The neutron is a fascinating particle, and one which has kept experimental physicists busy for almost a century now. Discovered by James Chadwick in 1932 in a cunning experiment which deserves a separate post (it is a promise, or a threat if you prefer), the neutron has been all along a protagonist in the development of nuclear weapons as well as in the extraction of nuclear power from fission reactors. And of more relevance to our discussion here, it has powered endless studies both in the context of nuclear and subnuclear physics.
Today we know that the neutron can be understood as a bag full of quarks and gluons; of all these constituents, there are three that determine the static properties of the particle: two down-type quarks and one up-type quark. Down quarks have an electric charge of -1/3, and up quarks a charge of +2/3, so the neutron is electrically neutral. In contrast, the proton contains two up quarks and a down quark, and its charge is therefore +1.
As quarks carry a spin of 1/2, a trio of quarks can be measured to have a total spin of 1/2 or 3/2. Neutrons have spin 1/2, like protons; quantum mechanics also allows for spin configurations of the same quarks where the total spin is 3/2, but these states have more internal energy - so a higher mass. These "excited" versions of the neutron and proton are respecitvely named Delta^0 and Delta^+, and their higher mass forces them to quickly decay back into more sober states.
Because the down quark is slightly more massive than the up quark, the neutron is a bit more massive than the proton. Talk about the health risk of obesity to a neutron, and you will get a very sorry smile in return: by virtue of having a mass ever so slightly higher (it weighs 939.565 MeV, a mere 1.293 MeV more, so 1 per mille too high), the neutron gets to die in a matter of about 15 minutes, while the proton is immortal! That inconvenience is brought about by a fundamental rule of physics - everything that is not forbidden is compulsory.
In fact, both the neutron and the proton carry one unit (+1) of baryonic number B, a quantity that in Physics is posited to be conserved, no less than other continuous quantities like energy or momentum. So while the proton is forbidden to decay into any other physical system, as there exist no lighter siblings possessing one unit of B, the heavier neutron can decay into a proton --and so it does--, by yielding it its baryon number unit along with some excess kinetic energy. The rest of the available energy (what is left of the 1.293 MeV I mentioned above after the proton kinetic energy is accounted for) is temporarily assigned to a virtual W boson -the carrier of charged-current weak interactions- and swiftly turned into an electron-antineutrino pair.
[Above: a picture of the decay. Image credit: Bartosz Fornal]
What I described above is what has been called Beta decay since even before the neutron was discovered, as the reaction had been studied for many years in radioactive transitions among heavy nuclei before it was realized what were the constituent particles involved. Beta decay is the template of weak interactions and indeed the main object of nuclear and subnuclear physics studies involving neutrons to this day.
The plot
I feel I have stretched your patients for a bit too long now, as I got carried away into describing more detail of neutron decay than you probably cared to be briefed on. So let me get to the point of this post. Today I read a paper in the Cornell ArXiv that describes a beautiful experiment called Nab. The experiment measures with high statistics and extreme accuracy both the proton and the electron emitted in neutron decay.
A copious flux of neutrons is provided by the Spallation Neutron Source at the Oak Ridge laboratory in the US, and the Nab detection apparatus is based on thick, large-area, highly segmented silicon detectors in a cryogenic system. When I say thick I say it in a relative sense, as these detectors have a width of 2 millimeters - still about seven times more than conventional ones used in high-energy physics applications. Thick silicon sensors are needed to fully stop the beta-decay electrons within the material, guaranteeing that a precise energy estimate can be obtained.
The extracted proton and electron energy and direction are used to put points in a scatterplot which describe the topology of the three-body decays. These sort of graphs are called "Dalitz plots" to recognize their original proponent, the australian physicist Richard Dalitz. In the version of the plot used by Nab, the horizontal axis measures the electron energy, and the vertical axis describes the inverse of the squared difference in time of flight of protons and electrons. The larger this variable, the smaller the delay between electrons and protons, which relates to their kinetic energy - hence the vertical axis in a way measures the proton energy.
Now, remember that the neutron decay is a three-body process: there are three particles in the final state. The neutrino cannot be observed as it escapes undetected. Depending on the relative configuration on the decay plane of the three momentum vectors, you can imagine the decay of a still neutron to produce (1) a fast proton ejected in one direction, recoiling against an electron-neutrino pair traveling roughly in the opposite direction, or (2),(3) the same topology with a permutation of the role of the three particles. Of course, these are limiting cases of the decay, which in most configurations will rather distribute more evenly the momenta to the three final state particles.
Estimating the relative abundance of decays where the electron and neutrino are emitted in opposite directions or in the same direction is of high importance because these configurations betray the relative importance of two different contributions in the matrix element that encodes the decay kinematics: a vector and an axial-vector component. In the vector case (transitions called "A' la Fermi") the electron-neutrino pair goes in the same direction, globally carrying no unit of spin (as they are a fermion-antifermion pair with left-handed helicity), and the emitted proton travels fast to balance the momentum carried away by the lepton pair; the neutron and proton then have the same spin. In the axial-vector case instead the nucleon does a spin flip, and the proton is of lower momentum; this transition is also called "A' la Gamow-Teller".
There have been many speculations of the possibility that new physics could be spotted in a small difference of the rate of vector and axial-vector decays of the neutron, so measuring it with high precision was a goal of the Nab experiment. You can read about that in the article, but here I just want to show the extremely nice Dalitz plot produced by the study of large sample of neutron decays.
[Above: the background-subtracted density of neutron decays categorized by energy of the emitted electron (horizontal axis) and inverse squared time of flight of proton and electron (vertical axis)].
There are several things to note in the graph. As I explained below, decays where the inverse squared time flight difference 1/t^2_pe is small correspond to slow protons, and thus a Gamow-Teller decay; these populate the lower part of the blue area (ignore the red points, that correspond to a fluctuation in the background subtraction). Instead, Fermi transitions populate the higher part of the ellipsoid. Also to note is the feature at the far left in the graph, where for small electron energy (<100 keV) instrumental effects caused by electrons and protons hitting the same detector area cause a mismeasurement of those events.
Overall, this measurement far exceeds the precision of previous studies of the same phenomenon. To note, this was possible with only 81 hours of data taking, which allowed the instrument to record 16 million decays. A number of important results are extracted on possible new physics scenarios - but needless to say, the short summary is "all is well under the sun", as otherwise the title of this post would have been quite different...