Quantum Diaries

For what it’s worth, neutrinos are weird. They are probably the strangest bits of matter in the Universe, and I do not mean in the quark sense either. Assuming that neutrinos are not actually trans-dimensional beings in search of a new home, there is probably no particle in Physics Past, Present, & Future that has bore more brunt of physicists’ creativity. On the other hand, as far as I know, there is no other particle that has solved as many problems in physics as neutrinos. The higgs boson is a good contender, but I still think neutrinos take the cake due to the fact that they have been around longer. Well, that and actually having been found to exist.

Figure 1: The (Left) Electron-, (Center) Muon-, and (Right) Tau-Neutrino, in plushie representation, brought to you by ParticleZoo. [Images: ParticleZoo]

I am sure by now you are wondering, “What are you talking about?”, and in all fairness, that is a very good question. In physics, neutrinos have a long history of being either the particle that broke the mold or the particle that saved physics. In doing so, neutrinos have developed this reputation for being the go-to particle for a new theory. In all fairness though, neutrinos are not doing themselves any favors if experiments keep finding contradictions with known laws of physics *cough*. I am sure for every flavor of ice cream at Baskin-Robbins or Ben & Jerry’s, there is a neutrino that has either been discovered or hypothesized.

Figure 2: The (Left) Electron-, (Center) Muon-, and (Right) Tau-Antineutrino, in plushie representation, also brought to you by ParticleZoo. [Images: ParticleZoo]

For today’s post, I though I would share with you a few of the many flavors of neutrinos. It is also my secret goal to mention “neutrinos” so often in this post that it will be at the top of Google’s queue. The table of contents is just below with the full list today’s neutrino flavors. Believe it or not, there are still plenty of types omitted. I suppose I have to write a future post to include these. 😀

Happy Halloween & Happy Colliding!

– richard (@bravelittlemuon)

Table of Contents

1. The First Neutrino: Pauli’s Neutron
2. Chadwick’s  Neutrino: The Neutron
3. Fermi’s Neutrino: The Key to the Weak Nuclear Force
4. Majorana’s Neutrino
5. The Super Massive Neutrino
6. The Extra, Extra Neutrino
7. The Sterile Neutrino: Type I
8. The Sterile Neutrino: Type II
9. The Tachyon Neutrino

1. The First Neutrino: Pauli’s Neutron

Back in the days when particle physics was still a young field in physics, about a decade before the discovery of Quantum Mechanics, experimentalists studying radioactive decay discovered something very startling: When a radioisotope decayed and emitted a high speed electron, then energy & momentum were not conserved. This was a very worrisome result because these conservation laws were, and still are, pillars of physics. In 1930, Wolfgang Pauli, after whom the famed Pauli-Exclusion Principle is named, made an audacious suggestion that perhaps radioactive decay involving electron emission also involved the production of an additional particle. Pauli’s stated that his neutrino, then named the neutron (different from today’s neutron), that was (1) electrically neutral and (2) massless, or nearly massless, (3) did not travel at the speed of light, and (4) virtually undetectable by contemporary, experimental standards.

Figure 3. The Nobel Foundation’s official portrait of Prof. Pauli (Nobel 1945). Yes, this is the man responsible for suggesting the existence of the neutrino. As father of all hypothetical particles, Pauli would later come to regret (mid-page) proposing an undetectable objects. [Image: Nobel Foundation]

At the end of the day Pauli was spot on with his suggestion. Radioactive decay involving electron emission does, indeed, require a very light, electrically neutral particle. In fact, the following generation of neutrino detectors were able to discover it without a problem. It turns out, all someone needed was a nuclear reactor and patience.

2. Chadwick’s  Neutrino: The Neutron

Figure 4: The (real) neutron is composed of one up-flavor quark and two down-flavor quarks. [Image: Internet]

James Chadwick‘s discovery of the neutron proved one thing very, very well: that the Universe has an odd sense of humor and likes to confuse those to attempt to understand it. Having uses from nuclear power to cancer therapy, at the end of the day neutrons have been a boon for the scientific community and society as a whole. When first discovered, however, Chadwick initially misidentified it as Pauli’s neutron (a.k.a. the real neutrino). Today, the names we have for many particles are really artifacts of the confusion in particle physics through the 1930s & 40s. (For those of the physics history persuasion, this is just like the discovery of the “μ” meson.) Here is a time line the discovery of Chadwick’s neutrino (a.k.a. the fake neutrino):

• 1911 – The gold foil experiment is carried showing that the atom consists of a dense center. It is later found that an atom’s nucleus is too heavy to be composed only of protons. Fifty years later, gold foil is also discovered to be a source of unlimited amounts of chocolate.
• 1911 – β-decay, the mechanism through which some radioisotopes decay, appears initially to violate the Law of Conservation of Energy.
• 1930 – Pauli proposes, in his famous “Dear Radioactive Ladies and Gentlemen” letter, the existence of a massless (0r near massless), electrically neutral particle, called the “neutron” (actually the electron-neutrino), to resolve the apparent energy non-conservation in radioactive β-decay.
• 1932 – Chadwick claims possible discovery of a massive, electrically neutral, particle within the nucleus of an atom. Believing it to be Pauli’s neutron (actually the electron-neutrino), he calls it the “neutron” (actually the real neutron).
• 1934 – Enrio Fermi, using the newly created framework of Quantum Field Theory, proposes a simple four-particle interaction to describe β-decay (See 3. Fermi’s Neutrino). With known experimental results, Fermi was able to determine that Chadwick’s neutron (real neutron) was much too heavy to be Pauli’s neutron (fake neutron; real neutrino) and renamed Pauli’s neutron the “neutrino,” which is Italian for “little neutral one.” The only thing more impressive than the accuracy to which this model actually describes Nature is how short the paper is.
• 1942 – Pauli’s neutrino is discovered. In full disclosure, the particle he proposed to solve the problems of β-decay and what was actually discovered first is really the anti-electron-neutrino.

The real neutron is not really a neutrino; it just stole the real neutrino’s name. That jerk (the neutron not Chadwick).

[Note: It is really hard to write “neutrino,” “neutron,” and embed hyperlinks, all while focusing on the historical context.]

3.Fermi’s Neutrino: The Key to the Weak Nuclear Force

The mathematical and physical description of radioactive decay is, by far, one of the most beautiful things I have every seen in either Mathematics or Physics. (The second is probably the metric structure in Special Relativity.) What is so amazing about it is how it changes at higher energies. On one end of the energy spectrum, you have everyday radioactive decay; somewhere near the middle, you have the restoration of electroweak symmetry and higgs boson production; and on the far end, you have the grand unification of all forces.

In attempt to explain a type of radioactive decay known as β-decay, Enrico Fermi, in 1934, supposed that during this process a radioisotope will decay into a more stable isotope, a high speed electron (β-particle), and a hypothetical particle predicted to exist by Pauli, called the neutrino (See 2. Chadwick’s Neutrino). They Feynman diagram that illustrates this interaction is just below. I should note now that what Pauli really predicted is a neutrino’s antimatter equivalent call the anti-neutrino.

Figure 5: Enrico Fermi’s 4-fermion interaction model to describe β-decay. n represents an incoming neutron, p represents an outgoing proton, e is an outgoing electron, and note the outgoing anti-electron-neutrino (νe). [Image: Mine]

Being a fermion, a neutrino has an antimatter partner called an anti-neutrino. Under the rules of Quantum Field Theory, one can then induce β-decay by directing a beam of neutrinos into a bunch of heavy nuclei, like a thick plate of steel. Such a process would be drawn like this:

Figure 6: Enrico Fermi’s 4-fermion interaction model to describe neutrino scattering. n represents an incoming neutron, p represents an outgoing proton, e is an outgoing electron, and note the incoming electron-neutrino (ν_e). [Image: Mine]

Though the probability of inducing β-decay is very small but it becomes larger with higher energy. If you extrapolate this to very high energies, you find out that eventually the probability of inducing β-decay becomes larger than 100%, which is total nonsense. You can never have a 101% of your interactions result in anything. In particle physics, the sum of all probabilities must add up to 100%; in such cases where they do not, we say that “unitarity has been violated.” This terminology originates from the fact that the matrix containing all possible interaction outcomes is a unitary matrix, implying that total probability is (1) conserved and (2) identically equal to 1 (or 100%).

How does Nature avoid breaking math at high energies? Well at around 100 GeV, rather than two particles smashing into each other to produce two different particles, a neutrino will radiate a W boson and become the high speed electron (β-particle). This W boson is then absorbed by a neutron (Chadwick’s neutron) and is turned into a proton, thereby transmuting one isotope into another isotope. Since producing a W boson (mW = 80.399 GeV/c²) is not cheap and requires a lot of energy, the probability of scattering a neutrino off a nucleus is driven down and prevents unitarity from being violated.

In summary, Fermi’s neutrino & Weak Nuclear Theory model is the  foundation for the Electroweak component of the Standard Model.

Figure 7: Tree-level diagram of the neutrino scattering process in which (1) a neutrino will emit a W and become an electron, and is followed by (2) a down-type quark absorbing the W boson and becoming an up-type quark. The 4-fermion model is the low-energy approximation of this description. Color represents the QCD charge held by the quarks in a nuclei. Color also makes things look nicer. [Image: Mine]

4. Majorana’s Neutrino

Antimatter, the destroyer of basilicas, the stuff of warp drives, and just all around fascinating piece of science, was predicted to exist in 1928 by the great Paul Dirac, and discovered shortly thereafter (1932) by Caltech’s Carl Anderson. This is the same Anderson who is discovered the muon, and so he probably qualifies to be my hero. One way to describe antimatter is to imagine regular, ordinary matter, but for each charge a piece of matter has its antimatter partner has the opposite charge. For example, the top quark has a number of charges: +2/3 electric charge; it can have a red, blue, or green charge from the Strong Nuclear force (QCD); and it also has a “topness” (or “truthfulness”) charge under the Weak Nuclear force. An anti-topquark then must have: a -2/3 electric charge; an anti-red, anti-blue, or anti-green “color” charge; and has “anti-topness” (or “anti-truthfulness”… does that make anti-topquarks liars?).

Well, I suppose one has to wonder if it is possible for a particle to ever be its own anti-particle. The answer is yes. Such particles are called Majorana particles. Italian physicist Ettore Majorana speculated and determined a number of constraints, namely to conserve all the various types of charges (electric, color, weak) a Majorana particle must be neutral under all its charges. To get this right, I need an electrically neutral, colorfully neutral, and weakly neutral. To me, this sounds just like a neutrino! If it smells like a neutrino, looks like a neutrino, and tastes like a neutrino, then clearly it must be a duck neutrino.

What is the problem? Well, if neutrinos are their own antiparticle then physicists expect to see something called neutrino-less double β-decay (or 0νββ for short). In this process, a radioisotope will undergo β-decay and emit a high speed electron and an anti-electron neutrino. If neutrinos are indeed Majorana particles, then the anti-electron-neutrino is also an electron-neutrino and can force a second radioisotope to also emit a high speed electron.

To date, 0νββ has not been observed but that does not mean it does not exist. It is possible that 0νββ does exist, it must just be a really, really rare process.

Figure 8: Feynman diagram demonstrating how neutrino-less double β can occur if neutrinos are also Majorana particles. [Image: Wikipedia]

5. The Super Massive Neutrino

According to the Standard Model of Particle Physics, there are only three “light” neutrinos. “Light” is defined as less than 1/2 the mass of the Z boson, which m_Z = 91.1876 GeV/c². We have observed this empirically by producing Z bosons in copious amounts at the large electron positron collider and looking at all possible ways we can observe a Z boson can decay. The total number of observed Z decays is then used to calculate the Z boson’s average lifetime (or rate of decay). The observed decay rate is subtracted from the Standard Model’s prediction for the total decay rate. The difference between the theoretical prediction and the experimental observation is then compared to the situation where the Z boson were able to decay into 1, 2, 3, … different pairs of particles that could not be observed with our detectors. These sorts of decays are called “invisible decays” or “invisible decay modes.” From this data, all signs point to three different invisible decay modes, which correspond to the three neutrino flavors in the Standard Model (electron, muon, tau).

Time for caveat number 4,321: Z bosons can only decay into particles lighter than itself, otherwise all sorts of bad things would happen. By bad things, I mean violations of conservation laws. If any particle were to decay into two (almost) identical particles, then at most each daughter particle could weight half of the mother particle. This means, according to invisible decay searches of the Z boson, there are only three types of neutrinos with mass less than 1/2 the mass of the Z boson. It is fair game for neutrinos to be heavier than half the Z mass; in fact, it is possible for a neutrino to be as heavy as ten top quarks! (The top quark is currently the most heavy particle known to exist.)

The most recent experimental results have found that for a stable (non-decaying) neutrino, its mass must be at least 45.0 GeV/c² (39.5 GeV/c²) for an ordinary (Majorana) neutrino. For a short-lived (decaying) neutrino, it must have a mass of at least 90.3 GeV/c² (80.5 GeV/c²) for an ordinary (Majorana) neutrino.

6. The Extra, Extra Neutrino

Neutrinos can oscillate. What do I mean by that? Well, if you make a beam of neutrinos and look at the beam composition (% of electron-neutrinos v.s. % of muon-neutrinos, v.s. % of tau-neutrinos),  as a function of distance, then one will notice that the relative composition changes.

For example: If I measure the beam to be made of 100% electron-neutrinos & 0% muon-neutrinos, and a few football pitches away I find that it is now 50% electron-neutrinos, 50% muon-neutrinos, then a few football pitches away from that I can expect to see 100% electron-neutrinos & 0% muon-neutrinos once again. I made up the exact numbers, but I hope you get the idea. It has only been recently (1,2) that all oscillation permutations have been observed.

Figure 9: To measure neutrino oscillations, a neutrino beam is typically shot into the Earth (right), measured by a detector close to the beam’s origin (near detector), and then detected by a detector on the opposite side of the planet (left). Yes, we literally shoot a beam a particles into the Earth and wait for them to come out the other side. PHYSICS. IS. AWESOME. [Image: Interactions]

Well, back in 2001 (that was over 10 years ago, weird…) a Los Alamos experiment LSND (Liquid Scintillator Neutrino Detector) saw a signal that could be explained if neutrinos were also oscillating into a fourth type of neutrino. The MiniBooNE experiment at Fermilab tried to verify this result and was unable to make a conclusive determination. In other words, the jury is still out on the existence of a 4th type of neutrino.

7. The Sterile Neutrino: Type I

I like sterile neutrinos; they are fun. According to the Standard Model, all observed neutrinos are (1) colorless (no interactions via the Strong Nuclear Force), (2) electrically neutral (no interactions via Electromagnetism), and (3) are left handed (Weak charge). This means that Standard Model neutrinos can only interact with the W bosons and sometimes with the Z boson. Well, suppose there were a right-handed neutrino (opposite Weak charge from left-handed neutrino). It is still invisible to the Strong Nuclear Force, the Electromagnetic Force, and the W± bosons (because all W‘s are left-handed). In principle right-handed neutrinos can interact with the Z boson, trying to separate the corresponding signal from background data is like trying to find a find a needle, in a haystack, at a fair. Did I mention this fair is a tri-state fair?

Right-handed neutrinos and other neutrinos that are invisible to the Standard Model forces are examples of what physicists call “sterile neutrinos.” (Personally, I like to qualify these sorts of little tykes with the title “Type I.” See 8. The Sterile Neutrino: Type II why I do so.) If right-handed neutrinos do exist, then there is no way to see detect them given our current understanding of physics. However, this does not mean they cannot interact through some new, undiscovered force.

To date, there is no confirmed evidence, direct or indirect, of the existence of a right-handed or any other type  sterile neutrino. To date, there is no evidence for a new fundamental force either. Though interestingly enough, since sterile neutrinos, in principal, cannot be detected, then it is logical that there could be hundred or even thousands of slightly different sterile neutrinos. Alternatively, we can also a universe filled with a single type of neutrino and we would not be able to detect them outside of gravity (assuming they have mass), which brings me to mention that sterile neutrinos have even been proposed as a dark matter candidate. Neutrinos are resourceful, I will give them that.

Figure 10: A snow-covered hay bale at Fermilab. Imagine trying to find a needly in that field. [Image: FNAL]

8. The Sterile Neutrino: Type II

Sterile neutrino type II (again, I made up the “type” nomenclature) is very much like type I but with one glaring difference. Even if there are are new forces in the Universe, these types of neutrinos will still not interact with anything. The only possible forces through which these neutrinos might interact are gravity and whatever unified force that produced these oddballs.

9. The Tachyon Neutrino

In September, the Italian neutrino experiment OPERA (Oscillation Project with Emulsion-tRacking Apparatus) shocked the world when the collaboration announced it had observed neutrinos traveling at a speed faster than that at which light travels. My colleagues have blogged about it here, here, here, and more recently here. This is a huge deal because, according to Special Relativity, the speed of light (numerically c = 299,792, 458 m/s or 983, 571, 056 ft/s) is pretty much a cosmic speed limit that no real particle can surpass. So I am not sure which makes me happier, the fact that tachyons are seriously being floated as an explanation for this claim or that #FTLneutrinos is a thing. (“FTL” stands for “faster than light.”)

Metaphorically, tachyons are interesting sorts of creatures. I do not know too much about them beyond the fact that they have (in the mathematical sense) a purely imaginary mass. The last time I checked quantum mechanics, we cannot observe strictly imaginary quantities, but I digress. What I do know is that special relativity implies that having a purely imaginary mass should then enable tachyons to permanently travel at speeds faster than c. If neutrinos do travel at speeds faster than the speed of light, then they may also be tachyons. I think it is a perfectly reasonable argument. However, there is a very big elephant in the room that I have to address. Having imaginary mass means that all tachyons always travel at superluminal speeds. If some neutrinos are found to travel at subluminal speeds then the idea that neutrinos are tachyons is tossed out. End of story.

So in light of the considerable implications of any particle traveling faster than the speed of light, it is very appropriate to remain cautious and wait for OPERA to reproduce their results and independent verification, possibly by Fermilab’s MINOS Experiment or KEK’s T2K Experiment.

Figure 11: A real life tachyon. [Image: ParticleZoo]