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### Understanding the Higgs search

It’s been over a month since CERN hosted a seminar on the updated searches for the Higgs boson. Since then ATLAS and CMS and submitted papers showing what they found, and recently I got news that the ATLAS paper was accepted by Physics Letters B, a prestigious journal of good repute. For those keeping score, that means it took over five weeks to go from the announcement to publication, and believe it not, that’s actually quite fast.

Crowds watch the seminar from Melbourne, Australia (CERN)

However, all this was last month’s news. Within a week of finding this new particle physicists started on the precision spin measurement, to see if it really is the Higgs boson or not. Let’s take a more detailed look at the papers. You can see both papers as they were submitted on the arXiv here: ATLAS / CMS.

### The Higgs backstory

In order to fully appreciate the impact of these papers we need to know a little history, and a little bit about the Higgs boson itself. We also need to know some of the fundamentals of scientific thinking and methodology. The “Higgs” mechanism was postulated almost 50 years ago by several different theorists: Brout, Englert, Guralnik, Hagen, Higgs, and Kibble. For some reason Peter Higgs seems to have his name attached to this boson, maybe because his name sounds “friendliest” when you put it next to the word “boson”. The “Brout boson” sounds harsh, and saying “Guralnik boson” a dozen times in a presentation is just awkward. Personally I prefer the “Kibble boson”, because as anyone who owns a dog will know, kibble gets everywhere when you spill it. You can tidy it up all you like and you’ll still be finding bits of kibble months later. You may not find bits often, but they’re everywhere, much like the Higgs field itself. Anyway, this is all an aside, let’s get back to physics.

It helps to know some of history behind quantum mechanics. The field of quantum mechanics started around the beginning of the 20th century, but it wasn’t until 1927 that the various ideas started to get resolved into a consistent picture of the universe. Some of the greatest physicists from around the world met at the 1927 Solvay Conference to discuss the different ideas and it turned out that the two main approaches to quantum mechanics, although they looked different, were actually the same. It was just a matter of making everything fit into a consistent mathematical framework. At that time the understanding of nature was that fields had to be invariant with respect to gauge transformation and Lorentz transformations.

The Solvay Conference 1927, where some of the greatest physicists of the 20th century met and formulated the foundations of modern quantum mechanics. (Wikipedia)

A gauge transformation is the result of the kind of mathematics we need to represent particle fields, and these fields must not introduce new physics when they get transformed. To take an analogy, imagine you have the blueprints for a building and you want to make some measurements of various distances and angles. If someone makes a copy of the blueprints, but changes the direction of North (so that the building faces another direction) then this must not change any of the distances or angles. In that sense the distances and angles in blueprint are rotation-invariant. They are rotation-invariant because we need to use Euclidean space to represent the building, and a consequence of using Euclidean space is that any distances and angles described in the space must be invariant with respect to rotation. In quantum mechanics we use complex numbers to represent the field, and a gauge transformation is just a rotation of a complex number.

The Lorentz transformation is a bit simpler to understand, because it’s special relativity, which says that if you have a series of events, observers moving at different speeds and in different directions will agree on the causality of those events. The rest of special relativity is just a matter of details, and those details are a lot of fun to look at.

By the time all of quantum mechanics was coming together there were excellent theories that took these symmetries into account. Things seemed to be falling into place, and running the arguments backwards lead to some very powerful predictions. Instead of observing a force and then requiring it to be gauge and Lorentz invariant, physicists found they could start with a gauge and Lorentz invariant model and use that to predict what forces can exist. Using plain old Euclidean space and making it Lorentz invariant gives us Minkowski space, which is the perfect for making sure that our theories work well with special relativity. (To get general relativity we start with a space which is not Euclidean.) Then we can write the most general description of a field we can think of in this space as long as it is gauge invariant and that’s a valid physical field. The only problem was that there were some interactions that seemed to involve a massive photon-like boson. Looking at the interactions gave us a good idea of the mass of this particle, the $$W$$ boson. In the next few decades new particles were discovered and the Standard Model was proposed to describe all these phenomena. There are three forces in the Standard Model, the electromagnetic force, the weak force, and the strong force, and each one has its own field.

### Inserting the Higgs field

The Higgs field is important because it unifies two of the three fundamental fields in particle physics, electromagnetism and the weak fields. It does this by mixing all the fields up (and in doing so, it mixes the bosons up.) Flip Tanedo has tried to explain the process from a theorist’s point of view to me privately on more than one occasion, but I must admit I just ended up a little confused by some of the finer points. The system starts with three fields which are pretty much all the same as each other, the $$W_1$$, $$W_2$$, and the $$W_3$$. These fields don’t produce any particles themselves because they don’t obey the relevant physical laws (it’s a bit more subtle in reality, but that’s a blog post in itself.) If they did produce their own fields then they would generate massless particles known as Goldstone bosons, and we haven’t seen these, so we know there is something else going on. Instead of making massless bosons they mix amongst themselves to create new fields, giving us massive bosons, and the Goldstone bosons get converted into extra degrees of freedom. Along comes the Higgs field and suddenly these fields separate and mix, giving us four new fields.

The Higgs field, about to break the symmetry and give mass (Flip Tanedo)

The $$W_1$$ and $$W_2$$ mix to give us the $$W^+$$ and $$W^-$$ bosons, and then the $$W_3$$ field meets the $$B$$ field to give us the $$Z$$ boson and the photon. What makes this interesting is that the photon behaves well on its own. It has no mass and this means that its field is automatically gauge invariant. Nature could have decided to create just the electromagnetic field and everything would work out fine. Instead we have the photon and three massive bosons, and the fields of these massive bosons cannot be gauge invariant by themselves, they need something else to make it all balance out. By now you’ve probably guessed what this mystery object is, it’s the Higgs field and with it, the Higgs boson! This field fixes it all up so that the fields mix, we get massive bosons and all the relevant laws (gauge invariance and Lorentz invariance) are obeyed.

Before we go any further it’s worth pointing a few things out. The mass of the $$W$$ boson is so large in comparison to other particles that it slows down the interactions of a lot of particles, and this is one of the reasons that the sun burns so “slowly”. If the $$W$$ boson was massless then it could be produced in huge numbers and the rate of fusion in the sun would be much faster. The reason we have had a sun for billions of years, allowing the evolution of life on Earth (and maybe elsewhere) is because the Higgs field gives such a large mass to the $$W$$ boson. Just let that thought sink in for a few seconds and you’ll see the cosmic significance of the Higgs field. Before we get ahead ourselves we should note that the Higgs field leads to unification of the electromagnetic and weak forces, but it says nothing about the strong force. Somehow the Higgs field has missed out one of the three fundamental forces of the Standard Model. We may one day unite the three fields, but don’t expect it to happen any time soon.

### “Observation” vs “discovery”, “Higgs” vs “Higgs-like”

There’s one more thing that needs to be discussed before looking at the papers and that’s a rigorous discussion of what we mean by “discovery” and if we can claim discover of the Standard Model Higgs boson yet. “Discovery” has come to mean a five sigma observation of a new resonance, or in other words that probability that the Standard Model background in the absence of a new particle would bunch up like this is less than one part in several million. If we see five sigma we can claim a discovery, but we still need to be a little careful. Suppose we had a million mass points, what is the probability that there is one five sigma fluctuation in there? It’s about $$20\%$$, so looking at just the local probability is not enough, we need to look at the probability that takes all the data points into account. Otherwise we can increase the chance of seeing a fluctuation just by changing the way we look at the data. Both ATLAS and CMS have been conscious of this effect, known as the “Look Elsewhere Effect”, so every time they provide results they also provide the global significance, and that is what we should be looking at when we talk about the discovery.

Regular readers might remember Flip’s comic about me getting worked up over the use of the word “discovery” a few weeks back. I got worked up because the word “discovery” had been misused. Whether an observation is $$4.9$$ or $$5.1$$ sigma doesn’t matter that much really, and I think everyone agrees about that. What bothered me was that some people decided to change what was meant by a discovery after seeing the data, and once you do that you stop being a scientist. We can set whatever standards we like, but we must stick to them. Burton, on the other hand, was annoyed by a choice of font. Luckily our results are font-invariant, and someone said “If you see five sigma you can present in whatever durn font you like.”

Getting angry over the change of goalposts. Someone has to say these things.

In addition to knowing what we mean by “discovery” we also need to take hypothesis testing into account. Anyone who claims that we have discovered the Higgs boson is as best misinformed, and at worst willingly untruthful. We have discovered a new particle, there’s no doubt about that, but now we need to eliminate things are not the Higgs until we’re confident that the only thing left is the Higgs boson. We have seen this new particle decay to two photons, and this tells us that it can only only have spin 0 or spin 2. That’s eliminated spin 1, spin 3, spin 4… etc for us, all with a single measurement. What we are doing now trying to exclude both the spin 0 and spin 2 possibilities. Only one of these will be excluded, and then will know for sure what the spin is. And then we know it’s the Standard Model Higgs boson, right? Not quite! Even if we know it’s a spin 0 particle we would still need to measure its branching fractions to confirm that it is what we have been looking for all along. Bear this in mind when thinking about the paper- all we have seen so far is a new particle. Just because we’re searching for the Higgs and we’ve found something new it does not mean that it’s a the Higgs boson.

### The papers

Finally we get to the papers. From the titles we can see that both ATLAS and CMS have been suitably agnostic about the particle’s nature. Neither claim it’s the Higgs boson and neither even claim anything more than an “observation”. The abstracts tell us a few useful bits of information (note that the masses quoted agree to within one sigma, which is reassuring) but we have to tease out the most interesting parts by looking at the details. Before the main text begins each experiment dedicates their paper to the memories of those who have passed away before the papers were published. This is no short list of people, which is not surprising given that people have been working on these experiments for more than 20 years. Not only is this a moving start to the papers, it also underlines the impact of the work.

Both papers were dedicated to the memories of colleagues who did not see the observation. (CMS)

Both papers waste no time getting into the heart of the matter, which is nature of the Standard Model and how it’s been tested for several decades. The only undiscovered particle predicted by the Standard Model is the Higgs boson, we’ve seen everything else we expected to see. Apart from a handful of gauge couplings, just about every prediction of the Standard Model has been vindicated. In spite of that, the search for the Higgs boson has taken an unusually long time. Searches took place at LEP and Tevatron long before the LHC collided beams, and the good news is that the LEP limit excluded the region that is very difficult for the LHC to rule out (less than $$114GeV$$). CDF and D0 both saw an excess in the favored region, but the significance was quite low, and personally I’m skeptical since we’ve already seen that CDF’s dijet mass scale might have some problems associated with it. Even so we shouldn’t spend too long trying to interpret (or misinterpret) results, we should take them at face value, at least at first. Next the experiments tell us which final states they look for, and this is where things will get interesting later on. Before describing the detectors, each experiment pauses to remind us that the conditions of 2012 are more difficult than those of 2011. The average number of interactions per beam crossing increased by a factor of two, making all analyses more difficult to work with (but ultimately all our searches a little more sensitive.)

At this point both papers summarize their detectors, but CMS goes out of their way to show off how the design of their detector was optimized for general Higgs searches. Having a detector which can reconstruct high momentum leptons, low momentum photons and taus, and also tag b-jets is not as easy task. Both experiments do well to be able to search for the Higgs bosons in the channels they look at. Even if we limit ourselves to where ATLAS looked the detectors would still have trigger on leptons and photons, and be able to reconstruct not only those particles, but also the missing transverse energy. That’s no easy task at a hadron collider with many interactions per beam crossing.

The two experiments have different overall strategies to the Higgs searches. ATLAS focused their attention on just two final states in 2012: $$\gamma\gamma$$, and $$ZZ^*$$, whereas CMS consider five final sates: $$\gamma\gamma$$, $$ZZ^*$$, $$WW^*$$, $$\tau\tau$$, and $$b\bar{b}$$. ATLAS focus mostly on the most sensitive modes, the so-called “golden channel”, $$ZZ^*$$, and the fine mass resolution channel, $$\gamma\gamma$$. With a concerted effort, a paper that shows only these modes can be competitive with a paper that shows many more, and labor is limited on both experiments. CMS spread their effort across several channels, covering all the final states with expected sensitivities comparable to the Standard Model.

### $$H\to ZZ^*$$

The golden channel analysis has been presented many times before because it is sensitive across a very wide mass range. In fact it spans the range $$110-600GeV$$, which is the entire width of the Higgs search program at ATLAS and CMS. (Constraints from other areas of physics tell us to look as high as $$1000GeV$$, but at high masses the Higgs boson would have a very large width, making it extremely hard to observe. Indirect results favor the low mass region, which is less than around $$150GeV$$.) Given the experience physicists have had with this channel it’s no surprise that the backgrounds are very well understood at this point. The dominant “irreducible” background comes from Standard Model production of $$Z/\gamma*$$ bosons, where there is one real $$Z$$ boson, and one “off-shell”, or virtual boson. This is called irreducible because the source of background is the same final state as the signal, so we can’t remove further background without also removing some signal. This off-shell boson can be an off-shell $$Z$$ boson or an off-shell photon, it doesn’t really matter which since these are the same for the background. In the lower mass range there are also backgrounds from $$t\bar{t}$$, but fortunately these are well understood with good control regions in the data. Using all this knowledge, the selection criteria for $$8TeV$$ were revisited to increase sensitivity as much as possible.

The invariant mass spectrum for ATLAS's H→ZZ* search (ATLAS)

Since this mode has a real $$Z$$ boson, we can look for two high momentum leptons in the final state, which mames things especially easy. The backgrounds are small, and the events are easy to identify, so the trigger is especially simple. Events are stored to disk if there is at least one very high momentum lepton, or two medium momentum leptons which means that we don’t have to throw any events away. Some triggers fire so rapidly that we can only store some of the events from them, and we call this prescaling. When we keep $$1$$ in $$n$$ events then we have a prescale of $$n$$. For a Higgs search we want to have a high efficiency as possible so we usually require a prescale of $$1$$. Things are not quite so nice for the $$\gamma\gamma$$ mode, as we’ll see later.

The invariant mass spectrum for CMS's H→ZZ* search (CMS)

After applying a plethora of selections on the leptons and reconstructing the $$Z$$ and Higgs boson candidates the efficiency for the final states vary from $$15\%-37\%$$, which is actually quite high. No detector can cover the whole of the solid angle, and efficiencies vary with the detector geometry. The efficiency needs to be very high because the fraction of Higgs bosons that would decay to these final states is so small. At a mass of $$125GeV$$ the branching fraction to the $$ZZ^*$$ state is about $$2\%$$, and then branching fraction of $$Z$$ to two leptons is about $$6\%$$. Putting that all together means that only $$1$$ in $$10,000$$ Higgs bosons would decay to this final state. At a mass of $$125GeV$$ the LHC would produce about $$15,000$$ Higgs bosons per $$fb^{-1}$$. So for $$10fb^{-1}$$ we could expect to have about $$11$$ Higgs bosons decaying to this final state, and we could expect to see about $$3$$ of those events reconstructed. This is a clean mode, but it’s an extremely challenging one.

The selection criteria are applied, the background is estimated, and the results are shown. As you can see there is a small but clear excess over background in the region around $$125GeV$$ and this is evidence supporting the Higgs boson hypothesis!

CMS see slightly fewer events than expected, but still see a clear excess (CMS)

### $$H\to\gamma\gamma$$

Out of the $$H\to ZZ^*$$ and $$H\to\gamma\gamma$$ modes the $$\gamma\gamma$$ final state is the more difficult one to reconstruct. The triggers are inherently “noisy” because they must fire on something that looks like a high energy photon, and there are many sources of background for this. As well as the Standard Model real photons (where the rate of photon production is not small) there are jets faking photons, and electrons faking photons. This makes the mode dominated by backgrounds. In principle the mode should be easy: just reconstruct Higgs candidates from pairs of photons and wait. The peak will reveal itself in time. However ATLAS and CMS are in the middle of a neck and neck race to find the Higgs boson, so both collaborations exploit any advantage they can, and suddenly these analyses become some of the most difficult to understand.

A typical H→γγ candidate event with a striking signature (CMS)

To get a handle on the background ATLAS and CMS each choose to split the mode into several categories, depending on the properties of the photons or the final state, and each one with its own sensitivity. This allows the backgrounds to be controlled with different strategies in each category, leading to increased overall sensitivity. Each category has its own mass resolution and signal-to-background ratio, each is mutually independent of the others, and each has its own dedicated studies. For ATLAS the categories are defined by the presence of two jets, whether or not the photon converts (produces an $$e^-e^+$$ pair) in the detector, the pseudorapidity of the photons, and a kinematic quantity called $$p_{T_T}$$, with similar categories for CMS.

When modelling the background both experiments wisely chose to use the data. The background for the $$gamma\gamma$$ final state is notoriously hard to predict accurately, because there are so many contributions from different backgrounds, from real and fake photon candidates, and many kinematic or detector effects to take into account. The choice of background model even varies on a category by category basis, and choices of model vary from simple polynomial fits to the data, to exponential and skewed Gaussian backgrounds. What makes these background models particularly troublesome is that the background has to be estimated using the signal region, so small deviations that are caused by signal events could be interpreted by the fitting algorithm as a weird background shape. The fitting mechanism must be robust enough to fit the background shapes without being fooled into thinking that a real excess of events is just a slightly different shape.

ATLAS's H→γγ search, where events are shown weighted (top) and unweighted (bottom) (ATLAS)

To try to squeeze even more sensitivity out of the data CMS use a boosted decision tree to aid signal separation. A boosted decision tree is a sophisticated statistical analysis method that uses signal and background samples to decide what looks like signal, and then uses several variables to return just one output variable. A selection can be made on the output variable that removes much of the background while keeping a lot of the signal. Using boosted decision trees (or any multivariate analysis technique) requires many cross checks to make sure the method is not biased or “overtrained”.

CMS's H→γγ search, where events are shown weighted (main plot) and unweighted (inset) (CMS)

After analyzing all the data the spectra show a small bump. The results can seem a little disappointing at first, after all the peak is barely discernable, and so much work has gone into the analyses. Both experiments show the spectra after weighting the events to take the uncertainties into account and this makes the plots a little more convincing. Even so, what matters is the statistical significance of these results, and this cannot be judged by eye. The final results show a clear preference for a boson with a mass of $$125GeV$$, consistent with the Higgs boson. CMS see a hint at around $$135GeV$$, but this is probably just a fluctuation, given that ATLAS do not see something similar.

ATLAS local significance for H→γγ (ATLAS)

(If you’ve been reading the blog for a while you may remember a leaked document from ATLAS that hinted at a peak around $$115GeV$$ in this invariant mass spectrum. That document used biased and non peer-reviewed techniques, but the fact remains that even without these biases there appear to be a small excess in the ATLAS data around $$115GeV$$. The significance of this bump has decreased as we have gathered more data, so it was probably just a fluctuation. However, you can still see a slight bump at $$115GeV$$ in the significance plot. Looking further up the spectrum, both ATLAS and CMS see very faint hints of something at $$140GeV$$ which appears in both the $$ZZ^*$$ and $$\gamma\gamma$$ final states. This region has already been excluded for a Standard Model Higgs, but there may be something else lurking out there. The evidence is feeble at the moment, but that’s what we’d expect for a particle with a low production cross section.)

### $$H\to WW^*$$

One of the most interesting modes for a wide range of the mass spectrum is the $$WW(*)$$ final state. In fact, this is the first mode to be sensitive to the Standard Model Higgs boson searches, and exclusions were seen at ATLAS, CMS, and the Tevatron experiments at around $$160GeV$$ (the mass of two on-shell $$W$$ bosons) before any other mass region. The problem with this mode is that it has two neutrinos in the final state. It would be nice to have an inclusive sample of $$W$$ bosons, including the hadronic final states, but the problems here are the lack of a good choice of trigger, and the irreducible and very large background. That mean that we must select events with two leptons and two neutrinos in them. As the favored region excludes more and more of the high mass region this mode gets more challenging, because at first we lose the mass constraint on the second $$W$$ boson (as it must decay off-shell), and secondly because we must be sensitive in the low missing transverse energy region, which starts to approach our resolution for this variable.

While we approach our resolution from above, the limit on the resolution increases from below, because the number of interactions per beam crossing increases, increasing the overall noise in the detector. To make progress in this mode takes a lot of hard work for fairly little gain. Both papers mention explicitly how difficult the search is in a high pileup scenario, with CMS stating

“The analysis of the $$7TeV$$ data is described in [referenced paper] and remains unchanged, while the $$8TeV$$ analysis was modified to cope with more difficult conditions induced by the higher pileup of the 2012 data taking.”

and ATLAS saying

“The analysis of the $$8TeV$$ data presented here is focused on the mass range $$110<m_H<200GeV$$ It follows the procedure used for the $$7TeV$$ data described in [referenced paper], except that more stringent criteria are applied to reduce the $$W$$+jets background and some selections have been modified to mitigate the impact of the high instantaneous luminosity at the LHC in 2012.”

It’s not all bad news though, because the final branching fraction to this state is much higher than that of the $$ZZ^*$$ final state. The branching fraction for the Standard Model Higgs boson to $$WW^*$$ is about $$10$$ times higher than that for $$ZZ^*$$, and the branching fraction of the $$W$$ boson to leptons is also about $$3$$ times higher than the $$Z$$ boson to leptons, which gives another order of magnitude advantage. Unfortunately all these events must be smeared out across a large spectrum. There is one more trick we have up our sleeves though, and it comes from the spin of the parent. Since the Standard Model Higgs boson has zero spin the $$W$$ bosons tend to align their spins in opposite directions to make it all balance out. This then favors one decay direction over another for the leptons. The $$W^+$$ boson decays with a neutrino in the final state, and because of special relativity the neutrino must align its spin against its direction of motion. The $$W-$$ boson decays with an anti-neutrino, which takes its spin with its direction of motion. This forces the two leptons to travel in the same direction with respect to the decay axis of the Higgs boson. The high momenta of the leptons smears things out a bit, but generally we should expect to see one high momentum lepton, and a second lower momentum lepton n roughly the same region of the detector.

The transverse mass for ATLAS's H→WW* search (ATLAS)

ATLAS did not actually present results for the $$WW^*$$ final state on July 4th, but they did show it in the subsequent paper. CMS showed the $$WW^*$$ final state on July 4th, although it did somewhat reduce their overall significance. Both ATLAS and CMS spend some of the papers discussing the background estimates for the $$WW^*$$ mode, but ATLAS seem to go to more significant lengths to describe the cross checks they used in data. In fact this may help to explain why ATLAS did not quite have the result ready for July 4th, whereas CMS did. There’s a trade off between getting the results out quickly and spending some extra time to understand the background. This might have paid off for ATLAS, since they seem to be more sensitive in this mode than CMS.

The invariant mass for CMS's H→WW* search (CMS)

After looking at the data we can see that both ATLAS and CMS are right at the limits of their sensitivity in this mode. They are not limited by statistics, they are limited by uncertainties, and the mass point $$125GeV$$ sits uncomfortably close some very large uncertainties. The fact that this mode is sensitive at all is a tribute to the hard work of dozens of physicists who went the extra mile to make it work.

CMS's observed and expected limits for H→WW*, showing the dramatic degradation in sensitivity as the mass decreases (CMS)

### $$H\to b\bar{b}$$

At a mass of $$125GeV$$ by far the largest branching fraction of the Standard Model Higgs boson is to $$b\bar{b}$$. CDF and D0 have both seen a broad excess in this channel (although personally I have some doubts about the energy scale of jets at CDF, given the dijet anomaly they see that D0 does not see) hinting at a Higgs boson of $$120-135GeV$$. The problem with this mode is that the background is many orders of magnitude larger than the signal, so some special tricks must be used to remove the background. What is done at all four experiments is to search for a Higgs boson that is produced in associated with a $$W$$ or $$Z$$ boson, and this greatly reduces the background. ATLAS did not present an updated search in the $$b\bar{b}$$ channel, and taking a look at the CMS limits we can probably see why, the contribution is not as significant as in other modes. The way CMS proceed with the analysis is to use several boosted decision trees (one for each mass point) and to select candidates based on the output of the boosted decision tree. The result is less than $$1$$ sigma of significance, about half of what is expected, but if this new boson is the Higgs boson then this significance will increase as we gather more data.

A powerful H→bb search requires a boosted decision tree, making the output somewhat harder to interpret (CMS)

It’s interesting to note that the $$b\bar{b}$$ final state is sensitive to both a spin 0 and a spin 2 boson (as I explained in a previous post) and it may have different signal strength parameters for different spin states. The signal strength parameter tells us how many events we see compared to how many events we do see, and it is denoted with the symbol $$\mu$$. A there is no signal then $$\mu=0$$, if the signal is exactly as large as we expect then $$\mu=1$$, and any other value indicates new physics. It’s possible to have a negative value for $$\mu$$ and this would indicate quantum mechanical interference of two or more states that cancel out. Such an interference term is visible in the invariant mass of two leptons, as the virtual photon and virtual $$Z$$ boson wavefunctions interfere with each other.

### $$H\to\tau\tau$$

Finally, the $$\tau\tau$$ mode is perhaps the most enlightening and the most exciting right now. CMS showed updated results, but ATLAS didn’t. CMS’s results were expected to approach the Standard Model sensitivity, but for some reason their results didn’t reach that far, and that is crucially important. CMS split their final states by the decay mode of the $$\tau$$, where the final states include $$e\mu 4\nu$$, $$\mu\mu 4\nu$$, $$\tau_h\mu 3\mu$$, and $$\tau_h e3\nu$$, where $$\tau_h$$ is a hadronically decaying $$\tau$$ candidate. This mode has at least three neutrinos in the final state, so like the $$WW^*$$ mode the events get smeared across a mass spectrum. There are irreducible backgrounds from $$Z$$ bosons decaying to $$\tau\tau$$ and from Drell-Yan $$\tau\tau$$ production, so the analysis must search for an excess of events over these backgrounds. In addition to the irreducible backgrounds there are penalties in efficiency associated with the reconstruction of $$\tau$$ leptons, which make this a challenging mode to work this. There are dedicated algorithms for reconstructing hadronically decaying $$\tau$$ jets, and these have to balance out the signal efficiency for real $$tau$$ leptons and background rejection.

CMS's H→τtau; search, showing no signal (CMS)

After looking at the data CMS expect to see an excess of $$1.4$$ sigma, but they actually see $$0$$ sigma, indicating that there may be no Standard Model Higgs boson after all. Before we jump to conclusions it’s important to note a few things. First of all statistical fluctuations happen, and they can go down just as easily as they can go up, so this could just be a fluke. It’s a $$1.5$$ sigma difference, so the probability of this being due a fluctuation if the Standard Model Higgs boson is about $$8\%$$. On its own that could be quite low, but we have $$8$$ channels to study, so the chance of this happening in any one of the channels is roughly $$50\%$$, so it’s looking more likely that this is just a fluctuation. ATLAS also have a $$\tau\tau$$ analysis, so we should expect to see some results from them in the coming weeks or months. If they also don’t see a signal then it’s time to start worrying.

CMS's limit of H→ττ actually shows a deficit at 125GeV. A warning sign for possible trouble for the Higgs search! (CMS)

### Combining results

Both experiments combine their results and this is perhaps the most complicated part of the whole process. There are searches with correlated and uncorrelated uncertainties, there are two datasets at different energies to consider, and there are different signal-to-background ratios to work with. ATLAS and CMS combine their 2011 and 2012 searches, so they both show all five main modes (although only CMS show the $$b\bar{b}$$ and $$\tau\tau$$ modes in 2012.)

When combining the results we can check to see if the signal strength is “on target” or not, and there is some minor disagreement between the modes. For the $$ZZ^*$$ and $$WW^*$$ modes, the signal strengths are about right, but for the $$\gamma\gamma$$ mode it’s a little high for both experiments, so there is tension between these modes. Since these are the most sensitive modes, and we have more data on the way then this tension should either resolve itself, or get worse before the end of data taking. The $$b\bar{b}$$ and $$\tau\tau$$ modes are lower than expected for both experiments (although for ATLAS the error bars are so large it doesn’t really matter), suggesting that this new particle may a non-Standard Model Higgs boson, or it could be something else altogether.

Evidence of tension between the γγ and fermionic final states (CMS)

While the signal strengths seem to disagree a little, the masses all seem to agree, both within experiments and between them. The mass of $$125GeV$$ is consistent with other predictions (eg the Electroweak Fit) and it sheds light on what to look for beyond the Standard Model. Many theories favor a lower mass Higgs as part of a multiplet of other Higgs bosons, so we may see some other bosons. In particular, the search for the charged Higgs boson at ATLAS has started to exclude regions on the $$\tan\beta$$ vs $$m_{H^+}$$ plane, and the search might cover the whole plane in the low mass region by the end of 2012 data taking. Although a mass of $$125GeV$$ is consistent with the Electroweak Fit, it is a bit higher than the most favored region (around $$90GeV$$) so there’s certainly space for new physics, given the observed exclusions.

The masses seem to agree, although the poor resolution of the WW* mode is evident when compared to the ZZ* and γγ modes (ATLAS)

To summarize the results, ATLAS sees a $$5.9$$ sigma local excess, which is $$5.1$$ sigma global excess, and technically this is a discovery. CMS sees a $$5.0$$ sigma local excess, which is $$4.6$$ sigma global excess, falling a little short of a discovery. The differences in results are probably due to good luck on the part of ATLAS and bad luck on the part of CMS, but we’ll need to wait for more data to see if this is the case. The results should “even out” if the differences are just due to fluctuations up for ATLAS and down for CMS.

ATLAS proudly show their disovery (ATLAS)

If you’ve read this far then you’ve probably picked up on the main message, we haven’t discovered the Standard Model Higgs boson yet! We still have a long road ahead of us and already we have moved on to the next stage. We need to measure the spin of this new boson and if we exclude the spin 0 case then we know it is not a Higgs boson. If exclude the spin 2 case then we still need to go a little further to show it’s the Standard Model Higgs boson. The spin analysis is rather complicated, because we need to measure the angles between the decay products and look for correlations. We need to take the detector effects into account, then subtract the background spectra. What is left after that are the signal spectra, and we’re going to be statistically limited in what we see. It’s a tough analysis, there’s no doubt about it.

We need to see the five main modes to confirm that this is what we have been looking for for so long. If we get the boson modes ($$ZZ^*$$, $$WW^*$$, $$\gamma\gamma$$) spot on relative to each other, then we may have a fermiophobic Higgs boson, which is an interesting scenario. (A “normal” fermiophobic Higgs boson has already been excluded, so any fermiophobic Higgs boson we may see must be very unusual.)

There are also many beyond the Standard Model scenarios that must be studied. As more regions of parameter space are excluded, theorists tweak their models, and give us updated hints on where to search. ATLAS and CMS have groups dedicated to searching for beyond the Standard Model physics, including additional Higgs bosons, supersymmetry and general exotica. It will be interesting to see how their analyses change in light of the favored mass region in the Higgs search.

A favored Higgs mass has implications for physics beyond the Standard Model. Combined with the limits on new particles (shown in plot) many scenarios can be excluded (ATLAS)

2012 has been a wonderful year for physics, and it looks like it’s only going to get better. There are still a few unanswered questions and tensions to resolve, and that’s what we must expect from the scientific process. We need to wait a little longer to get to the end of the story, but the anticipation is all part of the adventure. We’ll know is really happening by the end of Moriond 2013, in March. Only then can we say with certainty “We have proven/disproven the existence of the Standard Model Higgs boson”!

I like to say “We do not do these things because they are easy. We do them because they are difficult”, but I think Winston Churchill said it better:

This is not the end. It is not even the beginning of the end, but it is perhaps the end of the beginning.” W. Churchill

### References etc

Plots and photos taken from:
“Webcast of seminar with ATLAS and CMS latest results from ICHEP”, ATLAS Experiment, CERN, ATLAS-PHO-COLLAB-2012-014
Wikipedia
“Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC”, ATLAS Collaboration, arXiv:1207.7214v1 [hep-ex]
“Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC”, CMS Collaboration, arXiv:1207.7235v1 [hep-ex]
Flip Tanedo

It’s been a while since I last posted. Apologies. I hope this post makes up for it!

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### 34 Responses to “Understanding the Higgs search”

2. Tay says:

As a technical layperson with a profound interest in this research, this post immensely helped me to understand what’s going on. Thank you!

3. Joe says:

What’s wrong with “Hagen Boson” as suggested (in jest I think) at the Sakurai Prize Lecture – all six won the APS Sakurai Prize in 2010. See link for lecture (near end of lecture).

• That’s fantastic, thanks!

• Vijay says:

Vide9o tre8s sympathique !! C’est tre8s agre9able e0 raeredgr, tre8s bien explique9 et e7a fournit les explications ne9cessaire pour comprendre en gros le proce9de9 expe9rimental.Il y a cependant quelques de9fauts:1) c’est en anglais, tout le monde n’est pas force9ment capable de comprendre l’anglais e0 ce niveau. Le Monde est un journal frane7ais, autant que les explications y soient toutes en frane7ais.2) Cela va tre8s vite, beaucoup de bases the9oriques sont survole9es, il faut donc avoir de9je0 un tre8s solide bagage scientifique pour comprendre toutes les explications.Dans un souci de vulgarisation au grand publique, s’il y a d’autres vide9os du meame genre e0 venir (et je le souhaite, car j’ai vraiment appre9cie9 la vide9o !) il serait bienvenu que e7a aille un tout petit peu moins vite, avec un peu plus d’explications et surtout que ce soit en frane7ais.

4. Ilya Kuryakin says:

Best summary of Higgs research I’ve come across – and no mention of treacle, molasses or wading through crowds!

• Thanks! I make it a point to not patronize my readers. People who read these posts are usually armed with enough knowledge to handle the more complicated parts of the subject matter, and that makes these posts all the more fun to write.

5. A K Puri says:

Wish I had a tablet so I could lie in bed and read all this.
I have a point which states that the universe could start with two atoms of hydrogen and two atoms of oxygen plus electricity.When through electrolosis you seperate oxygen and hydrogen from water the energy required for electrolysis is less than the energy given from explosion of hydrogen and oxygen to form water.thus the two atoms eaqch of hydrogen and oxygen can keep multiplying energy through siries of rection through electricity of the two oxygen and hydrogen.Then the intensity of energy is so much that there is the big bang.Where the two atoms of hydrogen and oxygen came I cannot tell.Water electrolosis can also be used to develop transportation systems which simultaneous charge batteries.You just have to turn steam to water and recycle the water.You will get work plus energy generation.You can travel the universe and back without refuelling.

• Thanks for the comment! I’m sorry to say that the 2H2+O2 < => 2H20 cycle is a no win game. Going around this cycle once leaves you exactly where you started in term of energy, unless I’ve missed something. Also, atoms are far too big the for the start of the universe

6. You wrote:
“The W+ boson decays with a neutrino in the final state, and because of special relativity the neutrino must align its spin with its direction of motion. The W− boson decays with an anti-neutrino, which takes its spin against its direction of motion.”

Isn’t it the other way around, neutrinos being left-handed, and anti-neutrinos being right-handed?

• Hi Glen, thanks for spotting that, it’s fixed! Fortunately it’s one of those errors that cancels itself out, and leaves the argument intact.

7. Bob Anderson says:

Hi Aiden,

Indeed it has been too long since you last posted on US-LHC. I particularly liked your explanation of gauge and Lorentz transformations and how these lead to so many predictions of what particles or fields should should or should not exist in nature (gauge invariance and Lorentz invariance have to be obeyed). A great job of explaining some of the abstruse theory to the rest of us non theorists.

That section really needs to be a post on its own – more please!

8. Mark Lancaster says:

An excellent blog, however as a CDF member I would like to understand better what you mean by the statement “and personally I’m skeptical since we’ve already seen that CDF’s dijet mass scale might have some problems associated with it” could you please explain how this affects the conclusions presented in the 4 Higgs CDF PRLs that are now accepted for publication. I’d be particularly interested to hear your views on how an excess over a broad mass region is affected by problems in a dijet mass scale and your insight into the different characteristics of a W+dijet sample (with no b-tags) and the event sample used for the Higgs analysis.

• Hi Mark, thanks for the comment! My skepticism concerning the CDF result is (as you pointed out) referring to the dijet anomaly. In that instance there was a similar peak (in presumably an independent sample of events) which CDF saw, but D0 did not. From what I recall of the July 2nd announcement and subsequent papers there was a broad dijet excess observed around 125GeV, which was significantly more pronounced in the CDF dataset than the D0 dataset. Taking a mini literature review of the most recent papers from both CDF and D0 shows the following results:

For D0 HZ(ll) gives a 1.5sigma excess over a range mH>110GeV, HZ(nunu) sees no excess at all, and HW(lnu) sets a limit of 5.2xSM vs an expectation of 4.7xSM. To me this suggests little evidence from D0 in favor of a Higgs boson.

For CDF things are little more exciting: HZ(ll) gives 7.1xSM (vs 3.9xSM), HZ(nunu) gives 6.7xSM (vs 3.6xSM) and HW(lnu) gives 4.9xSM (vs 2.8xSM). This looks more impressive, however the excess is shown for all mass points above 115GeV (90GeV in the case of HW) with some deficits below 100GeV.

These results are then combined in the joint CDF/D0 paper, but there is little space given a breakdown of sensitivities mode by mode and collaboration by collaboration. To an outsider this looks like once again CDF has observed a broad mass in a dijet spectrum that has not been confirmed by D0. As far as I’m aware CDF have not updated the analysis for the dijet anomaly since adding additional data. Since D0 does not see the excess, and the significance of the dijet anomaly excess at CDF increased after addition of more data this suggests a systematic bias somewhere in the jet reconstruction at CDF. If b jets are treated differently from light jets at the detector level I would be very interested to hear how this is done. I’ll admit that I don’t know as much about the CDF and D0 results as I could, so if you can provide evidence to convince me that there is not a systematic problem with dijet searches at CDF and localized excesses I’ll be happy to revise my opinion.

(For reference the arXiv hep-ex numbers for the papers are 1207.1703, 1207.1704, 1207.1711, 1207.5689, 1207.5819, 1207.6436, 1208.0653)

9. If you’re still looking for a better understanding of how the Higgs mechanism works, I tried in the wake of the announcement to throw together a reasonably coherent explanation of the classical version of a toy example in four posts on my (math-oriented) weblog.

• Hi John. Thanks for the links, those posts are excellent! Much more rigorous than what I could have written here. (PS You might want to looking in to MathJax, a Javascript based LaTeX interpreter for your blog. It makes equations (even inline equations) quite pretty on the page and they scale seamlessly with text as the user zooms in and out.)

• That’s a good idea, but I don’t think WordPress supports it directly. At least it didn’t when I started back in 200…7?

10. Richard Engkraf says:

Your link to the arXiv article for ATLAS sent me right where I wanted to go, CMS brought me back to this same article. I can find it, I just thought that you might want to know.

• Hi Richard, thanks for catching this! It’s fixed now. Maybe it was some subconscious ATLAS bias on my part

11. Brian Champness says:

Oh dear, here we go. Now that a Nobel Prize is getting nearer, people naturally are quibbling about why it is called the ‘Higgs’ rather than the ‘Kibble’ or ‘Brout’. I am sure that most of you know that Peter Higgs was the only one of the group members who pointed out explicitly the existence of the particle that bears his name and calculated some of its properties. An excellent summary article, though.

12. Carlo says:

In the very first graph I see other ‘signals’ apart from the one at 125 GeV, meaning, intervals where data doesn’t match the expected value. What’s that?

13. Carlo says:

For example, isn’t there a small signal at around 162 GeV in both the 2 first graphs?

• Hi Carlo, thanks for the comments! These are most likely fluctuations. What’s important in these searches is how many combined “error bars” the data points are above the background only hypothesis. In the first plot we see two data points and they are about 2 and 1.5 error bars away from the background only histograms (ignore the blue histogram, this is signal simulation on top the background and we are not looking for deviations away from this). Each error bar is a measure of the deviation, and if we use the “sigma” nomenclature we can express the deviations in terms of probabilities. The probability of a 2 sigma deviation up is about 2.5% and the probability of a 1.5 sigma fluctuation up is about 5%, so the combined probability that these points are due to a fluctuation is about 0.1%. On the other hand the probability that the point at 162GeV is due to a fluctuation is the same as 1 sigma, or about 16%. We expect to see fluctuations up and down across the whole spectrum and we can characterize how likely they are (so on average 1 in 6 data points will have a 1 sigma fluctuation up). What we see around 125GeV is uncharacteristically improbable so it’s most likely not a fluctuation, it’s evidence in favor of a new particle. When combined with the other final states we get even stronger evidence. I hope that clears things up, if not please comment again!

14. [...] article on the science details of the Higgs search and recent observation of a new particle “Understanding the Higgs search” by Aidan [...]

15. Carlo says:

Alright. Anyway the fact that both CMS and ATLAS had this casual fluctuation at 162GeV is funny. I’ll keep an eye open on it ;-). Thanks!

16. Ilya Kuryakin says:

Greetings Aidan,

I’m interested in the angular correlation measurements, used to determine the ‘Higgs’ spin. Does this involve all decay channels?
Can the tracking detectors give information about the location of the primary decay products for all decay modes? As the W & Z have very short lifetimes, I’m assuming that the secondary decay products (leptons), are used to ‘track back’ to give the location of the primary decays.

• Hi Ilya, thanks for the comment! At the moment the angular analysis can only use channels where we can fully reconstruct all the final state particles. As we get more statistics (after the upgrade) we will be able to use other final states, such as WW* and tautau, but we need to wait a while for that. The other factor is the level of background, because we don’t know on an event-by-event basis what is a signal event and what is not, so we have to subtract off the background somehow (either using simulation, or using a control region in data to estimate the background) and only if what is left over is significant enough can we perform an angular analysis. As we subtract off the background we introduce a new uncertainty, and this uncertainty is larger than the signal yield then we cannot perform an angular analysis. So we are left with the ZZ* and gammagamma final states, and they’re both tough. ZZ* has few events, but almost no background, and gammagamma has many events, but huge backgrounds. The W and Z lifetimes are so short that we ignore their decay vertices altogether and just use the primary vertex instead. The separation between the primary vertex and the decay vertex of a W or Z is orders of magnitude smaller than our best resolution, so it makes sense to just point back to the primary vertex.

17. Ilya Kuryakin says:

Thanks for your detailed response!

18. Wow.

Hi Aidan,

I just found out you’re not merely a fabulous explainer of leading edge physics – you just demonstrated ESP

Your article here was so good I put a link to it. The only further question I had was – How can a 125 GeV particle decay into two 80 or 91 GeV particles, but I didn’t want to bother you about it just yet.

Well, I just found your comment on my article – precisely answering that question !

http://cosmologyscience.com/cosblog/did-cern-find-a-higgs-well-not-quite-but-they-probably-found-a-new-particle-and-extended-their-funding-for-years/

Too funny.

Thanks. Well done too.

19. Kevin says:

This is a very good post on the experimental results, but your notation for electroweak symmetry breaking is a little strange. The two fields pre-Higgs are the W+/W-/W0 (for weak isospin) and the B (for weak hypercharge). The W0 and B mix to give us the Z0 and the photon. I have not seen A used in this context; it’s usually either electromagnetic four-potential, or A0 in a two-Higgs-doublet model.

• Hi Kevin, thanks for pointing this out! How sloppy of me, I shouldn’t write about these gauge symmetries so late at night. I assume here you mean W1 and W2 by W+ and W-, right? From what I understand the massive charged W bosons can’t emerge without the Higgs mechanism. So it goes W1/W2->W+W- while for the other fields W0/B->A/Z.

20. Valery says:

I’m following another blog written by the son of Comay, a retired physicist who claims that the W,Z and the new particle are top quark mesons. I have two questions:

1. He explains here why the top mesons must appear: http://nohiggs.wordpress.com/2012/10/09/why-top-quark-mesons-must-exist/
2. The blog says that he recently published an article which claims that W equations cannot be equations of elementary particle.

What is your opinion about the two issues? What is the author’s mistake?

21. Zuzana says:

Please, how can I come to the number of Higgs bosons produced per inverse femtobarn? I mean, can you, please, write how can I compute it, what do I need for it and also the numbers? I am talking about the 4th and 5th sentence from the end of section “H→ZZ”. Thank you very much.