Particle Physics


Why is the Higgs So Light?

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.

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.

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.


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 footnote1.)

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 1038 GeV2.

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.

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Don Lincoln

    Don Lincoln is a senior experimental particle physicist at Fermi National Accelerator Laboratory and an adjunct professor at the University of Notre Dame. He splits his research time between Fermilab and the CERN laboratory, just outside Geneva, Switzerland. He has coauthored more than 500 scientific papers on subjects from microscopic black holes and extra dimensions to the elusive Higgs boson. When Don isn’t doing physics research, he spends his time sharing the fantastic world of science with anyone who will listen. He has given public lectures on three continents and has authored many magazine articles, YouTube videos and columns in the online periodical Fermilab Today. His most recent book "The Large Hadron Collider: The Extraordinary Story of the Higgs Boson and Other Stuff That Will Blow Your Mind" tells the tale of the Large Hadron Collider, the physics and the technology required to make it all work, and the human stories behind the hunt for the Higgs boson.

    • Huh?

    • Anon

      If the Higgs field is that by which other particles achieve mass, wouldn’t the minimum energy to be ascribed to the Higgs be the sum of masses of all particles in the experiment no matter how they are split including the mass of whatever particle appears to be the distinctly the Higgs? If this idea is correct, would this account for the large amount of missing mass that the article mentions?

    • Anonymous

      Thanks Professor Lincoln for an enlightening summary. I have a couple of questions. If Supersymmetry is true (I guess some version of it) would that in fact solve the mass problem regarding the fermion-boson mass problem in the mass equation – or would there still be a problem with a light Higgs mass? Second, what if Supersymmetry isn’t true (lately we’ve heard unhappy news)? Are there other ways that the fermion-boson mass sum or difference could be dealt with, or is that still a very open question? Third, how about mass fluctuations? Doesn’t the Standard Model suggest (?) the mass of the Higgs itself should fluctuate, even when it is not decayed? A mass value of 125 seems too stable for fluctuations, is that not so? I’m not sure if my last question here is meaningful.

      • One of the most attractive features of supersymmetry is how it solves the problem of the light Higgs boson. Because that second term in the equation is (boson – fermion) and because supersymmetry says that for every boson there is a fermion and vice versa, that second term is identically zero by construction.

        Of course, that perfect cancellation occurs only if the supersymmetric extra particles have the mass of their ordinary matter counter parts and we know that’s not true. In fact, when people say “supersymmetry is dead,” that’s what they’re talking about. You can calculate what that second term will be for a variety of mass differences between the supersymmetric and ordinary particles and there comes a point where the cancellation no longer works. We are approaching the point where in the simplest of the supersymmetric models that we can no longer zero out the second term. Hence people become disillusioned with supersymmetry. On the other hand, there are many kinds of models that incorporate supersymmetry. Definitively ruling it out is harder than it sounds in the press.

        There are other ways the boson-fermion sum can be handled. For instance the unnatural fine tuning. Maybe there is some other principle that causes the matching to be so good. While there are lots of theoretical ideas floating around, none have been explored to the same degree that supersymmetry does.

        Until we know the answer, this will all be an open question.

        The columns must have a finite length and I was unable to put in some other explanations…maybe a follow on column. However, another option is to tame the big 10^38 term. This can be done if extra dimensions exist or if the Higgs boson is composite.

        For your last question, all particles have a finite width. Typically, the longer they live, the more narrow the width. That isn’t an iron-clad rule, but it’s a good one. The mass range of the 125 GeV Higgs is narrow. I can say this with assurance, as it is a theoretical statement. The predicted width is about 10 MeV, which is about 0.01% the value of the mass of the Higgs. Experimentally, we can’t measure anything to that precision (and may well never be able to do that). However, there are other particles with a larger mass range and we’ve certainly demonstrated that.



    • Zach H.


    • his can be understood in terms of quantum impedances. details at

    • Jason

      Thanks! I appreciate the way you put it for us laymen…I think the new discovery at CERN will push physics and the universe as we see it to a whole different level.

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