The Higgs boson, explained

Yeah, that Higgs boson thing. Have you heard about it? I guess you probably have, right?

I don’t really know where to get started here, so to get started, let’s look at a very summarised version of the key exciting new results we have seen presented by the ATLAS and CMS collaborations in the last week.

These recent results delivered by the CMS and ATLAS collaborations were derived from datasets recorded in 2011 at a collision energy of 7 TeV and in 2012 at 8 TeV. The integrated luminosity delivered in 2011 was about 4.9 fb–1 (inverse femtobarns) at 7 TeV, and about 5.9 fb–1 delivered so far over the first few months in 2012 at 8 TeV.

(Integrated luminosity is essentially a number that represents the number of colliding protons delivered from the accelerator, integrated over time, which basically represents the amount of physics data collected. The massive ramping up in the integrated luminosity that we’ve seen over the last couple of years demonstrates the fantastic performance of the Large Hadron Collider itself, the detector experiments, the computing and data processing infrastructure associated with the detectors, and the infrastructure (such as power supplies and cryogenics) which supports the accelerator itself. The overall performance of these systems has been absolutely fantastic, surpassing all expectations.)

This means that the total data collected in less than 6 months at the start of 2012 has been greater than the total physics data collected in all of 2011. The physics data collected — and recently processed and published — so far in 2012 is only about one third of the total amount of physics data that is expected to be generated in all of 2012.

The collection of the experimental data which has gone into the recently processed results only stopped about three weeks ago. These are very preliminary and very early results.

- CMS shows an excess near 126 GeV in the gamma-​​gamma channel with a significance of 4.1 sigma.
 – CMS shows an excess near 126 GeV in the 4-​​lepton decay channel with a significance of 3.2 sigma.
 – Combined, the signals in these two channels are consistent with each other and have a combined significance of 5 sigma.

- CMS shows data for the decay channel of a Higgs to a b-​​quark-​​antiquark pair which in and of itself is compatible with either background or signal from a 125 GeV Higgs boson. In other words, nothing of any real significance can be discerned yet in this channel in and of itself.

- The decay channel of a Higgs boson to a tau lepton-​​antilepton pair shows no significant departure from Standard Model background-​​only expectations.

- If we “cherry-​​pick” only the photon-​​photon, WW and ZZ Higgs decay channels in the CMS data, we get a consistent signal of a new particle, with a combined significance of 5.1 sigma. However, we really shouldn’t do that, and if we look at all the channels overall, including the b-​​bbar and tau-​​tau channels where no really significant signal can be seen, the combined overall significance of the current CMS data is 4.9 sigma.

- The best fit for the mass of this new particle, based on all 2011 – 2012 data collected in CMS, is 125.3 +/​- 0.6 GeV.

- CMS has observed a new particle, a massive boson, with a mass of 125.3 +/​- 0.6 GeV. This is the heaviest boson ever discovered, with a mass significantly higher than the massive W and Z bosons. In fact, it is the second most massive fundamental particle known (the top quark has a mass which is a bit higher).

- The independent ATLAS experiment also observes a Higgs-​​candidate state with a best-​​fit mass centered around 126.5 GeV with a local significance of 4.5 sigma, based on combined 2011 – 2012 data, in the photon-​​photon channel.

- ATLAS also observes a Higgs-​​candidate state with a mass around 125 GeV with a local significance of 3.4 sigma, based on 2011 – 2012 data, in the 4-​​lepton channel alone. Adding together all the channels overall, ATLAS observes a new Higgs-​​candidate state, with the maximum excess observed at about 126.5 GeV, with a significance of 5 sigma.

- Correcting for the look-​​elsewhere effect [2], the global significance of this observation in ATLAS is 4.1 – 4.3 sigma.

The independent ATLAS and CMS results are consistent with each other, seeing the new state with masses consistent with each other, within uncertainties.

This is awesome! We now have something that quacks like a SM Higgs boson candidate at 5 sigma. We haven’t been foiled by the Higgs boson travelling back in time to sabotage its own discovery, like a subatomic Terminator, and we haven’t been foiled by birds dropping bread into equipment above the surface. The journalists might have had their fun then — but now hopefully they can see that the real science and real discovery is so much more remarkable.

However, next, we look at the extent to which the observed state is compatible, within present uncertainties, with the Standard Model Higgs boson. We observe a significant excess, i.e. the discovery of a new particle, but is this observed excess due to the production of a particle which really is the Higgs boson as it is predicted by the Standard Model?

Maybe. Probably, in fact. But it remains barely possible that it is not — and if it is not, it is something different, and that is extremely interesting.

Figure 1: A preliminary plot recently published by the ATLAS collaboration shows the distinctive 5-​​sigma candidate Higgs signal at approximately 125 GeV, and no other signals of interest in the mass region explored, all the way up to 600 GeV.

(Much thanks to Fabiola Gianotti, Joe Incandela, and the rest of the ATLAS and CMS collaborations, for these images which I’ve pinched from their presentations!)

Collecting and analysing more data over the coming months wil be essential to start to understand the nature and properties of this new particle in detail. Although, based on present analyses, this particle pretty much looks like and walks like and quacks like a Standard Model Higgs boson, appearing at a sensible mass and decaying in exactly the ways that we expected, comparing the properties of this new particle to the properties of the Higgs boson predicted by the Standard Model to a great level of detail will be important.

By the way, if the Higgs mechanism was excluded as the electroweak symmetry breaking mechanism because the Higgs boson was excluded at all reasonable energies, or if several different Higgs bosons were empirically found, it would have made for very exciting, interesting physics.

However, I think the result we have had, empirical confirmation of a single SM Higgs boson which is so far consistent with the Higgs mechanism, is probably the best outcome in terms of relatively easy, successful, positive, good public engagement and public communication and appreciation of the science, which has all been extremely positive and successful with the LHC in general.

“We’re looking for the Higgs, we found it” is much easier to communicate to the public and get a positive response then “We’re looking for the Higgs, but it doesn’t actually seem to exist at all, isn’t that awesome?”. The latter is interesting physics (how the hell does electroweak symmetry breaking actually occur?) but it’s a harder public sell.

The Large Hadron Collider has, overall, been an outstandingly successful project in terms of popular communication of science, public interest in science, public acceptance of science, science presence in the media, and (usually) sensible reception of science and engagement of science in the media. As a result of the outstanding work of the community of scientists and engineers worldwide who have contributed to the LHC and its detector experiments, we have seen science in the public consciousness, science in popular culture and science positively portrayed in the media in a positive way that I have never seen before in my life, and I’ve never read about or heard about in any way since the Apollo program.

Really, the Apollo program is the only other thing in history that I can think of which has generated comparable public interest and media interest in science — and just like the Apollo program, over the next 10 years or 20 years we’re going to see an extremely good return on investment, a return of tens of billions of dollars into global economies, in all likelihood, simply as a result of increased interest in pure and applied physics and engineering across an entire generation or a couple of generations of young people. It involves a timescale of a decade or two, longer than the units of time that politicians can think in, but just like how Apollo returned 14 dollars to the US economy over the following couple of decades for every dollar invested in the program, I’m convinced that within my lifetime the LHC will deliver a very substantial stimulus to tomorrow’s economies.

Some people ask how hard it was for scientists to convince European politicians to spend the money on the LHC — but really, it cost a pretty negligible amount of money. Six billion or so dollars, divided up amongst 20 or 30 countries, divided up over 20 or 30 years, is really a negligible amount of money per nation per year.

The total cost of the Large Hadron Collider, the accelerator, all the detectors, the computing infrastructure, the staff and everything was, after all, only about 5 times what taxpayers in the state of Victoria have spent for Myki — doesn’t that sound like good value?

And the experimental results published by the LHC experimental collaborations represent such brilliant examples of real, high-​​quality science to the public — with error bars, confidence limits, systematic errors, standard deviations, and all those other things that really make it clear that this is real science, science where we’re really careful not to fool ourselves, as Richard Feynman put it, and not just crap fake science.

After all, when was the last time you saw some homeopath or creationist or anti-​​vaccine activist present their results and say, “well, we got these results, with a statistical confidence of 4.9 sigma, but then we corrected for the look-​​elsewhere effect and that reduced the global significance of our result to only 4.1 sigma”?

Today, I’m really happy to see how the journalists and the media come to the actual scientists when they’re looking for information on the latest exciting news in experimental high-​​energy physics. The anti-​​LHC crackpot activists are completely marginalised and ignored. They don’t get media attention, they don’t get listened to, and they don’t get airtime. Hopefully we can extend this success story to other areas of science and technology as well, and eventually all anti-​​vaccination crackpots and anti-​​biotechnology and anti-​​nuclear-​​energy hysterical activists might eventually be treated the same way by the media. After all, real science is certainly more genuinely exciting and exhilarating than pseudoscience!

In the context of the above results, sigma is a measure of statistical confidence — a standard deviation. For a normal distribution, we know that 5 sigma statistical confidence means that 99.9999% of the data is within the confidence interval — 99.9999% of the values are within 5 standard deviations of the mean. This is the established standard of statistical confidence that experimental particle physicists have basically agreed to use when they announce “We have discovered a new particle!”. Until 5-​​sigma statistical confidence has been established for a particular candidate particle with a particular mass, “official” conclusions and announcements like this are not made.

The Statistics of Searching

Suppose you have a pair of dice, and you suspect that maybe the dice have been loaded — just slightly — in order to bias their results subtly. How do you test the dice to see if they’re loaded or if they’re normal unbiased dice? If you only perform a few rolls of the dice, there is no way to tell with any level of statistical confidence. The only way that you can really tell is to perform a very large number of rolls and see if the results you get — the number of sixes, or whatever — are abnormally high compared to unbiased dice.

If you perform a moderate number of rolls, you might begin to suspect that the dice are slightly biased — but can you really prove that you’re seeing the effects of loaded dice and not just normal statistical variance? The more rolls you perform, the greater the statistical confidence you have to eventually show that the dice are biased — or maybe to show that they’re not really biased at all.

You really just need to decide somewhat arbitrarily how much statistical confidence is good enough to draw a solid conclusion, and then run a very large number of events until you’ve reached the desired level of statistical confidence.

Experimental particle physics — such as these empirical searches for the Higgs boson — is just like that. You’re looking for low-​​probability events against the “background” of the normal statistical behaviour of a stochastic system. Therefore, the collection and analysis of lots and lots of data is required to try to extract conclusions — conclusions with good statistical confidence — from the background statistical noise. This is not so different to data collection and analysis in other scientific fields which require the statistical analysis of stochastic systems to try and see subtle phenomena — epidemiology for example.

What essentially happens in searching for the Higgs in a collider experiment is that we see normal “background” statistics every time we roll the dice, except when we roll the dice at just the right energy (which is related to the Higgs mass), where nature suddenly makes the dice slightly loaded when they’re rolled, but only at just the right energy.

The Standard Model does not predict the mass of the Standard Model Higgs boson, but it does allow us to predict the cross-​​section for Higgs production if its mass is known. So, we can experiment across different energies (corresponding to different possible Higgs masses) and see how the cross-​​section for possible Higgs production compares to what the Standard Model predicts.

In order to detect this we need millions of dice rolls, spanning every possible energy across the wide range of possible Higgs mass. At every possible energy value, we need to have enough rolls of the dice to generate enough statistical confidence. We take the data from millions of events and we identify how much energy each roll of the dice had and whether we can exclude the possibility of the Higgs existing at that energy with good confidence, or whether we get a possible Higgs signal at that energy — and if we have what might be an interesting signal emerging from the statistics, we need to know how much statistical confidence we have in that result based on the set of data we have collected thus far.

For example, over the last couple of years, the different detector groups at the LHC and the Tevatron have gradually been working their way through the possible Higgs mass range and excluding the existence of a Higgs boson across almost all of the possible mass range. Including all the data up to now, ATLAS has excluded all possible Higgs energies up to 523 GeV, except 121.8 GeV < mH < 130.7 GeV, at a 99% confidence limit.

Theoretical motivation for the Higgs boson

The existence of the Higgs boson is fundamental to the modern interpretation of the physics of the elementary particles. The empirical confirmation of the existence of and the characterisation of the Higgs boson (the single Higgs boson predicted by the Standard Model, not the 5 or so possible different Higgs bosons predicted by some supersymmetric theories of physics beyond the Standard Model) represents a complete confirmation of one of the cornerstones of the modern Standard Model of particle physics, the unified theory of the electroweak interaction — the unified description of two of the four known fundamental interactions in nature, electromagnetism and the weak interaction, as two aspects of the same interaction — for which Salam, Weinberg and Glashow were awarded the Nobel Prize in physics in 1979.

The theory of electroweak interactions and quantum chromodynamics (the theory of the strong force) form the basis of the Standard Model, and together they describe pretty much Everything. Except gravity.

In fact, the empirical confirmation of the existence of the Higgs boson represents the empirical confirmation of the very last fundamental particle predicted to exist by the Standard Model which has not already been demonstrated to exist. The fact that the Higgs boson is the last prediction of the Standard Model that has not already been empirically verified is the reason why experimental searches for it have been of great priority and interest over the last couple of decades.

The electroweak interaction is the unification of the quantum field theory of electromagnetism (quantum electrodynamics) and the quantum field theory of the weak interaction. That unification, of two of the fundamental forces of nature into one combined theory, is one of the great triumphs of the last 50 years of physics.

The Standard Model is wonderful because it does not just “clean up” the complicated “particle zoo” of dozens of different types of mesons and hadrons that plagued particle physicists of decades past into a clean, elegant, simple set of 6 quarks, 6 leptons, their associated antiparticles, and 6 gauge bosons, but it also provides a neat unification between this set of fundamental particles and the quantum field theories (such as quantum electrodynamics and quantum chromodynamics) that describe their fundamental interactions.

Notwithstanding the successes of the theory of the electroweak interaction, one interesting and challenging question was present during the early development of the theory — from a basic understanding of the electroweak theory, we expect that the electroweak bosons should have similar energies (i.e. masses). However, the photon is massless whilst the W and Z bosons, confirmed to exist in experiments based at CERN’s then-​​newish Super Proton Synchrotron in 1983, were discovered to have quite substantial masses!

How this asymmetry in the electroweak boson masses exists was (is?) a central question in the Standard Model. The resolution to this question comes from spontaneous symmetry breaking in the electroweak interaction, and the Higgs mechanism is basically one model (pretty much the model) of a mechanism by which electroweak symmetry breaking occurs.

In the model known as the Higgs mechanism (which was actually proposed by a couple of other groups of physicists independently at about the same time as Peter Higgs; Robert Brout and Francois Englert, as well as Gerald Guralnik, C.R. Hagen and Tom Kibble), electroweak symmetry breaking gives rise to the masses of the Z0 and W+- bosons whilst keeping the other gauge boson associated with the electroweak interaction, namely the photon, massless.

It is notable that this mechanism was actually proposed quite a long time ago, in 1964. (See [1] for more information on this now-​​famous set of independent but almost simultaneous papers in Physical Review Letters.) But it was only in the 1980s that accelerator and detector technology had developed to the point where we had the ability to experimentally confirm the existence of the weak bosons, even though their existence was proposed by the theorists in the ‘60s, and only in the last couple of decades that accelerator technology, detector technology, superconductor engineering, and computing have progressed to the point where we’re finally capable of empirical detection and characterisation of what certainly appears to be the Standard Model Higgs boson.

Basically, the Higgs mechanism postulates the existence of a new field, the Higgs field, and the interaction with this field allows the W and Z gauge bosons to acquire their masses without violating the gauge invariance of the interaction. But if the Higgs field exists then there must exist electrically-​​neutral spin-​​0 particles which are the quanta of the Higgs field, in the same way that photons are the quanta of the electromagetic field. This particle is the famous Higgs boson.

As I’m sure you would expect, the masses of the W and Z bosons must be independent of their location and orientation in the universe — just as you’d expect for the masses of any particles. Hence, the Higgs fields must be scalars. In the electroweak theory, there are four Higgs fields, one corresponding to each of the photon, the Z boson, and the positive and negative W bosons. During the cooling of the system, three of the Higgs bosons are absorbed by the Z and W+- bosons, giving them their masses. Since the photon remains massless, though, the fourth of these Higgs bosons is ”left over” as a free Higgs boson, and this is ”the” Higgs boson which we search for experimentally.

It should be noted that the Higgs mechanism — the breaking of electroweak symmetry — only actually directly gives us the origin of mass for two particles, the massive W and Z vector bosons, not all the other particles — the fermions of the Standard Model — that have non-​​zero masses. The quarks and the leptons can also acquire their non-​​zero masses from some sort of an interaction with the Higgs field, although this is different from and a little bit more complicated than the way that electroweak symmetry breaking gives us the origin of the masses of the W and Z bosons.

The origin of the non-​​zero masses of the neutrinos is also different — the fact that the neutrino masses are so disproportionately small compared to the masses of even the lightest other fundamental particles, such as the electron, means that explaining the potential origin of mass for the neutrinos is difficult indeed.

Higgs boson production mechanisms in proton-​​proton collisions

Figure 3: There are several different mechanisms by which Higgs bosons can be created in the LHC, when protons (and their constituent quarks and gluons) are collided together. Some of the important mechanisms are illustrated in the set of Feynman diagrams above.

Gluon fusion is a dominant Higgs production mechanism at the LHC, since there are plenty of very energetic gluons flying around in a ~10 TeV proton-​​proton collision. This is basically a process where two gluons “fuse” together to form a Higgs boson, and this is represented in the Feynman diagram (a) above.

Note that the Higgs has no color charge, and it cannot directly couple to the gluons. (The gluons are the two curly lines on the left of the Feynman diagram.) Therefore, a loop of virtual quarks (the three straight lines on the Feynman diagram) couple the gluons to the final Higgs boson. The top quark is a good representative choice in this example since it has a relatively strong coupling to the Higgs. (Like the other heavy quarks, such as the bottom quark, this relatively strong Higgs coupling is indeed why they’re so massive!)

Diagram (b) illustrates another Higgs-​​formation process of interest in LHC Higgs-​​search studies, known as VBF or vector boson fusion. Here, two weak vector bosons (wavy lines on the Feynman diagram), either neutral Z bosons or a W+/​W- pair, produced from a pair of interacting energetic quarks, undergo “fusion” to form a Higgs.

Diagram (c ) illustrates a W or Z boson emitting a Higgs boson and losing some of its energy in a process sort of similar to an electron coupling to a photon and emitting some of its energy as bremstrahlung radiation, whilst (d) illustrates two gluons generating top-​​antitop quark pairs, with a pair of the resulting top and antitop quarks fusing together into a Higgs.

Once a Higgs boson is created, though, it can decay in different ways — and the understanding and characterisation of these different decay channels is a crucial part of how physicists use detectors such as ATLAS and CMS to indirectly reconstruct the signature of the fleeting, unstable, Higgs boson.

Decay modes of the Standard Model Higgs

The Standard Model Higgs boson can be formed in a couple of different ways in proton-​​proton collisions in the Large Hadron Collider, and it can decay in numerous different ways. Understanding these different decay routes, or channels, is important in understanding the experimental searches for the decay signatures of Higgs bosons.

For example, the decay of the SM Higgs into four leptons via a pair of virtual W or Z bosons is one of the most important decay modes in Higgs-​​search experiments at the LHC.

Such a decay looks something like this:

H0 –> ZZ(*) –> l+ + l- + l+ + l-

Where l denotes some sort of general lepton, eg. two e-/​e+ pairs, two muon-​​antimuon pairs, or an e-/​e+ pair and a muon-​​antimuon pair.

Other Higgs decay channels of importance to LHC experiments include Higgs decay into pairs of heavy quarks, such as a b quark-​​antiquark pair. Some other decay channels, in particular the photon-​​photon or gamma-​​gamma channel, the decay of a Higgs boson into two photons, are particularly useful because they have very distinctive, “clean” signals in the detectors which are easier to reconstruct from the detector event.

When the two resulting photons are both captured in the detector, the result is a very “clean”, distinctive detector event, without too many daughter particles to reconstruct and no “missing” energy, momentum and information which has been carried away by neutrinos which escape without interacting with the detector. (The same is also true for the WW or ZZ –> 4l decay channels, too, for example).

The missing energy and momentum of the neutrinos can be reconstructed by “accounting” for it in decays where neutrinos are formed, since energy and momentum are conserved, but the loss of neutrinos from the detector is a phenomenon which is a little bit of a complication to precise event reconstruction in decay events where neutrinos are formed.

Figure 2: The various different Higgs decay channels studied in the ATLAS and CMS experiments.

The above chart shows the various different decay channels for the Standard Model Higgs that are studied in the ATLAS and CMS Higgs searches, such as the decay of the Higgs into a pair of tau leptons, or into a pair of photons, or several other things. The vertical axis is the product of the cross section (probability, sort of) for the formation of a Higgs boson at that energy and the branching ratio for the Higgs to decay in a particular way, or in other words it’s basically an expression which represents the overall rate at which we expect to observe the different particular kinds of Higgs decays in the detectors.

The photon-​​photon (gamma-​​gamma) final state is rare, but it’s interesting for another reason in addition to its relatively “clean” detector signature — since the Higgs doesn’t have any electric charge and photons are massless, the direct coupling of the Higgs to the photon is not something you might expect to occur. As with the formation of the Higgs from colliding quarks and gluons, this coupling is mediated by a loop of virtual particles, in particular the weak bosons and heavy quarks.

The W-/​W+ bosons and the top and bottom quarks are good representative examples of the virtual particles in these loops, since their high masses show that they have strong couplings to the Higgs and their electric charges mean that they also couple to the photon.

With the entire Standard Model on a good empirically-​​confirmed foundation, then, with all its predicted particles detected and characterised experimentally in all their right places, we then move into the exhilirating era of Physics Beyond the Standard Model. Where this will take us over the coming decades, well, we don’t completely know. Experimental investigations of the Higgs in greater detail, and related phenomena, will play a central role in experimental particle physics for many years to come.

Is supersymmetry dead? What happens if we actually detect a supersymmetric particle candidate at the LHC? Then supersymmetry will return to being one of the hottest topics in particle physics, with some promise for not only pointing us towards more fundamental unifications in particle physics, but also maybe explaining the nature of dark matter along the way, since some supersymmetric models predict the existence of relatively massive (but not that massive as far as supersymmetric particles are concerned), stable, weakly interacting particles that look like good dark matter candidates.

And what about extra spatial dimensions? Can their existence be demonstrated, for example by the production of a microscopic black hole at the terascale? Searches for black hole production at the LHC have so far, unfortunately, been unsuccessful. But we have really just begun the era of good science results from the LHC, and there is far, far more to come in the future, even in ways I can’t try to predict right now.

Well, now we come to the end of this post — but please feel free to leave your discussion, comments, peer-​​review, corrections and questions below! Thanks!

[1]: http://​en​.wikipedia​.org/​w​i​k​i​/​1​9​6​4​_​P​R​L​_​s​y​m​m​e​t​r​y​_​b​r​e​a​k​i​n​g​_​p​a​pers
[2]: http://​en​.wikipedia​.org/​w​i​k​i​/​L​o​o​k​-​e​l​s​e​w​h​e​r​e​_​e​f​fect