Posted on

The Search for Simplicity : The Higgs Boson’s Self Coupling

When students first learn quantum field theory, the mathematical language the underpins the behavior of elementary particles, they start with the simplest possible interaction you can write down : a particle with no spin and no charge scattering off another copy of itself. One then eventually moves on to the more complicated interactions that describe the behavior of fundamental particles of the Standard Model. They may quickly forget this simplified interaction as a unrealistic toy example, greatly simplified compared to the complexity the real world. Though most interactions that underpin particle physics are indeed quite a bit more complicated, nature does hold a special place for simplicity. This barebones interaction is predicted to occur in exactly one scenario : a Higgs boson scattering off itself. And one of the next big targets for particle physics is to try and observe it.

A feynman diagram consisting of two dotted lines coming merging together to form a single line.
A Feynman diagram of the simplest possible interaction in quantum field theory, a spin-zero particle interacting with itself.

The Higgs is the only particle without spin in the Standard Model, and the only one that doesn’t carry any type of charge. So even though particles such as gluons can interact with other gluons, its never two of the same kind of gluons (the two interacting gluons will always carry different color charges). The Higgs is the only one that can have this ‘simplest’ form of self-interaction. Prominent theorist Nima Arkani-Hamed has said that the thought of observing this “simplest possible interaction in nature gives [him] goosebumps“.

But more than being interesting for its simplicity, this self-interaction of the Higgs underlies a crucial piece of the Standard Model: the story of how particles got their mass. The Standard Model tells us that the reason all fundamental particles have mass is their interaction with the Higgs field. Every particle’s mass is proportional to the strength of the Higgs field. The fact that particles have any mass at all is tied to the fact that the lowest energy state of the Higgs field is at a non-zero value. According to the Standard Model, early in the universe’s history when the temperature were much higher, the Higgs potential had a different shape, with its lowest energy state at field value of zero. At this point all the particles we know about were massless. As the universe cooled the shape of the Higgs potential morphed into a ‘wine bottle’ shape, and the Higgs field moved into the new minimum at non-zero value where it sits today. The symmetry of the initial state, in which the Higgs was at the center of its potential, was ‘spontaneously broken’  as its new minimum, at a location away from the center, breaks the rotation symmetry of the potential. Spontaneous symmetry breaking is a very deep theoretical idea that shows up not just in particle physics but in exotic phases of matter as well (eg superconductors). 

A diagram showing the ‘unbroken’ Higgs potential in the very early universe (left) and the ‘wine bottle’ shape it has today (right). When the Higgs at the center of its potential it has a rotational symmetry, there are no preferred directions. But once it finds it new minimum that symmetry is broken. The Higgs now sits at a particular field value away from the center and a preferred direction exists in the system. 

This fantastical story of how particle’s gained their masses, one of the crown jewels of the Standard Model, has not yet been confirmed experimentally. So far we have studied the Higgs’s interactions with other particles, and started to confirm the story that it couples to particles in proportion to their mass. But to confirm this story of symmetry breaking we will to need to study the shape of the Higgs’s potential, which we can probe only through its self-interactions. Many theories of physics beyond the Standard Model, particularly those that attempt explain how the universe ended up with so much matter and very little anti-matter, predict modifications to the shape of this potential, further strengthening the importance of this measurement.

Unfortunately observing the Higgs interacting with itself and thus measuring the shape of its potential will be no easy feat. The key way to observe the Higgs’s self-interaction is to look for a single Higgs boson splitting into two. Unfortunately in the Standard Model additional processes that can produce two Higgs bosons quantum mechanically interfere with the Higgs self interaction process which produces two Higgs bosons, leading to a reduced production rate. It is expected that a Higgs boson scattering off itself occurs around 1000 times less often than the already rare processes which produce a single Higgs boson.  A few years ago it was projected that by the end of the LHC’s run (with 20 times more data collected than is available today), we may barely be able to observe the Higgs’s self-interaction by combining data from both the major experiments at the LHC (ATLAS and CMS).

Fortunately, thanks to sophisticated new data analysis techniques, LHC experimentalists are currently significantly outpacing the projected sensitivity. In particular, powerful new machine learning methods have allowed physicists to cut away background events mimicking the di-Higgs signal much more than was previously thought possible. Because each of the two Higgs bosons can decay in a variety of ways, the best sensitivity will be obtained by combining multiple different ‘channels’ targeting different decay modes. It is therefore going to take a village of experimentalists each working hard to improve the sensitivity in various different channels to produce the final measurement. However with the current data set, the sensitivity is still a factor of a few away from the Standard Model prediction. Any signs of this process are only expected to come after the LHC gets an upgrade to its collision rate a few years from now.

Limit plots on HH production in various different decay modes.
Current experimental limits on the simultaneous production of two Higgs bosons, a process sensitive to the Higgs’s self-interaction, from ATLAS (left) and CMS (right). The predicted rate from the Standard Model is shown in red in each plot while the current sensitivity is shown with the black lines. This process is searched for in a variety of different decay modes of the Higgs (various rows on each plot). The combined sensitivity across all decay modes for each experiment allows them currently to rule out the production of two Higgs bosons at 3-4 times the rate predicted by the Standard Model. With more data collected both experiments will gain sensitivity to the range predicted by the Standard Model.

While experimentalists will work as hard as they can to study this process at the LHC, to perform a precision measurement of it, and really confirm the ‘wine bottle’ shape of the potential, its likely a new collider will be needed. Studying this process in detail is one of the main motivations to build a new high energy collider, with the current leading candidates being an even bigger proton-proton collider to succeed the LHC or a new type of high energy muon collider.

Various pictorial representations of the uncertainty on the Higgs potential shape.
A depiction of our current uncertainty on the shape of the Higgs potential (center), our expected uncertainty at the end of the LHC (top right) and the projected uncertainty a new muon collider could achieve (bottom right). The Standard Model expectation is the tan line and the brown band shows the experimental uncertainty. Adapted from Nathaniel Craig’s talkhere

The quest to study nature’s simplest interaction will likely span several decades. But this long journey gives particle physicists a roadmap for the future, and a treasure worth traveling great lengths for.

Read More:

CERN Courier Interview with Nima Arkani-Hamed on the future of Particle Physics on the importance of the Higgs’s self-coupling

Wikipedia Article and Lecture Notes on Spontaneous symmetry breaking

Recent ATLAS Measurements of the Higgs Self Coupling

Posted on

Uncovering a Higgs Hiding Behind Backgrounds

Hello particle munchers,

hidingHiggs
Figure 1: Monsieur Higgs boson hiding behind a background.

Last time I discussed the Higgs boson decay into photons, i.e. `shining light on the Higgs boson‘. This is a followup discussing more generally the problem of uncovering a Higgs boson which is hiding buried behind what can often be a large background (see Figure 1).

Perhaps the first question to ask is, what the heck is a background? Well, basically a background is anything that we `already know about’. In this case, this means the well understood Standard Model (SM) processes which do not involve a Higgs boson (which in this case is our `signal’), but can nevertheless mimic one of the possible decays of the Higgs. For most of these processes, we have very precise theoretical predictions in addition to previous experimental data from the LEP and Tevatron experiments (and others) which previously searched for the Higgs boson. So it is in reference to these non-Higgs SM processes when we use the term `background’.

As discussed in my previous post, the Higgs can decay to a variety of combinations of SM particles, which we call `channels’. Each of these channels has its own corresponding background which obscures the presence of a Higgs. For some channels the backgrounds are huge. For instance the background for a Higgs decaying to a pair of bottom quarks is so large (due to QCD) that, despite the fact this is the dominant decay channel (about 60% of Higgs’ decay to bottom quarks at 125 GeV), this channel has yet to be observed.

This is in contrast to the Higgs decay to four charged leptons (specifically electrons and muons) channel. This decay (mediated by a pair of virtual Z bosons) was one of the first discovery channels of the Higgs at the LHC despite the fact that roughly only one in every 10,000 Higgs bosons decays to four charge leptons. This is because this channel has a small background and is measured with very high precision. This high precision allows LHC experiments to scan over a range of energies in very small increments or `windows’. Since the background is very small, the probability of observing a background event in any given window is tiny. Thus, if an excess of events is seen in a particular window, this is an indication that there is a non background process occurring at that particular energy.

hto4lpeak
Figure 2: The energy spectrum of a Higgs decaying to four charged leptons (red) and its associated background (blue).

This is how the Higgs was discovered in the decay to four charged leptons at around 125 GeV. This can be seen in Figure 2 where in the window around the Higgs signal (shown in red) we see the background (shown in blue) is very small. Thus, once about a dozen events were observed at around 125 GeV, this was already enough evidence for experiments at the LHC to be able to claim discovery of the long sought after monsieur Higgs boson.

 Further Reading:

Seeking and Studying the Standard Model Higgs Particle

Decays of the Standard Model Higgs

Posted on

Shining Light on the Higgs Boson

Figure 1: Here we give a depiction of shining light on monsieur Higgs boson as well as demonstrate the extent of my french.
Figure 1: Here we give a depiction of shining light on monsieur Higgs boson as well as demonstrate the extent of my french.

Hello Particle Nibblers,

This is my first Particlebites entry (and first ever attempt at a blog!) so you will have to bear with me =).

As I am sure you know by now, the Higgs boson has been discovered at the Large Hadron Collider (LHC). As you also may know, `discovering’ a Higgs boson is not so easy since a Higgs doesn’t just `sit there’ in a detector. Once it is produced at the LHC it very quickly decays (in about 1.6 \times 10^{-22} seconds) into other particles of the Standard Model. For us to `see’ it we must detect these particles into which decays. The decay I want to focus on here is the Higgs boson decay to a pair of photons, which are the spin-1 particles which make up light and mediate the electromagnetic force. By studying its decays to photons we are literally shining light on the Higgs boson (see Figure 1)!

The decay to photons is one of the Higgs’ most precisely measured decay channels. Thus, even though the Higgs only decays to photons about 0.2 % of the time, this was nevertheless one of the first channels the Higgs was discovered in at the LHC. Of course other processes (which we call backgrounds) in the Standard Model can mimic the decays of a Higgs boson, so to see the Higgs we have to look for `bumps’ over these backgrounds (see Figure 2). By carefully reconstructing this `bump’, the Higgs decays to photons also allows us to reconstruct the Higgs mass (about 125 GeV in particle physics units or about 2.2 \times 10^{-22} kg in `real world’ units).

Figure 2: Here we show the Higgs `bump' in the invariant mass spectrum of the Higgs decay to a pair of photons.
Figure 2: Here we show the Higgs `bump’ in the invariant mass spectrum of the Higgs decay to a pair of photons.

Furthermore, using arguments based on angular momentum the Higgs decay to photons also allows us to determine that the Higgs boson must be a spin-0 particle which we call a scalar ^1. So we see that just in this one decay channel a great deal of information about the Higgs boson can be inferred.

Now I know what you’re thinking…But photons only `talk to’ particles which carry electric charge and the Higgs is electrically neutral!! And even crazier, the Higgs only `talks to’ particles with mass and photons are massless!!! This is blasphemy!!! What sort of voodoo magic is occurring here which allows the Higgs boson to decay to photons?

The resolution of this puzzle lies in the subtle properties of quantum field theory. More specifically the Higgs can decay to photons via electrically charged `virtual particles‘ ^2. For present purposes its enough to say (with a little hand-waiving) that since the Higgs can talk to the massive electrically charged particles in the Standard Model, like the W boson or top quark, which in turn can `talk to’ photons, this allows the Higgs to indirectly interact with photons despite the fact that they are massless and the Higgs is neutral. In fact any charged and massive particles which exist will in principle contribute to the indirect interaction between the Higgs boson and photons. Crucially this includes even charged particles which may exist beyond the Standard Model and which have yet to be discovered due to their large mass. The sum total of these contributions from all possible charged and massive particles which contribute to the Higgs decay to photons is represented by the `blob’ in Figure 3.

Figure 3: Here we show how the Higgs decays to a pair of photons via `virtual charged particles' or more accurately disturbances in the quantum fields associated with these charge particles.
Figure 3: Here we show how the Higgs decays to a pair of photons via `virtual charged particles’ (or more accurately disturbances in the quantum fields associated with these charge particles)  represented by the grey`blob’.

It is exciting and interesting to think that new exotic charged particles could be hiding in the `blob’ which creates this interaction between the Higgs boson and photons. These particles might be associated with supersymmetry, extra dimensions, or a host of other exciting possibilities. So while it remains to be seen which, if any, of the beyond the Standard Model possibilities (please let there be something!) the LHC will uncover, it is fascinating to think about what can be learned by shining a little light on the Higgs boson!

 

Footnotes:

1. There is a possible exception to this if the Higgs is a spin-2 particle, but various theoretical arguments as well as other Higgs data make this scenario highly unlikely.

2. Note, virtual particle is unfortunately a misleading term since these are not really particles at all (really they are disturbances in their associated quantum fields), but I will avoid going down this rabbit hole for the time being and save it for a later post. See the previous `virtual particles’ link for a great and more in-depth discussion which takes you a little deeper into the rabbit hole.

Further Reading:

http://arxiv.org/abs/0910.4182

http://arxiv.org/abs/1206.1082

http://www.amazon.com/Introduction-Elementary-Particles-David-Griffiths/dp/3527406018/ref=sr_1_4?ie=UTF8&qid=1427166136&sr=8-4&keywords=particle+physics

http://www.amazon.com/Introduction-Quantum-Theory-Frontiers-Physics/dp/0201503972/ref=sr_1_1?ie=UTF8&qid=1427166621&sr=8-1&keywords=peskin+quantum+field+theory