Earlier this week I explained how neutrinos can get their mass within the Standard Model of particle physics, either by engaging with the Higgs field once, the way the other particles do, or by engaging with it twice. In the first case, the neutrinos would be “Dirac fermions”, just like electrons and quarks. In the second, they’d be “Majorana fermions”. Decades ago, in the original Standard Model, neutrinos were thought not to have any mass at all, and were “Weyl fermions.” Although I explained in my last post what these three types of fermions are, today I want go a little deeper, and provide you with a diagrammatic way of understanding the differences among them, as well as a more complete view of the workings of the “see-saw mechanism”, which may well be the cause of the neutrinos’ exceptionally small masses.
[N.B. On this website, mass means “rest mass” except when otherwise indicated.]
The Three Types of Fermions
What’s a fermion? All particles in our world are either fermions or bosons. Bosons are highly social and are happy to all do the same thing, as when huge numbers of photons are all locked in synch to make a laser. Fermions are loners; they refuse to do the same thing, and the “Pauli exclusion principle” that plays a huge role in atomic physics, creating the famous shell structure of atoms, arises from the fact that electrons are fermions. The Standard Model fermions and their masses are shown below.
Figure 1: The masses of the known elementary particles, showing how neutrino masses are much smaller and much more uncertain than those of all the other particles with mass. The horizontal grey bar shows the maximum masses from cosmic measurements; the vertical grey bars give an idea of where the masses might lie based on current knowledge, indicating the still very substantial uncertainty.
For the general reader interested in particle physics or astronomy:
Most of the Standard Model’s particles have a mass [a rest mass, to be precise], excepting only the photon (the particle of light) and the gluon (found in protons and neutrons.) For reasons not understood at all, these masses stretch out over a range of a trillion or more.
If it weren’t for the three types of neutrinos, the range would be a mere 400,000, from the top quark’s mass (172 GeV/c2) to the electron’s (0.000511 GeV/c2), still puzzling large. But neutrinos make the puzzle extreme! The universe’s properties strongly suggest that the largest mass among the neutrinos can’t be more than 0.0000000001 GeV/c2 , while other experiments tell us it can’t be too much less. The masses of the other two may be similar, or possibly much smaller.
Figure 1: The masses of the known elementary particles, showing how neutrino masses are much smaller and much more uncertain than those of all the other particles with mass. The horizontal grey bar shows the maximum masses from cosmic measurements; the vertical grey bars give an idea of where the masses might lie based on current knowledge, indicating the still very substantial uncertainty.
This striking situation is illustrated in Figure 1, in which
I’ve used a “logarithmic plot”, which compresses the vertical scale; if I used a regular “linear” plot, you’d see only the heaviest few masses, with the rest crushed to the bottom;
For later use, I’ve divided the particles into two classes: “fermions” and “bosons”.
Also, though some of these particles have separate anti-particles, I haven’t shown them; it wouldn’t add anything, since the anti-particle of any particle type has exactly the same mass.
As you can see, the neutrinos are way down at the bottom, far from everyone else? What’s up with that? The answer isn’t known; it’s part of ongoing research. But today I’ll tell you why
once upon a time it was thought that the Standard Model solved this puzzle;
today we know of two simple solutions to it, but don’t know which one is right;
each of these requires a minor modification of the Standard Model: in one case a new type of particle, in another case a new phenomenon.
There has long been a question as to what types of events and processes are responsible for the highest-energy neutrinos coming from space and observed by scientists. Another question, probably related, is what creates the majority of high-energy cosmic rays — the particles, mostly protons, that are constantly raining down upon the Earth. As scientists’ … Read more
As promised in my last post, I’ve now written the answer to the second of the three questions I posed about how the Large Hadron Collider [LHC] can search for dark matter. You can read the answers to the first two questions here. The first question was about how scientists can possibly look for something … Read more
Well it’s not much to write home about, and I’m not going to write about it in detail right now, but the Resonaances blog has done so (and he’s asking for your traffic, so please click): A team of six astronomers reports that when they examine the light (more specifically, the X-rays) coming from clusters … Read more
Some readers may remember that back in May, as I discussed in some detail, the IceCube experiment reported a new and exciting observation — possibly the first discovery of high-energy astrophysical neutrinos: neutrinos, with energies 5 – 50 times higher than those of the protons at the Large Hadron Collider, created in outer space and arriving … Read more
In my last post, I promised you some comments on a couple of other news stories you may have seen. Promise kept! see below.
But before I go there, I should mention (after questions from readers) an important distinction. Wednesday’s post was about the simple process by which a Bs meson (a hadron containing a bottom quark and a down[typo] strange anti-quark, or vice versa, along with the usual crowd of gluons and quark/antiquark pairs) decays to a muon and an anti-muon. The data currently shows nothing out of the ordinary there. This is not to be confused with another story, loosely related but with crucially different details. There are some apparent discrepancies (as much as 3.7 standard deviations, but only 2.8 after accounting for the look-elsewhere effect) cropping up in details of the intricate process by which a Bd meson (a hadron containing a bottom quark and a down antiquark, or vice versa, plus the usual crowd) decays to a muon, an anti-muon, and a spin-one Kaon (a hadron containing a strange quark and a down anti-quark, or vice versa, plus the usual crowd). The measurements made by the LHCb experiment at the Large Hadron Collider disagree, in some but not all features, with the (technically difficult) predictions made using the Standard Model (the equations used to describe the known particles and forces.)
Don’t confuse these two processes! (Top) The process B_s –> muon + anti-muon, covered in Wednesday’s post, agrees with Standard Model predictions. (Bottom) The process B_d –> muon + anti-muon + K* is claimed to deviate by nearly 3 standard deviations from the Standard Model, but (as far as I am aware) the prediction and associated claim has not yet been verified by multiple groups of people, nor has the measurement been repeated.
A few theorists have even gone so far as to claim this discrepancy is clearly a new phenomenon — the end of the Standard Model’s hegemony — and have gotten some press people to write (very poorly and inaccurately) about their claim. Well, aside from the fact that every year we see several 3 standard deviation discrepancies turn out to be nothing, let’s remember to be cautious when a few scientists try to convince journalists before they’ve convinced their colleagues… (remember this example that went nowhere? …) And in this case we have them serving as judge and jury as well as press office: these same theorists did the calculation which disagrees with the data. So maybe the Standard Model is wrong, or maybe their calculation is wrong. In any case, you certainly musn’t believe the news article as currently written, because it has so many misleading statements and overstatements as to be completely beyond repair. [For one thing, it’s a case study in how to misuse the word “prove”.] I’ll try to get you the real story, but I have to study the data and the various Standard Model predictions more carefully first before I can do that with complete confidence.
Ok, back to the promised comments: on twists and turns for neutrinos and for muons…
I’ve finished (more or less) a version of the promised article on IceCube — the giant neutrino experiment that may have made a major discovery, as announced last week, and that had an opportunity to make another a few weeks ago (though apparently nature didn’t provide). The article is admittedly a bit rushed (darn computer … Read more
