Checking the Higgs Particle's Mass-Making

[lpetrich]

Who gets their mass from the Higgs?

The Higgs particle is a spin-0 particle that has a sizable nonzero value of its field when in its ground state. It thus acts like it is always present, and that's what makes masses for all the particles that it interacts with. The "particle" that we have observed is an excitation of this field, just like other elementary particles. From the theory of this particle, one can predict how much it interacts with other particles. it ought to interact more strongly with particles that it gives greater masses to.

Particle Data Group - 2018 Review has a feature called pdgLive that gives the latest results. Here are some decay rates normalized to the Standard Model's predictions.

• WW(virt) -- 1.08+0.18−0.16
• ZZ(virt) -- 1.14+0.15−0.13
• photon-photon -- 1.16±0.18 (through W and top loops)
• bottom-bottom -- 0.95±0.22
• muon-muon -- 0.0±1.3
• tau-tau -- 1.12±0.23
• Z-photon -- <6.6 (though W and top loops)

virt = virtual, since the Higgs particle is not massive enough to produce a pair of real W's or Z's.

Back to the phys.org article.

Because the top quark is much more massive than the Higgs boson, it's impossible for a Higgs boson to decay into a pair of top quarks. Luckily, there is another way to measure how strongly the Higgs boson couples to top quarks: looking for the rare case of simultaneous production of top quarks and a Higgs boson.

"Higgs boson production is rare – but Higgs production with top quarks is rarest of them all, amounting to only about 1 percent of the Higgs boson events produced at the LHC," said Chris Neu, a physicist at the University of Virginia who worked on this analysis.

...
"A top quark decays almost exclusively into a bottom quark and a W boson," Neu said. "The Higgs boson, on the other hand, has a rich spectrum of decay modes, including decays to pairs of bottom quarks, W bosons, tau leptons, photons and several others. This leads to a wide variety of signatures in events with two top quarks and a Higgs boson. We pursued each of these and combined the results to produce our final analysis."

Phys. Rev. Lett. 120, 231801 (2018) - Observation of $t\overline{t}H$ Production

An excess of events is observed, with a significance of 5.2 standard deviations, over the expectation from the background-only hypothesis. The corresponding expected significance from the standard model for a Higgs boson mass of 125.09 GeV is 4.2 standard deviations. The combined best fit signal strength normalized to the standard model prediction is 1.26+0.31−0.26.

[1806.00425] Observation of Higgs boson production in association with a top quark pair at the LHC with the ATLAS detector
For data collected for 13-TeV center-of-mass energy for LHC protons, the observed (expected) statistical significance is 5.8 (4.9). Adding data collected at 7 and 8 TeV, it becomes 6.3 (5.1) stdevs. Or observation = 1.24 * Standard-Model prediction.


So the Higgs particle interacts with the other more massive Standard-Model particles at the right strengths to give those particles their observed masses.

 

[lpetrich]

Higgs boson observed decaying to b quarks (2018 July 10)

The b quark has the honor of being the most massive particle that a Higgs particle can decay into as all real particles. If a Higgs particle decays into two W's or two Z's, then at least one of them must be virtual, reducing the decay rate.

The Higgs particle has a nonzero ground-state or vacuum value, as a result of it having a potential-energy curve shaped like a bowl with a hump in the middle of it. The masses thus generated are:

(mass of X) = (coupling to X) * (vacuum field value)

However, the decay of a Higgs particle into an X and an anti-X has a rate proportional to

(coupling to X) ^ 2

One can thus test Higgs-particle mass-making by checking on whether the decay rate is proportional to

(mass of X) ^ 2


So far, that test has been done with the W, the Z, and the tau lepton, with good agreement with the Standard Model. The bottom quark is more massive than the tau lepton, at 4.2 GeV as opposed to 1.8 GeV. That gives a factor of 5.4 more. An additional factor comes from quarks having a degree of freedom called "color". A Higgs particle can decay into a red bottom, a green bottom, or a blue bottom, giving an additional factor of 3, for a total factor of 16.

But tau decay was detected well before bottom decay.

The difference is from what each kind of particle decays into.

A tau lepton quickly decays into a tau neutrino and a virtual W, and that virtual W decays in turn into an electron and its neutrino, a muon and its neutrino, or some pair of light quarks. Those quarks in turn make hadrons as they separate from each other.

So a tau lepton can make an electron or a muon, and that particle can be easy to see above the noise of background events. It can also make some hadrons, and they are much more difficult to see above the noise. But one can correct for their non-observation.

A bottom-antibottom pair of quarks, however, does not directly make leptons, only hadrons. So it's also more difficult to see above the LHC's background. But those quarks emerge with a lot of energy, and as a result, they make jets of hadrons. There are some fancy "b-tagging" algorithms for looking at the particles in such jets to see if there was a bottom quark in them. That quark decays into a charm quark, then into a strange quark, then into an up quark, and it makes a recognizable pattern of decay products as it does so.

So one must look for a pair of b-tagged jets that gives the right original-particle energy. That is what the ATLAS team did with data collected over the LHC's history. It recently got more than 5 standard deviations of significance, meaning that the ATLAS team is confident that it has detected the decay of Higgs particles into bottom quarks.

 

[lpetrich]

The masses of the Standard-Model particles:

• Top quark: 173.0 GeV
• Higgs particle: 125.18 GeV
• Z particle: 91.1876 GeV
• W particle: 80.379 GeV
• Bottom quark: 4.18 GeV
• Tau lepton: 1.77686 GeV
• Charm quark: 1.275 GeV
• Strange quark: 95 MeV (energy scale: 2 GeV)
• Muon: 105.6583745 MeV
• Down quark: 4.7 MeV (energy scale: 2 GeV)
• Up quark: 2.2 MeV (energy scale: 2 GeV)
• Electron: 0.5109989461 MeV
• Neutrinos: <~ 0.01 eV
• Photon, Gluon: 0

So far, we've seen decays of the Higgs particle into WW*, ZZ*, tau-tau, and now bb. Though rate(bb) ~ 16 * rate(tau-tau), its hadronic nature made it difficult to observe.

Let's see what's next.

Charm? That's about 1/11 of bottom, and since (error) ~ 1/(number of data points)^(1/2), one would need a run 115 times as long to see it. That is because it is also hadronic.

Muon? Currently, the error is the size of the Standard-Model prediction. So to get it down by a factor of 3, one will need 10 times the observations. But this is a very clean test of the Higgs mechanism, since the muons come directly from the decay, and since muons last long enough to make it into the detectors.

Less massive quarks? The electron? The neutrinos? Too small.