# ATLAS and CMS see signs of Higgs->muons decay

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Mentor

## Summary:

Both experiments see hints of this difficult to find decay - at the expected rate.
The Higgs boson couples to mass, muons are relatively light, that makes a decay to a pair of muons (muon+antimuon) very rare. In addition there are many other processes that produce pairs of muons, making this decay mode challenging to find. For a long time it was expected that the experiments would need the high luminosity upgrade for a clear signal. Recent improvements in analysis methods have made it possible to get some hint of this decay much earlier. No one questions that this decay exists - but measuring if it happens at the expected rate is still an important test. New physics could change the rate.

At ICHEP both ATLAS and CMS presented analyses of a dataset of 140/fb - about 5% of the expected size of the total dataset the LHC will collect.
CERN press release
ATLAS preprint
CMS document

Both experiments see a hint of the signal with an observed significance of 2.0 (ATLAS) and 3.0 (CMS) standard deviations, a bit above the expectations (1.7 and 2.5, respectively). As the Higgs mass is known from other observations there is no look-elsewhere effect to consider. In both cases the best fit is 20% more signal than predicted but experiment and prediction are perfectly compatible within the (big) uncertainties. The uncertainties are completely dominated by statistics, so it would be relatively easy to combine the measurements. I don't expect this to happen, however. Not much we would learn from it, and the experiments will collect much larger datasets in the future. In the next years the collected luminosity is expected to increase to ~350/fb. At this time a combination of ATLAS and CMS might reach 5 standard deviations and (more importantly) the uncertainty for the branching fraction could drop to ~25%. A naive extrapolation to 3000/fb would suggest an uncertainty below 10%.

5 Higgs decay modes have been measured clearly: Two photons, two Z bosons (the main modes for the discovery), tau/antitau, two W bosons and bottom/antibottom quarks. Higgs -> Z photon has some initial weak hints, this is another decay that will get more attention in the next years. H->muons see above. H->charm/anticharm is something people think about, but it's a really challenging analysis. These are all decay modes we can expect to see at the LHC, but there is always the chance to find something unexpected. Higgs->gluons is the third most common decay mode but there is way too much background to do anything there.

ohwilleke, dlgoff, atyy and 4 others

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Are there any reasonable, known proposals for new physics which would modify this rate but match the other existing data? If not, is it a case of never say never but rather unlikely that this would deviate from expected rate, given what we've seen so far from other channels?

Mentor
I don't know specific models, but if the measured rate would have been different we see many of them on arXiv.
Out of the studied decays the muon is by far the lightest particle which is produced in a tree-level process, i.e. through direct coupling to the Higgs.

A while ago CMS saw slightly more tau mu (or was it tau e?) events than expected from background (went away with more statistics), theory papers citing that would be a good place to start if you look for specific ideas.

Lord Crc and vanhees71
Staff Emeritus
2019 Award
Are there any reasonable, known proposals for new physics which would modify this rate but match the other existing data?
Suppose there are two Higgses -one couples to W's and Z's and the 3rd generation, and the other couples to everything else. Is this "reasonable"? Maybe not, but it is not excluded by anything.

ohwilleke, Lord Crc and vanhees71
vanhees71
Gold Member
2019 Award
That's another interesting question: How much is now known about the specific realization of the Higgs mechanism? In other words, is it just the minimal Higgs model (i.e., just a wiso doublet) or are there hints for "more Higgses". Some interesting possibility is also a Higgs triplet etc. So what's the experimental status about this question?

Staff Emeritus
2019 Award
How much is now known about the specific realization of the Higgs mechanism?
Very little. We can't even trace the potential if there is only a single Higgs.

vanhees71
Thank you all. I realize I could have been a bit more specific than a plain "reasonable", point taken.

Another naive question if I may. When doing an analysis like this where they combine data between runs, would they have to segment the data based on f.ex. 3 TeV vs 7 TeV run etc, do separate analysis for each segment and combine? Or can it all be parameterized so they can operate on the aggregate dataset?

Was just curious how much the changes to the LHC due to upgrades, changes to operating parameters etc affected how one does an analysis like this.

Staff Emeritus
2019 Award
I started typing the answer, but realized this is covered in the CMS document that mfb linked to.

Lord Crc
ohwilleke
Gold Member
Does anyone have a link to a nice simple summary chart showing signal strength and margin of error for each of the decay channels that has been measured for the Higgs (ideally compared juxtaposed against a chart showing the percentage of decays expected in each channel so one can compare the amount of undetected rare channels to the detected ones in relative significance)?

Mentor
ICHEP ended a few days ago. Here is the Higgs plenary talk
There are too many measurements to put all of them on one slide. Consider slide 8 for example: That's only from ATLAS, only in the gamma gamma decay mode, split by production mode, kinematics and so on. Many other slides have many results, too. I guess you can combine the merged results for each mode to a single plot. So far no deviations from predictions.

The plots are always observed strength relative to expected, so you have the comparison directly included.

vanhees71 and ohwilleke
ChrisVer
Gold Member
Does anyone have a link to a nice simple summary chart showing signal strength and margin of error for each of the decay channels that has been measured for the Higgs (ideally compared juxtaposed against a chart showing the percentage of decays expected in each channel so one can compare the amount of undetected rare channels to the detected ones in relative significance)?
Do you mean plots like these?
https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CombinedSummaryPlots/HIGGS/
e,g the "Run 2 cross section and partial decay width ratios"?

ChrisVer
Gold Member
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....

ohwilleke
Gold Member
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. The 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 thats 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.

Last edited:
vanhees71
Mentor
H->gg is a difficult decay, that has an impact on the other uncertainties.
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.
You don't hope to find the neutrinos. You look for pp -> H+X where the Higgs is not detected ("invisible decay") but the recoil shows up in other particles X (like Z bosons). These searches exist, but their upper limits are quite high. They are not looking for neutrinos, they look for possible decays to dark matter particles or other unknown particles as long as they are below half the Higgs mass.

ohwilleke and vanhees71
ChrisVer
Gold Member
Yup, but I meant something more basic. If you had for example a figure that looked like this for some decay channel (not very likely but you get the point):
$\mu_{th} = 1\pm 0.5$
$\mu_{exp} = 1.4\pm 0.02$
would you claim new physics ? probably not, you would contact your theorists and ask for them to determine better the uncertainties on the SM. Right? Because to check the agreement you would (naively) add the two errors and see that theory and experiment are not distinguishable.

So I was trying to understand the utility of splitting the errors in two parts and attributing them to two different values that you want to compare (in consistency). E.g. say:
$\mu_{th} = 1$
$\mu_{exp} = 1.4\pm 0.5004$

I suppose it's related to wanting to keep your measurement model independent (if you add for example uncertainties related to the SM, you make it SM-dependent).

vanhees71
Mentor
By keeping experimental result and theory prediction independent you make it easier to compare with different predictions. Theorist A predicts 40+-5 fb in 2018, theorist B predicts 41+-2 fb in 2020 after calculating higher orders. Theorist C predicts 46+-2 fb for their favorite BSM idea. If you publish a cross section then you don't need to update anything.

ohwilleke
ohwilleke
Gold Member
Yup, but I meant something more basic. If you had for example a figure that looked like this for some decay channel (not very likely but you get the point):
$\mu_{th} = 1\pm 0.5$
$\mu_{exp} = 1.4\pm 0.02$
would you claim new physics ? probably not, you would contact your theorists and ask for them to determine better the uncertainties on the SM.
When you have uncertainty in two qualities stated in like units, you square each uncertainty, add them up, and take the square root. In the example you give, the theory and experiment and consistent with each other at the one sigma level, so it wouldn't be new physics.

But, if you had $\mu_{exp} = 3.9\pm 0.02$ you would suspect new physics (that would be a more than five sigma difference which some fudge factor left over.