At a cost of $10 billion, a 40-year-old problem remains unsolved

As physicists face three decades of fruitless searches for new fundamental particles that explain why nature is the way it is, they are reexamining a long-standing assumption: that any object is made up of smaller things.

By Natalie Wolchover

Translator: Li Yuting

In The Structure of Scientific Revolutions, philosopher of science Thomas Kuhn observed that scientists take long, slow steps forward. They raise and solve puzzles while interpreting all data uniformly within a fixed worldview or theoretical framework, which Kuhn called a paradigm. Sooner or later, though, facts emerge that conflict with the established paradigm. A crisis ensues. Scientists rack their brains, reexamine their assumptions, and eventually make a revolutionary shift toward a new paradigm, with a radically different and more realistic understanding of the natural world. Then incremental progress resumes.

For several years, particle physicists who study nature's fundamental building blocks have been in the midst of a textbook Kuhn crisis.

The crisis became undeniable in 2016, when, despite a major upgrade, the Large Hadron Collider in Geneva failed to produce any of the new elementary particles that theorists had been expecting for decades. These extra particles would solve a major puzzle about a known particle, the famous Higgs boson. The hierarchy problem, as the puzzle is called, asks why the Higgs boson is so lightweight—a hundred million times less massive than at the highest energy scales that exist in nature. The Higgs mass seems unnaturally tuned down relative to these higher energies, as if the huge numbers in the underlying equations that determine its value miraculously all cancel out.

The extra particles should have explained the tiny Higgs mass, restoring what physicists call the “naturalness” of their equations. But after the LHC — the third and largest collider — searched in vain for them, it seemed that the logic of what is natural in nature might be wrong. “We are faced with the need to reconsider the guiding principles that have been used for decades to address the most fundamental questions about the physical world,” Gian Giudice, head of the theory department at CERN, the laboratory that houses the LHC, wrote in 2017.

At first, the scientific community despaired.

“You could feel the pessimism,” says Isabel Garcia Garcia, a particle theorist at the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara, who was a graduate student at the time. Not only had the $10 billion proton smasher failed to answer a 40-year-old question, but the beliefs and strategies that had long guided particle physics could no longer be trusted. People are wondering more urgently than before whether the universe is simply unnatural, the product of fine-tuned mathematical cancellations. Perhaps there is a multiverse of multiple universes, all with random Higgs masses and other parameters, and we find ourselves here only because the special properties of our universe promoted the formation of atoms, stars, and planets, and thus life. This “anthropic principle,” although it might be correct, is frustratingly unprovable.

Many particle physicists have moved on to other areas of research “where the problems haven’t gotten as hard as the hierarchy problem,” says Nathaniel Craig, a theoretical physicist at the University of California, Los Angeles.

Image | Nathaniel Craig and Isabel Garcia Garcia explored how gravity helps reconcile the vastly different energy scales in nature. (Source: Jeff Liang)

Some of those who stayed behind began to take a closer look at decades-old assumptions. They began to rethink the striking features of nature that seemed unnaturally fine-tuned—the small mass of the Higgs boson and a seemingly unrelated question about the unnaturally low energy of space itself. “The real fundamental question is the question of naturalness,” Garcia Garcia said.

Their reflections are bearing fruit. Increasingly, researchers are zeroing in on what they see as a weakness in traditional reasoning about naturalness. It rests on a seemingly correct assumption that has informed science since the ancient Greeks. The idea that big things are made of smaller, more fundamental things is called reductionism. “The reductionist paradigm … is intrinsic to the problem of naturalness,” says Nima Arkani-Hamed, a theorist at the Institute for Advanced Study in Princeton, New Jersey.

Now, a growing number of particle physicists think the naturalness problem and the LHC null results may be linked to the breakdown of reductionism. “Is this a game changer?” Arkani-Hamed says.

In a series of recent papers, researchers have thrown reductionism out the window. They are exploring new ways that large and small distance scales might be coordinated, yielding parameter values ​​that are unnaturally fine-tuned from a reductionist perspective.

"Some people are calling it a crisis. There's an air of pessimism here, but I don't feel that way," Garcia Garcia said. "This is a time when I feel like we're doing something profound."

What is naturalness

The LHC did make one key discovery: In 2012, it finally discovered the Higgs boson, the cornerstone of a 50-year-old set of theories in particle physics known as the Standard Model, which describes the 17 known elementary particles.

The Higgs discovery confirms a fascinating story already written in the Standard Model theory.

Moments after the Big Bang, an entity that permeated space, called the Higgs field, suddenly became infused with energy. This Higgs field split apart to create Higgs bosons, particles that have mass because of the field's energy. As electrons, quarks, and other particles move through space, they interact with the Higgs bosons in such a way that they, too, gain mass.

Almost immediately after the Standard Model was completed in 1975, its designers noticed a problem.

When the Higgs imparts mass to other particles, they immediately give it back; the masses of the particles jiggle together. Physicists can write an equation for the mass of the Higgs boson that includes a relationship for every particle it interacts with.

All massive Standard Model particles contribute to this equation, but those aren't the only ones. The Higgs boson should also be mathematically mixed in with even heavier particles, including Planck-scale phenomena, an energy level associated with the quantum nature of gravity, black holes, and the Big Bang. The contribution of Planck-scale phenomena to the Higgs mass should be enormous -- almost 100 million times larger than the actual Higgs mass.

Naturally, you would expect the Higgs boson to be as heavy as they are, thus strengthening the other elementary particles as well. The particles would be too heavy to form atoms, and the universe would be empty.

For the Higgs boson, which, despite its dependence on enormous energies, ends up being so light, you have to assume that there are both positive and negative Planck contributions to its mass, and that they both have just the right amount to cancel out completely.

Unless there was some reason for this cancellation, it would be ridiculous—just as it is impossible for air currents and the vibrations of a table to cancel each other out to keep the tip of a pencil balanced. This kind of fine-tuned cancellation is what physicists consider "unnatural."

Within a few years, physicists found a satisfying solution: the theory of supersymmetry, which posits that nature's fundamental particles have a dual nature. Supersymmetry says that every boson (one of two types of particles) has a partner, a fermion (the other type), and vice versa. Bosons and fermions contribute positive and negative terms to the Higgs mass, respectively.

Therefore, if these terms always appear in pairs, they will always cancel out.

The search for supersymmetric partner particles began at the Large Hadron Collider in the 1990s. Researchers hypothesized that these particles would be slightly heavier than their Standard Model counterparts and require more raw energy to make, so they accelerated the particles to nearly the speed of light, smashed them together, and looked for the emergence of the heavy objects in the debris.

At the same time, another naturalness issue surfaced.

The fabric of space, even in the absence of matter, seems to ought to possess energy—the net activity of all the quantum fields flowing through it.

When particle physicists added up all the putative contributions to the energy of space, they found that, like the Higgs mass, an infusion of energy from Planck-scale phenomena should have blown it up.

Einstein reasoned that the energy of space—which he called the cosmological constant—had a gravitational repulsive effect that caused space to expand faster and faster. If space were infused with energy at the Planck density, the universe would have torn itself apart in the moments after the Big Bang. But that didn't happen.

Instead, cosmologists observed that the expansion of space was only slowly accelerating, suggesting that the cosmological constant was small.

Measurements in 1998 put it at a trillion times lower than the Planck energy. Again, in the equation for the cosmological constant, it seems that all these huge injections and extractions of energy cancel out perfectly, leaving space eerily calm.

"Gravity...mixes the physics of all length scales—short distances, long distances. And because it does that, it gives you this way out." — Nathaniel Craig

These two big naturalness problems had been apparent since the late 1970s, but for decades physicists treated them as irrelevant.

“This is at a stage where people are split about it,” Arkani-Hamed said. The cosmological constant problem seemed to be related to the mysterious, quantum aspects of gravity, since the energy of space is detected only through its gravitational effects. The hierarchy problem looked more like a “nasty little detail problem,” Arkani-Hamed explained — the kind of problem that, like two or three others in the past, would eventually reveal some missing puzzle piece. The “Higgs weakness,” as Giudice calls its unnatural lightness, is not something that a few supersymmetric particles from the Large Hadron Collider can’t cure.

In hindsight, these two naturalness issues seem more like symptoms of a deeper problem.

“It’s useful to think about how these questions arise,” Garcia Garcia said in a Zoom call from Santa Barbara this winter. “The hierarchy problem and the cosmological constant problem arise in part because of the tools we use to try to answer them — the way we try to understand certain features of our universe.”

Just the right reductionism

Physicists have their own interesting way of honestly counting the contributions of the Higgs mass and the cosmological constant.

This computational approach reflects the strange nested structure of nature.

Zoom in on something and you'll see that it's actually many smaller things.

What looks like a galaxy from a distance is actually a collection of stars; each star is many atoms; an atom is further dissolved into a hierarchy of subatomic parts.

Furthermore, when you zoom out to shorter distance scales, you see heavier, more energetic elementary particles and phenomena - this is a profound connection between high energies and short distances, explaining why high-energy particle colliders are like microscopes for the universe.

There are many examples throughout physics of the connection between high energy and short distances. For example, quantum mechanics states that every particle is also a wave, and the greater the mass of a particle, the shorter its associated wavelength. Another is that energy must be packed more densely together to form smaller objects. Physicists call low-energy, long-distance physics "infrared" and high-energy, short-distance physics "ultraviolet," using the wavelengths of infrared and ultraviolet light as an analogy.

In the 1960s and 1970s, particle physics giants Kenneth Wilson and Steven Weinberg pointed out something remarkable about nature’s hierarchical structure: It allows us to describe some interesting properties on large, infrared scales without knowing what’s “really” going on on even more microscopic, ultraviolet scales. For example, you can model water using a fluid dynamics equation that treats it as a smooth fluid, masking the complex dynamics of its H2O molecules. The fluid dynamics equations include a term that represents the water’s viscosity—a single number, measurable on the infrared scale, that summarizes all these molecular interactions that occur on the ultraviolet scale. Physicists say that “decoupling” the infrared and ultraviolet scales allows them to effectively describe aspects of the world without knowing what’s going on at the deep Planck scale—the ultimate ultraviolet scale, equivalent to a billionth of a trillionth of a centimeter, or energies of 100 billion billion electron volts (GeV), where the fabric of spacetime may dissolve into something else.

Kenneth Wilson, an American particle and condensed matter physicist active from the 1960s to the early 2000s, developed a formal mathematical method to describe how the properties of a system vary depending on the scale at which it is measured. (Source: Cornell University Faculty Biographical Archives, #47-10-3394. Rare and Manuscript Collections, Cornell University Library.)

"We can study physics because we can remain ignorant of what happens at short distances," said Riccardo Rattazzi, a theoretical physicist at the Swiss Federal Institute of Technology in Lausanne.

Wilson and Weinberg each developed fragments of the framework that particle physicists use to model different levels of our nested world: effective field theory. It is in the context of effective field theory that the question of naturalness arises.

The effective field theory models a system — let’s say a beam of protons and neutrons — over a certain range of scales. Scale up the protons and neutrons for a while, and they’ll keep looking like protons and neutrons, and you can describe their dynamics over that range using a “chiral effective field theory.” But then the effective field theory will reach its “ultraviolet cutoff,” a short-range, high-energy scale where the effective field theory is no longer a valid description of the system. At a cutoff of 1 GeV, for example, the chiral effective field theory stops working because the protons and neutrons no longer behave like individual particles but instead like trios of quarks. A different theory comes into play.

The point is that there is a reason why effective field theories break down at their ultraviolet cutoffs—the point where new, high-energy particles or phenomena not included in the theory must be found.

Within its range of validity, the effective field theory accounts for the UV physics below the cutoff by adding "corrections" that represent these unknown effects. This is like a fluid equation having a viscosity term to capture the net effect of short-range molecular collisions. Physicists don't need to know what actual physics is going on at the cutoff to write these corrections; they just use the scale of the cutoff as a rough estimate of the range of validity.

Normally, when you calculate something on the infrared scale of interest, the UV corrections are small, proportional to the (relatively small) length scale associated with the cutoff. However, this changes when you calculate parameters like the Higgs mass or the cosmological constant using effective field theory, because these parameters have units of mass or energy. The UV corrections to the parameters will be large, because (in order to have the right units) the corrections are coordinated with the energy, not with the length associated with the cutoff. When the length is small, the energy is high. Such parameters are said to be "UV-sensitive".

The concept of naturalness emerged in the 1970s along with effective field theory itself as a strategy for identifying where effective field theory must stop.

Therefore, new physics must exist. The logic goes like this. If a mass or energy parameter has a high cutoff, its value should naturally be large, pushed higher by all the UV corrections. Therefore, if the parameter is small, then the cutoff energy must be low.

Some critics have dismissed naturalness as a mere aesthetic preference. But others have pointed out that the strategy reveals precise, hidden truths about nature. “The logic works,” says Craig, a leader in a recent re-engagement with it. The question of naturalness “has always been a sign that things are changing and that something new should be coming.”

What can nature do?

In 1974, years before the term “naturalness” was coined, Mary K. Gaillard and Ben Lee used this strategy to stunningly predict the mass of a hypothetical particle then known as the charm quark. “Her successful prediction and its relevance to the hierarchy problem have been greatly underestimated in our field,” Craig said.

In the summer of 1974, Gaillard and Lee were puzzled by the difference in the masses of two quark particles—composite particles of quarks. The measured difference was tiny.

But when they tried to calculate this mass difference using the equations of effective field theory, they saw that its value was in danger of exploding. Because the hyon mass difference has units of mass, it is sensitive to ultraviolet light and receives high-energy corrections from unknown physics at the cutoff point. The cutoff point of the theory was not known, but physicists at the time reasoned that it could not be very high, otherwise the resulting hyon mass difference would be oddly small relative to the correction value—unnatural, as physicists now say.

Gaillard and Lee deduced a low cutoff scale for their effective field theory, where the new physics should emerge. They concluded that a then-proposed type of quark called the charm quark would have to be found with a mass no greater than 1.5 GeV.

Three months later, the charm quark emerged, weighing 1.2 GeV. The discovery ushered in a renaissance of knowledge known as the November Revolution and rapidly advanced the Standard Model. In a recent video call, Gaillard, now 82, recalled that she was in Europe visiting CERN when the news broke. Lee sent her a telegram: Charm had been discovered.

In 1974, Mary K. Gaillard (pictured in the 1990s) and Ben Lee used the naturalness argument to predict the mass of a hypothetical elementary particle called the charm quark. A few months later, the charm was already there. (Credit: AIP Emilio Segrè Visual Archives)

Such triumphs convinced many physicists that the hierarchy problem should also predict that the new particles would not be much heavier than those of the Standard Model.

If the Standard Model cutoff was somewhere near the Planck scale (where researchers are convinced the Standard Model fails because it doesn't account for quantum gravity), then the UV corrections to the Higgs mass would be so huge that it would seem unnatural. Putting a cutoff not far above the mass of the Higgs boson itself would make the Higgs mass as heavy as the corrections from the cutoff, and everything would look natural.

“This approach has been the starting point for the last 40 years of work trying to solve the hierarchy problem,” Garcia Garcia said. “People have come up with great ideas like supersymmetry, [Higgs] synthesis, and we haven’t seen them realized in nature.”

In 2016, GarciaGarcia was a PhD student in particle physics at Oxford University. A few years later, it became clear to her that a reckoning was needed. “That’s when I started to get more interested in this missing piece that we don’t usually think about when we talk about problems, which is gravity. And that’s a problem that can be seen more in quantum gravity than in effective field theory.”

Gravity mixes everything together

Theorists learned in the 1980s that gravity doesn't play by the usual reductive rules.

If you smash two particles together hard, their energy becomes concentrated at the point of collision, forming a black hole—a region of extreme gravity from which nothing can escape. Smash the particles together even harder, and they form a larger black hole. More energy no longer lets you see shorter distances; quite the opposite: the harder you smash, the larger the invisible region you create. Black holes, and the theories of quantum gravity that describe their interiors, completely reverse the usual relationship between high energies and short distances. “Gravity is anti-reductionist,” says Sergei Dubovsky, a physicist at New York University.

Quantum gravity seemed to play with the architecture of nature, mocking the neat system of nested scales of effective field theories that physicists had grown accustomed to. Like Garcia, Craig began thinking about the implications of gravity soon after the Large Hadron Collider search came up empty. While trying to think of new solutions to the hierarchy problem, Craig reread a 2008 paper on naturalness written by Giudice, a theorist at CERN.

He began to wonder what Giudice meant: Giudice had written that the solution to the cosmological constant problem might involve “some complicated interplay between the infrared and ultraviolet effects.” If the infrared and ultraviolet had a complicated interplay, that would violate the usual decoupling that allows effective field theory to work. “I just Googled things like ‘ultraviolet-infrared mixing,’ ” Craig said, which led him to some interesting papers from 1999, “and I started.”

"This is a time when I feel like we are onto something profound." - Isabel Garcia Garcia

UV-IR hybridization has the potential to solve the naturalness problem by breaking the reductionist scheme of effective field theory. In effective field theory, the naturalness problem arises when quantities like the Higgs mass and the cosmological constant become sensitive in the UV, but somehow doesn't blow up, as if there were a conspiracy between all the UV physics to invalidate their effects in the infrared. "In the logic of effective field theory, we throw out that possibility," Craig explains.

Reductionism tells us that infrared physics follows from ultraviolet physics—water's viscosity follows from its molecular dynamics, protons get their properties from their internal quarks, and explanations emerge with magnification—not the other way around. The ultraviolet is not affected or explained by the infrared, "so there can't be a conspiracy [of the ultraviolet effect] that makes the Higgs thing work out on a very different scale."

The question Craig is asking now is, “Does the logic of effective field theory break down?” Maybe explanations really can flow in both directions, from the UV to the IR.

“It’s not completely outlandish because we know gravity works like this,” he said. “Gravity violates normal effective field theory reasoning because it mixes the physics of all length scales, both short and long distances. And because it does that, it gives you this way out.”

How UV-IR hybridization can save naturalness

Several new studies of UV-IR mixing and how it might solve the naturalness problem refer to two papers that appeared in 1999. “There’s a growing interest in these more exotic, non-effective field-theory approaches to solving problems,” said Patrick Draper, a professor at the University of Illinois at Urbana-Champaign whose most recent work was based on a 1999 paper.

Draper and his colleagues studied the CKN constraint, named after the authors of the 1999 paper, Andrew Cohen, David B. Kaplan and Ann Nelson. They posited that if you put a particle in a box and heat it up, you can only increase the particle’s energy so much before the box collapses into a black hole.

They calculated that the number of high-energy particle states you can fit in before the box collapses scales with the surface area of ​​the box raised to the cube-quarter power, rather than the volume of the box as you might think.

This, they realized, represented a strange UV-infrared relationship. The size of the box, which sets the infrared scale, severely constrains the number of high-energy particle states that can exist within the box — the UV scale.

They then realized that if their same constraints applied to the entire universe, then it solved the cosmological constant problem. In this case, the observable universe is like a very large box. The number of high-energy particle states it can contain is proportional to the surface area of ​​the observable universe to the third power, not to the (much larger) volume of the universe.

This means that the usual effective field-theoretic calculations of the cosmological constant are too simple.

This calculation tells you that when you zoom in on the fabric of space, high-energy phenomena should appear, and there should be energy to blow up space. But the CKN constraint means there could be much less high-energy activity than the effective field theory calculations assume, which means there are only a few high-energy states for particles to occupy. Cohen, Kaplan, and Nelson did a simple calculation, and for a box the size of our universe, their constraint more or less accurately predicted the tiny observed value of the cosmological constant.

Their calculations suggest that the large and small scales may be correlated in a way that becomes apparent when you look at infrared properties of the entire universe, such as the cosmological constant.

Draper and Nikita Blinov confirmed last year in another back-of-the-envelope calculation that the CKN constraint predicts the observed cosmological constant. They also confirmed that it does not undermine the many successes of effective field theories in small-scale experiments.

The CKN constraint doesn't tell you why the UV and IR are correlated, i.e. why the size of the box (IR) severely constrains the number of high energy states inside the box (UV). For that, you probably need to understand quantum gravity.

Other researchers have looked for answers in one particular theory of quantum gravity: string theory. Last summer, string theorists Steven Abel and Keith Dienes showed how ultraviolet-infrared mixing in string theory could resolve the hierarchy and cosmological constant problems.

String theory, a candidate for the fundamental theory of gravity and everything else, posits that all particles, up close, are little vibrating strings. Standard model particles like photons and electrons are low-energy vibrational modes of fundamental strings. But strings can also wiggle more energetically, giving rise to an infinite spectrum of string states with higher and higher energies. In this case, the hierarchy problem asks why these string-state corrections don't cause it to expand if there's no such thing as supersymmetry to protect the Higgs.

Dienes and Abel calculated that, because of a different symmetry of string theory, called modular invariance, string corrections at all energies across the infinite spectrum from infrared to ultraviolet would cancel each other out in just the right way to make both the Higgs mass and the cosmological constant small. The researchers note that this collusion between low-energy and high-energy string states doesn’t explain why there’s such a big gap between the Higgs mass and the Planck energy in the first place, only that the gap is stable. Still, to Craig, “It’s a really good idea.”

The new model represents a growing body of thinking about UV-IR mixing. Craig’s angle can be traced back to another 1999 paper, written by Nathan Seiberg, a prominent theorist at the Institute for Advanced Study, and two co-authors. They looked at the case where there is a background magnetic field filling space. To understand how UV-IR mixing arises here, imagine a pair of charged particles connected by a spring flying through space, perpendicular to the magnetic field. As you increase the energy of the magnetic field, the charged particles speed apart, stretching the spring. In this scenario, higher energy corresponds to longer distances.

“Gravity is anti-reductionist.” —Sergei Dubovsky

Seiberg and his colleagues found that the UV corrections in this case have special features that suggest that reductionism can be reversed, that is, the infrared affects what happens in the UV. This model is not realistic because the real universe does not have a magnetic field that imposes a background directionality. However, Craig has been exploring whether something similar could be a solution to the hierarchy problem.

Craig, Garcia Garcia and Seth Koren also worked together on a proposition about quantum gravity known as the weak gravity conjecture, which, if true, could impose consistency conditions that would naturally require a large separation between the Higgs mass and the Planck scale.

Dubovsky of New York University has been mulling over these questions since at least 2013, when it became clear that supersymmetric particles were sluggish at the Large Hadron Collider. That year, he and two collaborators discovered a new model of quantum gravity that solved the hierarchy problem: In it, the arrows of reductionism point from an intermediate scale to both the ultraviolet and the infrared. As appealing as it sounded, the model worked only in two dimensions, and Dubovsky had no idea how to unfold it. He turned to other problems. Last year, he encountered the ultraviolet-infrared mixing again. He found that the naturalness problem that arose in studying colliding black holes was solved by a “hidden” symmetry that links low-frequency and high-frequency deformations of the black hole’s shape.

Like other researchers, Dubovsky doesn’t seem to think that any of the specific models found so far bear clear signs of a Kuhnian revolution. Some think the whole UV-IR hybrid concept lacks promise. “There’s no sign of a breakdown of effective field theory,” says David E. Kaplan, a theoretical physicist at Johns Hopkins University (no relation to the CKN paper). “I don’t think there’s anything there.”

To convince everyone, the idea needs experimental evidence, but so far, existing hybrid UV-IR models are woefully inadequate in terms of testable predictions. They are generally designed to explain why we haven't seen new particles beyond the Standard Model, rather than predict what we should see. But in cosmology, there's always hope for future predictions and discoveries, even if not from a collider.

Taken together, the new hybrid UV-IR model illustrates the weaknesses of the old paradigm—a paradigm based entirely on reductionism and effective field theory—and this may be just the beginning.

“When you get to the Planck scale, you lose reductionism, so gravity is anti-reductionist,” Dubovsky said. “I think in some sense it would be unfortunate if this fact didn’t have a profound impact on what we observe.”

References:

https://www.quantamagazine.org/crisis-in-particle-physics-forces-a-rethink-of-what-is-natural-20220301/

Academic headlines