**The Coupling Strengths of the Higgs Bosons**

A Higgs boson coupling in the context used in this post, is the likelihood that a Higgs boson will decay to a particular kind of pair of fundamental particles, which depends upon mass but has otherwise been known for a long time at various possible Higgs boson masses in the Standard Model. As a refresher, the decays of a 125 GeV Higgs boson in the Standard Model are approximately as follows:

b-quark pairs, 58%

c-quark pairs, 3%

tau-lepton pairs, 6.3%

muon pairs, 0.02%

gluon pairs, 8%

photon pairs, 0.2%

W boson pairs, 21.3%

Z boson pairs, 2.8%

The total does not add to 100% due to rounding errors and due to omitted low probability decays (e.g. electron pairs, s-quark pairs, etc.).

The observed decays can be normalized for each kind of decay by comparing the observed decay of the Higgs boson into particular kinds of pairs of particles to the Standard Model expectation. And, combined appropriately, you can combine all of the observed normalized Higgs boson decay rates into a single measure, mu, of the fit of the observed decays to the theoretical expectation in the Standard Model.

At last week's ICHEP 2018 conference, ATLAS and CMS released their latest results on the fit of the couplings of the Higgs boson that are observed so far to the Standard Model predicted couplings of the Higgs boson for a Higgs boson of the measured mass, which is summed up in a statistic known as mu for which a value of 1.0 is a perfect fit to the Standard Model prediction. This is summed up at Gauge Connection as follows:

About the Higgs particle, after the important announcement about the existence of the ttH process, both ATLAS and CMS are pursuing further their improvement of precision. About the signal strength they give the following results. For ATLAS (see here)

and CMS (see here)

The news is that the error is diminished and both agrees. They show a small tension, 13% and 17% respectively, but the overall result is consistent with the Standard Model.

This works out to a result that is 1.46 sigma from the Standard Model at ATLAS and 1.68 sigma from the Standard Model at CMS, both easily within the two sigma benchmark for consistency of experimental results with the predicted values (in a Gaussian distribution the average sigma amount with only statistical error present should be one sigma). The combined value of mu is about 1.15 or within 15% of the Standard Model expectation (and again consistent with it because it is less than two sigma from the expected value).

UPDATE July 18, 2018

The latest CMS search for muon pair decays from a Higgs boson did not observe them but only because the search was not sensitive enough to do so if the Higgs boson behaves as expected in the Standard Model. A maximum possible muon pair decay rate of 2.95 time the Standard Model expectation with 95% probability was established.

END UPDATE

Experimental constraints of the Higgs self-coupling, which is very rare, are that it is not more than 22 times the Standard Model expectation.

UPDATE July 18, 2018

The latest CMS search for muon pair decays from a Higgs boson did not observe them but only because the search was not sensitive enough to do so if the Higgs boson behaves as expected in the Standard Model. A maximum possible muon pair decay rate of 2.95 time the Standard Model expectation with 95% probability was established.

END UPDATE

Experimental constraints of the Higgs self-coupling, which is very rare, are that it is not more than 22 times the Standard Model expectation.

Every time mu gets smaller, the parameter space for beyond the Standard Model theories that change the properties of the Higgs boson relative to the Standard Model gets smaller.

The combined ATLAS and CMS Higgs boson mass measurements at the end of Run 1 had the value 125.09 +/- 0.24 GeV.

A year ago, the combined ATLAS and CMS Higgs boson mass measurements were 125.14 +/- 0.17 GeV, with the ATLAS value equal to 124.98 +/- 0.28 GeV and the CMS value equal to 125.26 +/- 0.22 GeV.

Other properties of the Higgs boson like the relative strength of the channels by which it is produced, its width, its spin, its charge and its CP even v. odd status remain perfectly consistent with a Standard Model Higgs boson as well, something that we already knew quite a while ago.

**The Higgs Boson Mass**The combined ATLAS and CMS Higgs boson mass measurements at the end of Run 1 had the value 125.09 +/- 0.24 GeV.

A year ago, the combined ATLAS and CMS Higgs boson mass measurements were 125.14 +/- 0.17 GeV, with the ATLAS value equal to 124.98 +/- 0.28 GeV and the CMS value equal to 125.26 +/- 0.22 GeV.

The current Run-2 value from CMS is 125.26 +/- 0.21 GeV, more or less unchanged from a year ago. We don't have a new measurement from ATLAS so far this year.

A Higgs boson mass of 124.65 GeV is theoretically notable because it is the value of the Higgs boson mass if if the the sum of the square of the boson masses equals the sum of the square of the fermion masses which in turn each equal one half of the square of the Higgs vacuum expectation value.

This theoretically significant value is just under 2.88 sigma from last year's combined value which so far remains unchanged; about 2.9 sigma from the CMS result and 1.2 sigma from the ATLAS result. Something as simple as a lower margin of error in a new ATLAS result could shift that balance, however, bringing the combined measurement closer to this theoretically notable value.

So far, the Higgs boson mass has been a bit heavy relative to this theoretically significant value, while the top quark mass, which is the dominant factor on the fermion side of the ledger has been a bit lighter than the theory would predict.

So far, the Higgs boson mass has been a bit heavy relative to this theoretically significant value, while the top quark mass, which is the dominant factor on the fermion side of the ledger has been a bit lighter than the theory would predict.

## 12 comments:

does SUSY change mu?

This is great. Thanks for these important updates. Greetings from Group32 in Prague.

Totally off-topic.

We would like your insights on the human dual spindle mitosis that just came out from EMBL.

Cheers,

Guy

@Marni Thanks.

@neo IIRC, the SM Higgs is very similar in properties to the light scalar SUSY Higgs "h", so mu shouldn't be very different, probably within the existing margin of error in experimental results.

@GuyTipton I think that the paper you are referring to is this one: http://science.sciencemag.org/content/361/6398/189

I missed it when it came out at the end of last week. Thanks for the tip. I'll take a look.

@neo The properties of SUSY Higgs bosons, as a function of mass are here:

https://arxiv.org/pdf/1706.06435.pdf

Recall that there are at least five SUSY Higgs bosons: h, H, A, H+ and H-.

Himpsel's (2017) interpretation of a Higgs boson pair as a composite of gauge bosons, which becomes half the vev Higgs boson,

https://arxiv.org/ftp/arxiv/papers/1502/1502.06438.pdf

is given greater credibility. Tree level accuracy revised from ~2% to ~0.8%.

@andrew

"Recall that there are at least five SUSY Higgs bosons: h, H, A, H+ and H-."

what are the prospects of LHC or other near term experiments finding them?

do they cause deviations in any SM parameter or decay channel?

@neo They have been ruled out up to the mid to high 100s of GeVs of mass at the LHC, although some proponents stubbornly claim that a 40-60 GeV A boson isn't entirely foreclosed by the data if it has certain properties and would explain the muon g-2 if it did. https://arxiv.org/abs/1807.05379

Impact on the Standard Model of two Higgs Doublets is discussed here: https://arxiv.org/abs/1807.05876

@Graham I remember the 2015 and every now and then hoped that someone would do the calculation to see if the tree level calculation was compatible at additional loops with what was observed, but never heard anything further.

@Graham The new paper is https://arxiv.org/abs/1801.04604

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