How the Higgs Is, and Is Not, Like an Eel

In the past, what did we know about eel reproduction? What do we know now?

The answer to both questions is, surprisingly little! For those who don’t know the story, I recommend this New Yorker article. Eels turn out to have a quite complicated life cycle, and can only reproduce in the very last stage. Different kinds of eels from all over Europe and the Americas spawn in just one place: the Sargasso Sea. But while researchers have been able to find newborn eels in those waters, and more recently track a few mature adults on their migration back, no-one has yet observed an eel in the act. Biologists may be able to infer quite a bit, but with no direct evidence yet the truth may be even more surprising than they expect. The details of eel reproduction are an ongoing mystery, the “eel question” one of the field’s most enduring.

But of course this isn’t an eel blog. I’m here to answer a different question.

In the past, what did we know about the Higgs boson? What do we know now?

Ask some physicists, and they’ll say that even before the LHC everyone knew the Higgs existed. While this isn’t quite true, it is certainly true that something like the Higgs boson had to exist. Observations of other particles, the W and Z bosons in particular, gave good evidence for some kind of “Higgs mechanism”, that gives other particles mass in a “Higgs-like-way”. A Higgs boson was in some sense the simplest option, but there could have been more than one, or a different sort of process instead. Some of these alternatives may have been sensible, others as silly as believing that eels come from horses’ tails. Until 2012, when the Higgs boson was observed, we really didn’t know.

We also didn’t know one other piece of information: the Higgs boson’s mass. That tells us, among other things, how much energy we need to make one. Physicists were pretty sure the LHC was capable of producing a Higgs boson, but they weren’t sure where or how they’d find it, or how much energy would ultimately be involved.

Now thanks to the LHC, we know the mass of the Higgs boson, and we can rule out some of the “alternative” theories. But there’s still quite a bit we haven’t observed. In particular, we haven’t observed many of the Higgs boson’s couplings.

The couplings of a quantum field are how it interacts, both with other quantum fields and with itself. In the case of the Higgs, interacting with other particles gives those particles mass, while interacting with itself is how it itself gains mass. Since we know the masses of these particles, we can infer what these couplings should be, at least for the simplest model. But, like the eels, the truth may yet surprise us. Nothing guarantees that the simplest model is the right one: what we call simplicity is a judgement based on aesthetics, on how we happen to write models down. Nature may well choose differently. All we can honestly do is parametrize our ignorance.

In the case of the eels, each failure to observe their reproduction deepens the mystery. What are they doing that is so elusive, so impossible to discover? In this, eels are different from the Higgs boson. We know why we haven’t observed the Higgs boson coupling to itself, at least according to our simplest models: we’d need a higher-energy collider, more powerful than the LHC, to see it. That’s an expensive proposition, much more expensive than using satellites to follow eels around the ocean. Because our failure to observe the Higgs self-coupling is itself no mystery, our simplest models could still be correct: as theorists, we probably have it easier than the biologists. But if we want to verify our models in the real world, we have it much harder.

3 thoughts on “How the Higgs Is, and Is Not, Like an Eel

  1. Chris Bolger

    I’ve never believed that the Higgs is the sole solution to EWSB. I don’t see how one particle can have so many different couplings to so many different particles that seem to have no pattern. Now, if there were a bunch of Higgs particles that mixed with each other and we have found the lightest that would make sense, one idea among many, many others. I do think we will find some more of them, maybe a lot more, but the rest maybe pretty massive.

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  2. ohwilleke

    Certainly, however, the reasons to doubt the hypothesis of a simple Standard Model Higgs boson are greatly diminished, however, from what they were as recently at 2011.

    We’ve confirmed not just that it exists and has a particular mass, but that it is to considerable certainty that as predicted, it is an even parity scalar boson whose couplings and width are to the limits of experimental accuracy consistent with that model, to bounds that are tolerably close. As of six months ago, a global measure of the Higgs boson signal strength was within 11 ± 8.5% of the SM value according to ATLAS and 17 ± 10% according to CMS (see http://pdg.lbl.gov/2019/reviews/rpp2019-rev-higgs-boson.pdf ) and indirect constraints put the best fit to the width (i.e. mean lifetime) at 4.1 MeV (the SM value) + 0.7 – 0.8 MeV (i.e. less than 20%).

    Equally important, we have no evidence of any kind tugging us in the direction of another or more complicated model. For example, direct searches for a pseudo-scalar Higgs, a charged Higgs, or a scalar Higgs at a different mass, have all come up empty over an increasingly wide range of masses.

    We also have the little nugget that surely has to be more than coincidence, first noted in a paper by Lopez Castro and Pestieau on May 17, 2013, https://arxiv.org/abs/1305.4208 , that continues to be consistent with all available data, which is that the sum of the square of the masses of the fundamental fermions (i.e. the six quarks and six leptons) and bosons of the Standard Model (i.e. the W, the Z and the Higgs) is equal to the square of the Higgs vacuum expectation value, to the limits of the accuracy of those experimental measurements (they are consistent at roughly a 1.3 sigma level with the latest PDG and FLAG19 values, which in absolute terms is a roughly 0.5% discrepancy, the uncertainty in the top quark mass and Higgs boson mass account for 98.8% of the uncertainty in the total square mass values with most of the rest from the b quark mass), a relationship which suggests that the particle content of the SM may be complete (with the possible exception of BSM particles much lighter than the Higgs boson and top quark, which the LHC has largely, but not necessarily completely, ruled out). Another way of stating the relationship is that the sum of the fundamental particle Yukawa’s (or Yukawa equivalents for particles whose Higgs boson coupling isn’t properly described in that way) sum to exactly 1 (incidentally, the sum of the square of the fundamental fermion masses is extremely likely to not be equal to the sum of the square of the fundamental boson masses at greater than 4 sigma level with the fermions a bit light and the bosons a bit heavy).

    Yes, ultimately, it is always better to test any hypothesis as directly as possible. But, at some point doesn’t it make sense to take a leap of faith and dramatically downgrade the Baysean priors on the alternatives?

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    1. 4gravitons Post author

      I’d quibble a bit with your statement that “whose couplings and width are to the limits of experimental accuracy consistent with that model, to bounds that are tolerably close” – if you check the PDG, you’ll see that the only coupling with any experimental constraint whatsoever is the top Yukawa, none of the other Yukawas nor the the Higgs self-coupling have any experimental constraints whatsoever, they’re purely inferred from the masses and the Standard Model.

      The coincidence you point out is, if it means anything, evidence for BSM physics, not against it, because it doesn’t have any explanation within the SM: unlike patterns in the charges of the fermions, there is no known anomaly condition that would make the sum of the Yukawas one. If it’s real it would suggest that no new particles get their mass from the Higgs (which is true of many BSM proposals), not that such particles don’t exist at all.

      (That passage is sprinkled liberally with “if”s because, well, I’m skeptical. I haven’t worked through the math, but it seems weird that couplings with very disparate forms are in there together…it makes me worry a bit about double-counting…one way to think about this is to look at equation (2) of that paper, which has g^2/2 but g’^2/4.)

      Also, I think you’re conflating/confusing the more “motivated” extensions of the Standard Model (“add an X to solve the Y problem”) with just raw uncertainty. There are a bunch of specific models that have been tweaked over and over again to avoid contact with the data, and I agree it’s worth being much less bullish about those at this point. But there are details of the SM for which we simply don’t have good evidence, which could pretty easily be otherwise, and until we have evidence for them we shouldn’t be assuming one way or another.

      In the analogy with eel reproduction, I would assume biologists have some pretty secure ideas of how it works: unlike Freud, modern biologists have been able to dissect mature eels. They still want to observe it, presumably there’s still some certainty there.

      (I’m going to say something more specific about the Higgs here, at the risk of it being stupid. I’ve asked people about the following a few times but haven’t yet gotten a convincing answer, so I don’t know whether there’s some obvious objection an expert would know.

      Experimentally, we know two things about the Higgs potential: the position of one of its minima, and the second derivative around that minimum. We don’t know anything else. In the simplest model, we think of the Higgs potential as having a quadratic term and a quartic term, with any terms of higher order being very very small. With that assumption, knowing the position of and second derivative at the minimum gives you the coefficients of those two terms, and lets you predict the triple-Higgs coupling.

      The trouble is, it’s not at all clear to me that that assumption (that the higher terms are small) is justified. It relies on some of the same logic as naturalness arguments: in crude terms, it assumes that unknown constants are close to one. Given that naturalness seems to be serving us pretty poorly these days, I don’t know how much you can trust those arguments. If you can’t, then we don’t know the triple-coupling at all: you can’t predict the third derivative of a function just from its first and second derivatives. With that in mind, the claim that we would see the Higgs triple-coupling at the next collider is a very specific prediction from a very particular approach, and anyone who doubts that approach should expect us to see something unexpected there.

      One possible issue with the above: there are bounds from unitarity on these higher coefficients. I don’t know if those bounds force the coefficients to be so small that this argument fails.

      Other possible issue with the above: I’m not a phenomenologist, this is very much not my corner of the field. Experts, feel free to tell me why I’m wrong!)

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