Neutrinos and Guarantees

The Higgs boson, or something like it, was pretty much guaranteed.

When physicists turned on the Large Hadron Collider, we didn’t know exactly what they would find. Instead of the Higgs boson, there might have been many strange new particles with different properties. But we knew they had to find something, because without the Higgs boson or a good substitute, the Standard Model is inconsistent. Try to calculate what would happen at the LHC using the Standard Model without the Higgs boson, and you get literal nonsense: chances of particles scattering that are greater than one, a mathematical impossibility. Without the Higgs boson, the Standard Model had to be wrong, and had to go wrong specifically when that machine was turned on. In effect, the LHC was guaranteed to give a Nobel prize.

The LHC also searches for other things, like supersymmetric partner particles. It, and a whole zoo of other experiments, also search for dark matter, narrowing down the possibilities. But unlike the Higgs, none of these searches for dark matter or supersymmetric partners is guaranteed to find something new.

We’re pretty certain that something like dark matter exists, and that it is in some sense “matter”. Galaxies rotate, and masses bend light, in a way that seems only consistent with something new in the universe we didn’t predict. Observations of the whole universe, like the cosmic microwave background, let us estimate the properties of this something new, finding it to behave much more like matter than like radio waves or X-rays. So we call it dark matter.

But none of that guarantees that any of these experiments will find dark matter. The dark matter particles could have many different masses. They might interact faintly with ordinary matter, or with themselves, or almost not at all. They might not technically be particles at all. Each experiment makes some assumption, but no experiment yet can cover the most pessimistic possibility, that dark matter simply doesn’t interact in any usefully detectable way aside from by gravity.

Neutrinos also hide something new. The Standard Model predicts that neutrinos shouldn’t have mass, since it would screw up the way they mess with the mirror symmetry of the universe. But they do, in fact, have mass. We know because they oscillate, because they change when traveling, from one type to another, and that means those types must be mixes of different masses.

It’s not hard to edit the Standard Model to give neutrinos masses. But there’s more than one way to do it. Every way adds new particles we haven’t yet seen. And none of them tell us what neutrino masses should be. So there are a number of experiments, another zoo, trying to find out. (Maybe this one’s an aquarium?)

Are those experiments guaranteed to work?

Not so much as the LHC was to find the Higgs, but more than the dark matter experiments.

We particle physicists have a kind of holy book, called the Particle Data Book. It summarizes everything we know about every particle, and explains why we know it. It has many pages with many sections, but if you turn to page 10 of this section, you’ll find a small table about neutrinos. The table gives a limit: the neutrino mass is less than 0.8 eV (a mysterious unit called an electron-volt, about ten-to-the-minus-sixteen grams). That limit comes from careful experiments, using E=mc^2 to find what the missing mass could be when an electron-neutrino shoots out in radioactive beta decay. The limit is an inequality, “less than” rather than “equal to”, because the experiments haven’t detected any missing mass yet. So far, they only can tell us what they haven’t seen.

As these experiments get more precise, you could imagine them getting close enough to see some missing mass, and find the mass of a neutrino. And this would be great, and a guaranteed discovery, except that the neutrino they’re measuring isn’t guaranteed to have a mass at all.

We know the neutrino types have different masses, because they oscillate as they travel between the types. But one of the types might have zero mass, and it could well be the electron-neutrino. If it does, then careful experiments on electron-neutrinos may never give us a mass.

Still, there’s a better guarantee than for dark matter. That’s because we can do other experiments, to test the other types of neutrino. These experiments are harder to do, and the bounds they get are less precise. But if the electron neutrino really is massless, then we could imagine getting better and better at these different experiments, until one of them measures something, detecting some missing mass.

(Cosmology helps too. Wiggles in the shape of the universe gives us an estimate of the total, the mass of all the neutrinos averaged together. Currently, it gives another upper bound, but it could give a lower bound as well, which could be used along with weaker versions of the other experiments to find the answer.)

So neutrinos aren’t quite the guarantee the Higgs was, but they’re close. As the experiments get better, key questions will start to be answerable. And another piece of beyond-the-standard-model physics will be understood.

8 thoughts on “Neutrinos and Guarantees

  1. Pavel

    I don’t know what the experiment measuring neutrino mass measure, but I’m pretty sure they don’t measure electron neutrino mass, because electron neutrino mass is not a well define measurable. Electron neutrino is a mixture of three neutrinos with well defined masses so I expect the experiments measure all three masses with some probability. However, as I wrote, I don’t understand what they really measure.

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    1. 4gravitons Post author

      Yeah, saying they measure electron-neutrino mass is a simplification. What they actually measure is a weighted average of the masses of the different neutrino mass states that contribute to the electron neutrino. This then lets you constrain the lightest or heaviest neutrino mass (depending on whether it’s an inverted or normal hierarchy).

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      1. Pavel

        I would say even your answer a simplification. Based on my naïve knowledge of the quantum mechanics, I would expect some interference pattern of the three neutrino mass eigenstates in the electron spectrum at low energies. However I don’t know what information can be extracted from it.

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        1. 4gravitons Post author

          Still a simplification, yes. The full answer is that you don’t get an interference pattern or anything like that for two reasons:

          1) Currently the experiments are just establishing upper bounds, so you’re not seeing a distribution of masses to begin with.

          2) Even when they start seeing something, they may not have enough resolution to distinguish the different mass states.

          So in practice, what you’re measuring is a sum \sum_i |U_{ei}|^2 m_{\nu_i}^2, where U is the mixing matrix (so it gives the coefficients of the superposition). It’s that number that’s being constrained, and with other experiments constraining the entries of U, that gives you a constraint on the neutrino masses.

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  2. StrangeCharm

    Sorry for late reply

    I’m confused as to why neutrinos need mass. The PNMS matrices are centered on the neutrinos by convention, why can’t we shift the oscillation behavior onto the charged leptons and leave the neutrinos massless? Then we don’t need R-handed neutrinos?

    I’m obviously missing something major here but I’m too sleep-deprived to think through the math

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    1. 4gravitons Post author

      I think wherever you put the PMNS matrix, you still have the issue that it doesn’t do anything observable unless some other part of the Lagrangian couples to the other basis of states. Otherwise you could just do a unitary transformation and remove the matrix completely. That doesn’t need to be masses I suppose, but if not it would have to be an interaction with some hidden sector that lines up with the “mass basis” instead. (And if there’s a Higgs mechanism that gives neutrinos their masses, this would be how it would work.)

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