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Physics + MathPhysics & Math

Why is the Higgs So Light?

ByDon LincolnThe Nature of RealityThe Nature of Reality

On July 4, 2012, the CERN auditorium was full. That’s not unusual; the room often hosts scientific presentations to packed houses. What was unusual was that this seminar was watched by millions of people worldwide, including reporters from high-impact media outlets like BBC, CNN, and The New York Times.

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So what was the announcement that caused a hectic world to briefly pause and listen? A new subatomic particle had been discovered , and its properties were consistent with those predicted for the long-sought Higgs boson. The Higgs boson, if it exists, is the experimental evidence needed to confirm the existence of the Higgs field, which is thought to give fundamental subatomic particles their mass.

Physicists were careful to not claim that they had conclusively discovered the Higgs boson. The Higgs boson was predicted in 1964 to have a litany of very specific properties. Until scientists are able to demonstrate that the newly-discovered particle matches all of the predictions, there remains the possibility that the new particle is something wholly unexpected. Of the properties that had been tested prior to the seminar, all of them pointed to this being the Higgs, which is why scientists said “consistent with the Higgs boson.” Using a metaphor involving the senses, what was found looked and smelled like the Higgs boson, but nobody had been able to taste, feel and touch it. So some uncertainty remained. This uncertainty still remains today, and it will be some time before scientists can definitively state that the observed particle was the Higgs boson.

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But let’s imagine that the discovered particle, which is a boson of mass about 125 times that of the proton, is the Higgs boson. What then?

You’d think scientists would celebrate (and we did…more than a few champagne corks were popped), but once the confetti settled, there were some furrowed brows. Nobody understood why the mass of the Higgs boson was so low. Here’s the source of the conundrum.

A Higgs boson doesn’t always exist as a Higgs boson. Like other quantum particles, it can change forms . For instance, it can briefly convert into a pair of top quarks before coalescing back into a Higgs boson. These evanescent top quarks are called “virtual particles” and are just an example of the several kinds of particles into which a Higgs boson can temporarily fluctuate. So, if you want to predict the mass of the Higgs, you have to take all of these possible forms into account.

Why is the Higgs So Light?-higgs_virtual_fluctuations_500.jpg

Higgs bosons can spontaneously convert into pairs of other subatomic particles. These pairs exist only for a very short time, but their existence will alter the mass of the Higgs boson.

Mathematically, we split the mass of the Higgs into two parts: its “theoretical” mass—that is, the mass it would have if didn’t fluctuate into different particles—plus the effect of the fluctuations. (For the technically brave, I put the equation that describes this in a footnote 1 .)

To make things even more complicated, the effect of the fluctuations also comes in two pieces. These two terms are multiplied, not added, together. The first term involves the maximum energy for which the Higgs theory applies. This works out to be a huge number, about 10 38 GeV 2 .

The second term is, roughly speaking, the sum of the effect of the bosons (W, Z & Higgs) minus the sum of the effect of the fermions (top quark). Let’s call this the fermion/boson sum.

So, let’s take a birds-eye view of the whole equation. The mass of the Higgs is equal to the theoretical mass plus a monstrously large number multiplied by the fermion/boson sum. Unless the fermion/boson sum is practically zero, the observed mass of the Higgs boson should be huge.

The only way to escape this conclusion is to somehow balance the fermion/boson sum to be exceedingly small. And to have the balance so perfect is utterly unnatural, as if we added up all the monthly paychecks of everyone in the United States and subtracted their monthly bills and those two huge numbers canceled out neatly.

That doesn’t happen in bookkeeping, and it shouldn’t happen in physics, either; unless, that is, there is some new and as-yet-undiscovered physical principle that enforces it. Thus, the small mass of the Higgs boson all but ensures that there is new physics to be discovered. Otherwise, we have to “tune” the masses of these particles to very precise values. Such precise balancing is utterly unnatural in physics theories, leading theoretical physicists to propose a series of ways in which this cancellation could occur naturally.

The most popular is a principle called supersymmetry . At the core of supersymmetry is the idea that, for every known fermion (quarks and leptons), there is a cousin boson (called squarks and sleptons) that we haven’t yet discovered. Similarly, for every known boson (e.g. photon, W, Z, gluon and Higgs boson), there is a cousin, also-undiscovered, fermion (called a photino, wino, zino, gluino and Higgsino). Because every fermion has a cousin boson (and vice versa), the fermion/boson sum is identically zero. Each particle cancels out exactly the effect of the cousin particle predicted by supersymmetry.

There are many technical issues that need to be addressed, not the least of which is that the predicted cousin particles have never been observed. But, so far, scientists can get around that problem. Thus supersymmetry remains an interesting idea.

If the particle found in July of 2012 is the Higgs boson, it definitely brings with it a very puzzling problem. As physicists begin to accept that the Higgs boson has likely been found, they are turning their attention to this most unnatural quandary. The main focus of the LHC is now becoming a search for a natural solution to this difficult question: Why is the Higgs so light?

The actual equation is the following: Mass(Higgs, observed) 2 = Mass(Higgs, theoretical) 2 + [k Λ] 2 × [Mass(Z boson) 2 + 2 × Mass(W boson) 2 +Mass(Higgs, theoretical) 2 – 4 × Mass(top quark) 2 ]. k is a technical constant and Λ is the maximum energy that the theory applies.

Go Deeper
Editor’s picks for further reading

The Nature of Reality: Bittersweet Victory: Physics After the Higgs
A look at the implications of the Higgs on the future directions of physics research.

The Nature of Reality: Thanks, Mom! Finding the Quantum of Ubiquitous Resistance
In this blog post, physicist Frank Wilczek celebrates the July 4 Higgs announcement.

Quantum Diaries: Why The Higgs Boson Should Not Exist and Why This Is a Good Thing
Physicist Richard Ruiz asks why the Higgs boson is so light.

This project/research was supported by grant number FQXi-RFP-1822 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor-advised fund of Silicon Valley Community Foundation.