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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

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The Higgs Comes Out of its Shell

Title : “First evidence for off-shell production of the Higgs boson and measurement of its width”

Authors : The CMS Collaboration

Link : https://arxiv.org/abs/2202.06923

CMS Analysis Summary : https://cds.cern.ch/record/2784590?ln=en

If you’ve met a particle physicist in the past decade, they’ve almost certainly told you about the Higgs boson. Since its discovery in 2012, physicists have been busy measuring as many of its properties as the ATLAS and CMS datasets will allow, including its couplings to other particles (e.g. bottom quarks or muons) and how it gets produced at the LHC. Any deviations from the standard model (SM) predictions might signal new physics, so people are understandably very eager to learn as much as possible about the Higgs.

Amidst all the talk of Yukawa couplings and decay modes, it might occur to you to ask a seemingly simpler question: what is the Higgs boson’s lifetime? This turns out to be very difficult to measure, and it was only recently — nearly 10 years after the Higgs discovery — that the CMS experiment released the first measurement of its lifetime.

The difficulty lies in the Higgs’ extremely short lifetime, predicted by the standard model to be around 10⁻²² seconds. This is far shorter than anything we could hope to measure directly, so physicists instead measured a related quantity: its width. According to the Heiseinberg uncertainty principle, short-lived particles can have significant uncertainty in their energy. This means that whenever we produce a Higgs boson at the LHC and reconstruct its mass from its decay products, we’ll measure a slightly different mass each time. If you make a histogram of these measurements, its shape looks like a Breit-Wigner distribution (Fig. 1) peaked at the nominal mass and with a characteristic width .

Fig. 1: A Breit-Wigner curve, which describes the distribution of masses that a particle takes on when it’s produced at the LHC. The peak sits at the particle’s nominal mass, and production within the width is most common (“on-shell”). The long tails allow for rare production far from the peak (“off-shell”).

So, the measurement should be easy, right? Just measure a bunch of Higgs decays, make a histogram of the mass, and run a fit! Unfortunately, things don’t work out this way. A particle’s width and lifetime are inversely proportional, meaning an extremely short-lived particle will have a large width and vice-versa. For particles like the Z boson — which lives for about 10⁻²⁵ seconds — we can simply extract its width from its mass spectrum. The Higgs, however, sits in a sweet spot of experimental evasion: its lifetime is too short to measure, and the corresponding width (about 4 MeV) cannot be resolved by our detectors, whose resolution is limited to roughly 1 GeV.

To overcome this difficulty, physicists relied on another quantum mechanical quirk: “off-shell” Higgs production. Most of the time, a Higgs is produced on-shell, meaning its reconstructed mass will be close to the Breit-Wigner peak. In rare cases, however, it can be produced with a mass very far away from its nominal mass (off-shell) and undergo decays that are otherwise energetically forbidden. Off-shell production is incredibly rare, but if you can manage to measure the ratio of off-shell to on-shell production rates, you can deduce the Higgs width!

Have we just replaced one problem (a too-short lifetime) with another one (rare off-shell production)? Thankfully, the Breit-Wigner distribution saves the day once again. The CMS analysis focused on a Higgs decaying to a pair of Z bosons (Fig. 2, left), one of which must be produced off-shell (the Higgs mass is 125 GeV, whereas each Z is 91 GeV). The Z bosons have a Breit-Wigner peak of their own, however, which enhances the production rate of very off-shell Higgs bosons that can decay to a pair of on-shell Zs. The enhancement means that roughly 10% of H → ZZ decays are expected to involve an off-shell Higgs, which is a large enough fraction to measure with the present-day CMS dataset!

Fig. 2: The signal process involving a Higgs decay to Z bosons (left), and background ZZ production without the Higgs (right)

To measure the off-shell H → ZZ rate, physicists looked at events where one Z boson decays to a pair of leptons and the other to a pair of neutrinos. The neutrinos escape the detector without depositing any energy, generating a large missing transverse momentum which helps identify candidate Higgs events. Using the missing momentum as a proxy for the neutrinos’ momentum, they reconstruct a “transverse mass” for the off-shell Higgs boson. By comparing the observed transverse mass spectrum to the expected “continuum background” (Z boson pairs produced via other mechanisms, e.g. Fig. 2, right) and signal rate, they are able to extract the off-shell production rate.

After a heavy load of sophisticated statistical analysis, the authors found that off-shell Higgs production happened at a rate consistent with SM predictions (Fig. 3). Using these off-shell events, they measured the Higgs width to be 3.2 (+2.4, -1.7) MeV, again consistent with the expectation of 4.1 MeV and a marked improvement upon the previously measured limit of 9.2 MeV.

Fig. 3: The best-fit “signal strength” parameters for off-shell Higgs production in two different modes: gluon fusion (x-axis, shown also in the leftmost Feynman diagram above) and associated production with a vector boson (y-axis). Signal strength measures how often a process occurs relative to the SM expectation, and a value of 1 means that it occurs at the rate predicted by the SM. In this case, the SM prediction (X) is within one standard deviation of the best fit signal strength (diamond).

Unfortunately, this result doesn’t hint at any new physics in the Higgs sector. It does, however, mark a significant step forward into the era of precision Higgs physics at ATLAS and CMS. With a mountain of data at our fingertips — and much more data to come in the next decade — we’ll soon find out what else the Higgs has to teach us.

Read More

“Life of the Higgs Boson” – Coverage of this result from the CMS Collaboration

“Most Particles Decay — But Why?” – An interesting article by Matt Strassler explaining why (some) particles decay

“The Physics Still Hiding in the Higgs Boson” – A Quanta article on what we can learn about new physics by measuring Higgs properties

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LIGO and Gravitational Waves: A Hep-ex perspective

The exciting Twitter rumors have been confirmed! On Thursday, LIGO finally announced the first direct observation of gravitational waves, a prediction 100 years in the making. The media storm has been insane, with physicists referring to the discovery as “more significant than the discovery of the Higgs boson… the biggest scientific breakthrough of the century.” Watching Thursday’s press conference from CERN, it was hard not to make comparisons between the discovery of the Higgs and LIGO’s announcement.

 

 

The gravitational-wave event GW150914 observed by the LIGO Collaboration
The gravitational-wave event GW150914 observed by the LIGO Collaboration

 

Long standing Searches for well known phenomena

 

The Higgs boson was billed as the last piece of the Standard Model puzzle. The existence of the Higgs was predicted in the 1960s in order to explain the mass of vector bosons of the Standard Model, and avoid non-unitary amplitudes in W boson scattering. Even if the Higgs didn’t exist, particle physicists expected new physics to come into play at the TeV Scale, and experiments at the LHC were designed to find it.

 

Similarly, gravitational waves were the last untested fundamental prediction of General Relativity. At first, physicists remained skeptical of the existence of gravitational waves, but the search began in earnest with Joseph Webber in the 1950s (Forbes). Indirect evidence of gravitational waves was demonstrated a few decades later. A binary system consisting of a pulsar and neutron star was observed to release energy over time, presumably in the form of gravitational waves. Using Webber’s method for inspiration, LIGO developed two detectors of unprecedented precision in order to finally make direct observation.

 

Unlike the Higgs, General Relativity makes clear predictions about the properties of gravitational waves. Waves should travel at the speed of light, have two polarizations, and interact weakly with matter. Scientists at LIGO were even searching for a very particular signal, described as a characteristic “chirp”. With the upgrade to the LIGO detectors, physicists were certain they’d be capable of observing gravitational waves. The only outstanding question was how often these observations would happen.

 

The search for the Higgs involved more uncertainties. The one parameter essential for describing the Higgs, its mass, is not predicted by the Standard Model. While previous collider experiments at LEP and Fermilab were able to set limits on the Higgs mass, the observed properties of the Higgs were ultimately unknown before the discovery. No one knew whether or not the Higgs would be a Standard Model Higgs, or part of a more complicated theory like Supersymmetry or technicolor.

 

Monumental scientific endeavors

 

Answering the most difficult questions posed by the universe isn’t easy, or cheap. In terms of cost, both LIGO and the LHC represent billion dollar investments. Including the most recent upgrade, LIGO cost a total $1.1 billion, and when it was originally approved in 1992, “it represented the biggest investment the NSF had ever made” according to France Córdova, NSF director. The discovery of the Higgs was estimated by Forbes to cost a total of $13 billion, a hefty price to be paid by CERN’s member and observer states. Even the electricity bill costs more than $200 million per year.

 

The large investment is necessitated by the sheer monstrosity of the experiments. LIGO consists of two identical detectors roughly 4 km long, built 3000 km apart. Because of it’s large size, LIGO is capable of measuring ripples in space 10000 times smaller than an atomic nucleus, the smallest scale ever measured by scientists (LIGO Fact Page). The size of the LIGO vacuum tubes is only surpassed by those at the LHC. At 27 km in circumference, the LHC is the single largest machine in the world, and the most powerful particle accelerator to date. It only took a handful of people to predict the existence of gravitational waves and the Higgs, but it took thousands of physicists and engineers to find them.

 

Life after Discovery

 

Even the language surrounding both announcements is strikingly similar. Rumors were circulating for months before the official press conferences, and the expectations from each respective community were very high. Both discoveries have been touted as the discoveries of the century, with many experts claiming that results would usher in a “new era” of particle physics or observational astronomy.

 

With a few years of hindsight, it is clear that the “new era” of particle physics has begun. Before Run I of the LHC, particle physicists knew they needed to search for the Higgs. Now that the Higgs has been discovered, there is much more uncertainty surrounding the field. The list of questions to try and answer is enormous. Physicists want to understand the source of the Dark Matter that makes up roughly 25% of the universe, from where neutrinos derive their mass, and how to quantize gravity. There are several ad hoc features of the Standard Model that merit additional explanation, and physicists are still searching for evidence of supersymmetry and grand unified theories. While the to-do list is long, and well understood, how to solve these problems is not. Measuring the properties of the Higgs does allow particle physicists to set limits on beyond the Standard Model Physics, but it’s unclear at which scale new physics will come into play, and there’s no real consensus about which experiments deserve the most support. For some in the field, this uncertainty can result in a great deal of anxiety and skepticism about the future. For others, the long to-do list is an absolutely thrilling call to action.

 

With regards to the LIGO experiment, the future is much more clear. LIGO has only published one event from 16 days of data taking. There is much more data already in the pipeline, and more interferometers like VIRGO and (e)LISA, planning to go online in the near future. Now that gravitational waves have been proven to exist, they can be used to observe the universe in a whole new way. The first event already contains an interesting surprise. LIGO has observed two inspriraling black holes of 36 and 29 solar masses, merging into a final black hole of 62 solar masses. The data thus confirmed the existence of heavy stellar black holes, with masses more than 25 times greater than the sun, and that binary black hole systems form in nature (Atrophysical Journal). When VIRGO comes online, it will be possible to triangulate the source of these gravitational waves as well. LIGO’s job is to watch, and see what other secrets the universe has in store.