using the previous ATLAS (μ=1.18±0.14) and CMS (μ=1±0.14) results. Assuming the errors are Gaussian and uncorrelated, one would obtains this way the combined μ=1.09±0.10. Instead, the true number is (drum roll)

So, the official and naive numbers are practically the same.  This result puts important constraints on certain models of new physics. One important corollary is that the Higgs boson branching fraction to invisible (or any undetected exotic) decays is limited as  Br(h → invisible) ≤ 13% at 95% confidence level, assuming the Higgs production is not affected by new physics.

From the fact that, for the overall signal strength, the naive and official combinations coincide one should not conclude that the work ATLAS and CMS has done together is useless. As one can see above, the statistical and systematic errors are comparable for that measurement, therefore a naive combination is not guaranteed to work. It happens in this particular case that the multiple nuisance parameters considered in the analysis pull essentially in random directions. But it could well have been different. Indeed, the more one enters into details, the more the impact of the official combination becomes relevant.  For the signal strength measured in particular final states of the Higgs decay the differences are more pronounced:

One can see that the naive combination somewhat underestimates the errors. Moreover, for the WW final state the central value is shifted by half a sigma (this is mainly because, in this channel, the individual ATLAS and CMS measurements that go into the combination seem to be different than the previously published ones). The difference is even more clearly visible for 2-dimensional fits, where the Higgs production cross section via the gluon fusion (ggf) and vector boson fusion (vbf) are treated as free parameters. This plot compares the regions preferred at 68% confidence level by the official and naive combinations:

There is a significant shift of the WW and also of the ττ ellipse. All in all, the LHC Higgs combination brings no revolution, but it allows one to obtain more precise and more reliable constraints on some new physics models.  The more detailed information is released, the more useful the combined results become.