## Friday, July 13, 2018

### Higgs Data Still Consistent With Standard Model Higgs Boson

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)
$\mu=1.13\pm 0.05({\rm stat.})\pm 0.05({\rm exp.})^{+0.05}_{-0.04}({\rm sig. th.})\pm 0.03({\rm bkg. th})$
and CMS (see here)
$\mu=1.17\pm 0.06({\rm stat.})^{+0.06}_{-0.05}({\rm sig. th.})\pm 0.06({\rm other syst.}).$
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).

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.

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.

## Wednesday, July 11, 2018

### Does SUSY Really Lead To Gauge Unification?

There are three Standard Model constants that govern how strong the three Standard Model forces are and they vary in an exactly known way with energy scale. In the Standard Model as we know it, however, all three of these constants never take the same value at the same energy scale.

It is widely claimed that in Minimal Supersymmetric Standard Model (MSSM) which is one of the most studied version of Supersymmetry (SUSY) that there is an energy scale called the GUT scale at which all three coupling constants that govern the strength of the three forces of nature (other than gravity) do take the same numerical value (which is dimensionless).

The presentation cited below, at pages 38-40 (see also pages 57-59), however, argues that the widely touted claim that the MSSM gives rise to gauge unification isn't accurate. As Woit comments:
The question recently came up here (see this posting) of how good the SUSY GUT coupling constant unification prediction is. At a recent summer school lecture, Ben Allanach says the prediction is off by 5 sigma, i.e. that if you try and predict the strong coupling at the Z mass this way, you get 0.129 +/- 0.002, whereas the measured value is 0.119 +/- 0.002. Someone should tell Frank Wilczek…
In terms of "beauty" gauge unification is one of the most compelling arguments for SUSY, so this is a big deal.

Indeed, at this point it may take smaller tweaks to the running of the Standard Model constants for them to unify near the GUT scale than it does for the MSSM to produce this result.

Also, any theory that results in exact gauge unification in a pure GUT model without gravity almost certainly has to be wrong, because the addition of quantum gravity into a theory of gravity with its new force carrying boson, the graviton, necessarily tweaks the running all of the other experimentally determined constants in the Standard Model or any GUT that you want to devise.