ChrisVer said:
now that i look at them, is there a particular reason why one would keep the stat+syst uncertainty on the measured signal strength, but the SM uncertainty (I guess theory) on the "1" (SM expectation). Is it to have the measured signal strengths reinterpretable in other theories?
Because if it's just to see the compatibility of the measurement to the SM expectation, I'd add the theory uncertainty to the shown error...
I suspect that the SM expectation theory uncertainty is at least one or two orders of magnitude smaller, than the measurement error, to the point of being exact for all practical purposes when a ratio is used, although the better practice would be to state that explicitly (and the source body text probably does state the theory error someplace).
UPDATE: I was overly generous, as seen in the reference at the bottom of this post. I've left the analysis that made an overly generous estimate seem to make sense because more data points are always good. But skip to the bottom for the ultimate answer. END UPDATE PART ONE.
Most of the calculation of the branching fractions of a Higgs boson decay are QED and weak force calculations which are quite precise at a pretty small number of loops, unlike QCD calculations of SM expectations which are vastly more imprecise. I'm pretty sure that I've seen the predicted branching fractions calculated to at least three significant digits and those were probably truncations of the full result. T
he decays of a 125 GeV Higgs boson in the Standard Model are approximately as follows (with observed decays that are experimental hints of observations for as noted in previous posts on this thread, in bold):
b-quark pairs, 58%
W boson pairs, 21.3%
gluon pairs, 8%
tau-lepton pairs, 6.3%
c-quark pairs, 3%
Z boson pairs, 2.8%
photon pairs, 0.2%
muon pairs, 0.02%
Some of those, like the b-quark pairs, are hard to see because their are large backgrounds. Others, like the Z boson, photon and muon pairs are easier to see despite much smaller numbers of decay events due to small backgrounds or very precisely quantifiable backgrounds.
This total adds to 99.602% rather than 100% due to omitted low probability decay channels (three kinds of light quark pairs, u, d and s, and electron-positron pairs, possibly some mixed pairs (like Z-photon) and possibly some negligible probability of neutrino pairs, and it is also off due to rounding errors. But, again, I think I've seen more precise values that include more decay channels.
You'd also need to have an absolute value of a particular decay channel, but once you had one (or the overall value) either from experiment or theory, you could easily determine the theoretical prediction in terms of an absolute value of events for others with high school algebra from the relative decay percentages.
The electromagnetic force coupling constant is known to parts per billion, and Fermi's constant (which is proportional to the bare weak force coupling constant and from which the Higgs vev is derived) is known to parts per million.
The SM expectations are made for an assumed Higgs boson mass that is usually explicitly stated, so there is zero error in the Higgs boson mass since it is just assumed and thus exact.
Given how fast QED and weak force calculations converges (in terms of number of loops) and the precision with which we know those coupling constants, the main source of SM expectation uncertainty probably comes from uncertainty in the masses of the decay products of the Higgs such as the b quark mass, tau lepton mass, W and Z boson masses, charm quark mass, strange quark mass, and muon mass (there is not uncertainty in the photon mass or gluon mass, each of which is exactly zero). As of the last time, I checked, earlier this year, those values and their uncertainties were (at pole masses for fermions and 2 GeV energy scale for u, d and s quarks):
* W boson mass 80.379 ± 0.012 GeV
* Z boson mass 91.1876 ± 0.0021 GeV
* Electron mass 0.5109989461 ± 0.0000000031 MeV
* Muon mass 105.6583745 ± 0.0000024 MeV
* Tau lepton mass 1,776.86 ± 0.12 MeV
* Up quark mass 2.16 + 0.49 - 0.26 MeV
* Down quark mass 4.57 + 0.48 - 0.17 MeV
* Strange quark mass 93 + 11 -5 MeV
* Charm quark mass 1.27 ± 0.02 GeV
* Bottom quark mass 4.18 + 0.03 - 0.02 GeV
* Top quark mass 172.9 ± 0.4 GeV (direct measurements)
* Strong force, aka SU(3), coupling constant 0.1179 ± 0.0010 evaluated at the Z boson mass-energy scale.
* Fermi coupling constant 1.166 378 7 ± 0.000 0006 × 10^−5 GeV^−2 (functionally related to the weak force, aka SU(2), coupling constant)
* Fine structure constant 7.297 352 5693 ± 0.000 000 0011 ×10^−3 = 1/137.035 999 084 ± 0.000 000 021 (functionally related to the electromagnetic force, aka U(1), coupling constant)
Fortunately, the biggest relative uncertainties are in lighter quarks which have decay rates to tiny to observe anyway, and the impact of virtual top quark coupling mediated decays is profoundly suppressed because it has more mass than a Higgs boson.
Likewise, while there is serious question about whether neutrinos couple to the Higgs boson at all, the decay fractions would be so tiny anyway (and you can only detect a tiny share of neutrinos produced anyway as a reliable signal because they couple so weakly to other matter and because there are quite a few sources of irreducible background, e.g. from the Sun, cosmic rays, nuclear reactors, radioactive decays from radioactive elements naturally found in the Earth) that the deep fundamental question about whether they couple to the Higgs boson is irrelevant for experimenters.
Uncertainties in the CKM matrix parameters also shouldn't matter much in this calculation because constants derived from these parameters don't enter into the analysis at tree level.
The uncertainty in the b quark mass (which is about one part per 167 per PDG shown above, although FLAG has a more precise estimate) which is the heaviest decay product and a big branching fraction probably accounting for most of the uncertainty in the expected branching fractions. I suspect that the theoretical uncertainty in the 58% b quark decay channel value may be greater than the 0.398% discrepancy from 100.000% unitarity total, shown above from all other decays and the rounding errors in all of the other values.
The relative error in the charm quark mass is about one part per 64, which is greater than the b quark mass uncertainty. But, that uncertainty is affecting 3% of total decays instead of 58% of total decays, as with b quarks you have to statistically sort the Higgs boson sourced decays from lots of background with significant uncertainties in it. Double the physical constant error in a decay channel that is 19 times as small should e less significant than the b quark sourced uncertainty in the overall theoretical prediction.
The gluon pair uncertainty could also be pretty high, because while the gluon mass is theoretically exactly zero, the strong force coupling constant has only a little less than 1% uncertainty and probably factors into the calculation for gluon path decays somehow, and that's relative to 8% of total decays (about one-seventh of b pair decays involving only a little less physical constant sourced uncertainty than the b quark pair decays).
None of the decay channel measurements are more precise than low single digit percentages, and some are in the double digit percentages margin of error or worse. So, theory error can probably be safely ignored at this point.
UPDATE PART TWO all that analysis aside a
PDG review as of 2018, below, cites the uncertainties in the Standard Model expectation as higher than I would have expected, because in each of the three significant digit quoted branching ratios the relative uncertainty makes anything more than two significant digit values spurious accuracy.
These uncertainties are significantly smaller than the uncertainty in the experimental measurement uncertainties of signal strength, but hardly negligible either.
Figure 11.2 (right):
From the same source "the extremely small branching fraction to e +e −," is "approximately 40,000 times smaller than the branching fraction to dimuons."
From the same source, some of the experimental uncertainties as of 2018 (they are bit better now) were as follows (references omitted):
The signal strengths µ for the inclusive H → 4ℓ production measured by the ATLAS and CMS experiments are 1.44+0.40 −0.33 at mH = 125.36GeV and 0.93+0.29 −0.25 at mH = 125.6GeV respectively, in Run 1. The signal strengths measured by the ATLAS and CMS experiments in Run 2 are 1.28+0.21 −0.19 and 1.05+0.19 −0.25 respectively, both measurements are made at the combined Run 1 Higgs mass of mH = 125.09GeV. . . . The measured inclusive signal strength is µ = 1.09+0.23 −0.21. In the VBF category an excess with a significance of 3.2σ corresponding to a signal strength of µ = 1.27+0.53 −0.45 is observed [136].
For tau lepton decays:
When the ATLAS and CMS H → ττ Run 1 measurements are combined [143], the significance of the observed excess corresponding to mH = 125.09GeV is 5.5 standard deviations and the combined signal strength is µ = 1.11+0.24 −0.22, consistent with the Standard Model expectation.
For b quark decays:
At mH = 125GeV the observed signal strength µ = 1.59+0.69 −0.72.
