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Posts Tagged ‘Standard Model’

This is the last part of a series of three on supersymmetry, the theory many believe could go beyond the Standard Model. First I explained what is the Standard Model and show its limitations. Then I introduced supersymmetry and explained how it would fix the main flaws of the Standard Model. I now review how experimental physicists are trying to discover “superparticles” at the Large Hadron Collider (LHC) at CERN.

If Supersymmetry (or SUSY for short) is as good as it looks, why has none of the new SUSY particles been found yet? There could be many reasons, the simplest being that this theory is wrong and supersymmetric particles do not exist. If that were the case, one would still need another way to fix the Standard Model.

SUSY can still be the right solution if supersymmetric particles have eluded us for some reasons: we might have been looking in the wrong place, or in the wrong way or they could still be out of the reach of current accelerators.

So how does one go looking for supersymmetric particles? One good place to start is at CERN with the Large Hadron Collider or LHC. The 27-km long accelerator is the most powerful in the world. It brings protons into collisions at nearly the speed of light, generating huge amounts of energy in the tiniest points in space.  Since energy and matter are two forms of the same essence, like water and ice, the released energy materializes in the form of fundamental particles. The hope is to create some of the SUSY particles.

One major problem is that nobody knows the mass of all these new particles. And without the mass, it is very much like looking for someone in a large city without knowing the person’s address. All one can do then is comb the city trying to spot that person. But imagine the task if you don’t even know what the person looks like, how she behaves or even in which city, let alone which country she lives in.

Supersymmetry is in fact a very loosely defined theory with a huge number of free parameters. These free parameters are quantities like the masses of the supersymmetric particles, or their couplings, i.e. quantities defining how often they will decay into other particles. Supersymmetry does not specify which value all these quantities can take.

Hence, theorists have to make educated guesses to reduce the zone where one should search for SUSY particles. This is how various models of supersymmetry have appeared. Each one is an attempt at circumscribing the search zone based on different assumptions.

One common starting point is to assume that a certain property called R-parity is conserved. This leads to a model called Minimal SUSY but this model still has 105 free parameters. But with this simple assumption, one SUSY particle ends up having the characteristics of dark matter. Here is how it works: R-parity conservation states that all supersymmetric particles must decay into other, lighter supersymmetric particles. Therefore, the lightest supersymmetric particle or LSP cannot decay into anything else. It remains stable and lives forever, just like dark matter particles do. Hence the LSP could be the much sought-after dark matter particle.

SUSY-cascade-Fermilab Credit: Fermilab

How can the Large Hadron Collider help? Around the accelerator, large detectors act like giant cameras, recording how the newly created and highly unstable particles break apart like miniature fireworks. By taking a snapshot of it, one can record the origin, direction and energy of each fragment and reconstruct the initial particle.

Heavy and unstable SUSY particles would decay in cascade, producing various Standard Model particles along the way. The LSP would be the last possible step for any decay chain. Generally, the LSP is one of the mixed SUSY states with no electric charge called neutralino. Hence, each of these events contains a particle that is stable but does not interact with our detectors. In the end, there would be a certain amount of energy imbalance in all these events, indicating that a particle has escaped the detector without leaving any signal.

At the LHC, both the CMS and ATLAS experiments have searched billions of events looking for such events but to no avail. Dozens of different approaches have been tested and new possibilities are constantly being explored. Each one corresponds to a different hypothesis, but nothing has been found so far.

dijet-monjet Two events with jets as seen in the ATLAS detector. (Left) A very common event containing two jets of particles. The event is balanced, all fragments were recorded, no energy is missing. (Right) A simulation of a mono-jet event where a single jet recoils against something unrecorded by the detector. The imbalance in energy could be the signature of a dark matter particle like the lightest supersymmetric particle (LSP), something that carries energy away but does not interact with the detector, i.e. something we would not see.

One reason might be that all supersymmetric particles are too heavy to have been produced by the LHC. A particle can be created only if enough energy is available. You cannot buy something that costs more money than you have in your pocket. To create heavy particles, one needs more energy. It is still possible all SUSY particles exist but were out of the current accelerator reach. This point will be settled in 2015 when the LHC resumes operation at higher energy, going from 8 TeV to at least 13 TeV.

If the SUSY particles are light enough to be created at 13 TeV, the chances of producing them will also be decupled, making them even easier to find. And if we still do not find them, new limits will be reached, which will also greatly help focus on the remaining possible models.

SUSY has not said its last word yet. The chances are good supersymmetric particles will show up when the LHC resumes. And that would be like discovering a whole new continent.

Pauline Gagnon

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Supersymmetry: a tantalising theory

Wednesday, March 19th, 2014

This is the second part of a series of three on supersymmetry, the theory many believe could go beyond the Standard Model. First I explained what is the Standard Model and showed its limitations. I now introduce supersymmetry and explain how it would fix the main flaws of the Standard Model. Finally, I will review how experimental physicists are trying to discover “superparticles” at the Large Hadron Collider (LHC) at CERN.

Theorists often have to wait for decades to see their ideas confirmed by experimental findings. This was the case for François Englert, Robert Brout and Peter Higgs whose theory, elaborated in 1964, only got confirmed in 2012 with the discovery of the Higgs boson by the LHC experiments.

Today, many theorists who participated in the elaboration of what is now known as supersymmetry, are waiting to see what the LHC will reveal.

Supersymmetry is a theory that first appeared as a mathematical symmetry in string theory in early 1970s. Over time, several people contributed new elements that eventually led to a theory that is now one of the most promising successors to the Standard Model. Among the pioneers, the names of two Russian theorists, D. V. Volkov and V. P Akulov, stand out. In 1973, Julius Wess and Bruno Zumino wrote the first supersymmetric model in four dimensions, paving the way to future developments. The following year, Pierre Fayet generalized the Brout-Englert-Higgs mechanism to supersymmetry and introduced superpartners of Standard Model particles for the first time.

All this work would have remained a pure mathematical exercise unless people had noticed that supersymmetry could help fix some of the flaws of the Standard Model.

As we saw, the Standard Model has two types of fundamental particles: the grains of matter, the fermions with spin ½, and the force carriers, the bosons with integer values of spin.

The mere fact that bosons and fermions have different values of spin makes them behave differently. Each class follows different statistical laws. For example, two identical fermions cannot exist in the same quantum state, that is, something -one of their quantum numbers – must be different. Quantum numbers refer to various properties: their position, their charge, their spin or their “colour” charge for quarks. Since everything else is identical, two electrons orbiting on the same atomic shell must have different direction for their spin. One must point up, the other down. This means at most two electrons can cohabit on an atomic shell since there are only two possible orientations for their spins. Hence, atoms have several atomic shells to accommodate all their electrons.

On the contrary, there are no limitations on the number of bosons allowed in the same state. This property is behind the phenomenon called superconductivity. A pair of electrons forms a boson since adding two half spins gives a combined state with a spin of 0 or 1, depending if they are aligned or not. In a superconductor, all pairs of electrons can be identical, with exactly the same quantum numbers since this is allowed for combined spin values of 0 or 1. Hence, one can interchange two pairs freely, just like two grains of sand of identical size can swap position in quick sand, which makes it so unstable. Likewise, in a superconductor, all pairs of electrons can swap position with others, leaving no friction. An electric current can then flow without encountering any resistance.

Supersymmetry builds on the Standard Model and associates a “superpartner” to each fundamental particle. Fermions get bosons as superpartners, and bosons get associated with fermions. This unifies the building blocks of matter with the force carriers. Everything becomes more harmonious and symmetric.


Supersymmetry builds on the Standard Model and comes with many new supersymmetric particles, represented here with a tilde (~) on them. (Diagram taken from the movie “Particle fever” reproduced with permission from Mark Levinson)

But there are other important consequences. The number of existing fundamental particles doubles. Supersymmetry gives a superpartner to each Standard Model particle. In addition, many of these partners can mix, giving combined states such as charginos and neutralinos

This fact has many implications. First major consequence: the two superpartners to the top quark, called the stops, can cancel out the large contribution from the top quark to the mass of the Higgs boson. Second implication: the lightest supersymmetric particle (in general one of the mixed states with no electric charge called neutralino) has just the properties one thinks dark matter should have.

Not only supersymmetry would fix the flaws of the Standard Model, but it would also solve the dark matter problem. Killing two huge birds with one simple stone. There is just one tiny problem: if these supersymmetric particles exist, why have we not found any yet? I will address this question in the next part in this series.

Pauline Gagnon

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The ILC site has been chosen. What does this mean for Japan?

Credit: linearcollider.org

The two ILC candidate sites: Sefuri in the South and Kitakami in the North. Credit: linearcollider.org

Hi Folks,

It is official [Japanese1,Japanese2]: the Linear Collider Collaboration and the Japanese physics community have selected the Kitakami mountain range in northern Japan as the site for the proposed International Linear Collider. Kitakami is a located in the Iwate Prefecture and is just north of the Miyagi prefecture, the epicenter of the 2011 Tohoku Earthquake. Having visited the site in June, I cannot aptly express how gorgeous the area is, but more importantly, how well-prepared Iwate City is for this responsibility.

Science is cumulative: new discoveries are used to make more discoveries about how nature works, and physics is no different. The discovery of the Higgs boson at the Large Hadron Collider was a momentous event. With its discovery, physicists proved how some particles have mass and why others have no mass at all. The Higgs boson plays a special role in this process, and after finally finding it, we are determined to learn more about the Higgs. The International Linear Collider (ILC) is a proposed Higgs boson factory that would allow us to intimately understand the Higgs. Spanning 19 miles (31 km) [310 football pitches/soccer fields], if constructed, the ILC will smash together electrons and their antimatter partners, positrons, to produce a Higgs boson (along with a Z boson). In such a clean environment (compared to proton colliders), ultra-precise measurements of the Higgs boson’s properties can be made, and thereby elucidate the nature of this shiny new particle.

credit: li

The general overview schematic of the International Linear Collider. Credit: linearcollider.org

However, the ILC is more than just a experiment. Designing, constructing, and operating the machine for 20 years will be a huge undertaking with lasting effects. For staters, the collider’s Technical Design Report (TDR), which contains every imaginable detail minus the actual blueprints, estimates the cost of the new accelerator to be 7.8 billion USD (2012 dollars). This is not a bad thing. Supposing 50% of the support came from Asia, 25% from the Americas, and 25% from Europe, that would be nearly 2 billion USD invested in new radio frequency technology in England, Germany, and Italy. In the US, it would be nearly 2 billion USD invested in coastal and Midwestern laboratories developing new cryogenic and superconducting technology. In Asia, this would be nearly 4 billion USD invested in these technologies as well as pure labor and construction. Just as the LHC was a boon on the European economy, a Japanese-based ILC will be a boon for an economy temporarily devastated  by an historic earthquake and tsunami. These are just hypothetical numbers; the real economic impact will be  larger.

I had the opportunity to visit Kitakami this past June as a part of a Higgs workshop hosted by Tohoku University. Many things are worth noting. The first is just how gorgeous the site is. Despite its lush appearance, the site offers several geological advantages, including stability against earthquakes of any size. Despite its proximity to the 2011 earthquake and the subsequent tsunami, this area was naturally protected by the mountains. Below is a photo of the Kitakami mountains that I took while visiting the site. Interestingly, I took the photo from the UNESCO World Heritage site Hiraizumi. The ILC is designed to sit between the two mountains in the picture.


The Kitamaki Mountain Range as seen from the UNESCO World Heritage Site in Hiraizumi, Japan. Credit: Mine

What I want to point out in the picture below is the futuristic-looking set of tracks running across the photo. That is the rail line for the JR East bullet train, aka the Tohoku Shinkansen. In other words, the ILC site neighbours a very major transportation line connecting the Japanese capital Tokyo to the northern coast. It takes the train just over 2 hours to traverse the 250 miles (406.3 km) from Tokyo station to the Ichinoseki station in Iwate. The nearest major city is Sendai, capital of Miyagi, home to the renown Tohoku University, and is only a 10 minute shinkansen ride from Ichinoseki station.


The Kitamaki Mountain Range as seen from the UNESCO World Heritage Site in Hiraizumi, Japan. Credit: Mine

What surprised me is how excited the local community is about the collider. After exiting the Ichinoseki station I discovered this subtle sign of support:

There is much community support for the ILC: The Ichinoseki Shinkansen Station in Iwate Prefecture, Japan. Credit: Mine

The residents of Iwate and Miyagi, independent of any official lobbying organization, have formed their own “ILC Support Committee.” They even have their own facebook page. Over the past year, the residents have invited local university physicists to give public lectures on what the ILC is; they have requested that more English, Chinese, Korean, and Tagalog language classes be offered at local community centers; that more Japanese language classes for foreigners are offered in these same facilities; and have even discussed with city officials how to prepare Iwate for the prospect of a rapid increase in population over the next 20 years.

Despite all this, the real surprises were the pamphlets. Iwate has seriously thought this through.


Pamphlets showcasing the Kitakami Mountain Range in Iwate, Japan. Credit: Mine

The level of detail in the pamphlets is impressive. My favourite pamphlet has the phrase, “Ray of Hope: Tohoku Is Ready to Welcome the ILC” on the front cover. Inside is a list of ways to reach the ILC site and the time it takes. For example: it takes 12 hours 50 minutes to reach Tokyo from Rome and 9 hours 40 minutes from Sydney. The brochure elaborates that the Kitakami mountains maintain roughly the same temperature as Switzerland (except in August-September) but collects much more precipitation through the year. Considering that CERN is located in Geneva, Switzerland, and that many LHC experimentalists will likely become ILC experimentalists, the comparison is very helpful. The at-a-glance annual festival schedule is just icing on the cake.


“Ray of Hope” pamphlet describing how to each different ILC campuses by train.  Credit: Mine

Now that the ILC site has been selected, surveys of the land can be conducted so that blue prints and a finalized cost estimate can be established. From my discussions with people involved in the site selection process, the decision was very difficult. I have not visited the Fukuoka site, though I am told it is a comparably impressive location. It will be a while still before any decision to break ground is made. And until that happens, there is plenty of work to do.

Happy Colliding

- Richard (@bravelittlemuon)




Monday, April 22nd, 2013

This article originally appeared in symmetry on April 16, 2013.

When a scientific result fails the test of “naturalness,” it can point to new physics.

Suppose a team of auditors is tasked with understanding a particular billionaire’s bank account. Each month, millions of dollars flow into and out of the account. If the auditors look at the account on random days, they see varying amounts of money. However, on the last day of every month, the balance is briefly set to exactly zero dollars.

It’s hard to imagine that this zero balance is an accident; it seems as if something is causing the account to follow this pattern. In physics, theorists consider improbable cancellations like this one to be signs of undiscovered principles governing the interactions of particles and forces. This concept is called “naturalness”—the idea that theories should make seeming coincidences feel reasonable.

In the case of the billionaire, the surprising thing is that, on a set schedule, the cash flow reaches perfect equilibrium. But one would expect it to be more erratic. The ups and downs of the stock market should cause monthly variations in the tycoon’s dividends. A successful corporate raid could lead to a windfall. And an occasional splurge on a Lamborghini could cause a bigger withdrawal than usual.

This unnatural fiscal balance simply screams for an explanation. One explanation that would make this ebb and flow of funds make sense would be if this account worked as a charity fund. Each month, on the first day of the month, a specific amount would be deposited. Over the course of the month, a series of checks would be cut for various charities, with the outflow carefully planned to match identically the initial deposit. Under this situation, it would be easy to explain the recurring monthly zero balance. In essence, the “charity account principle” makes what at first seemed to be unnatural now appear to be natural indeed.

In physics, we see a similar phenomenon when we predict the mass of the Higgs boson. While Higgs bosons get their mass in the same way as all other fundamental particles (by interacting with the Higgs field), that mass is also affected by another process—one in which the Higgs boson temporarily fluctuates into a pair of virtual particles, either two bosons or two fermions, and then returns to its normal state. These fluctuations affect the mass of the Higgs boson, and the size of this effect can be calculated using the Standard Model—a theory that predicts, among other things, the behavior of Higgs bosons.

To calculate how much these quantum fluctuations affect the mass, scientists multiply two terms. The first involves the maximum energy for which the Standard Model applies—a huge number. The second is the sum of the effect of the fluctuations to different virtual bosons minus the sum of the effect of the fluctuations to different virtual fermions. If the Higgs mass is small, as recent measurements at the LHC suggest, the product of these two numbers must also be small.  This means the sum effect of the bosons must be almost identical to the sum effect of the fermions, an unlikely scenario that turns out to be true. For this near cancellation to happen “just by accident” is so utterly improbable that it beggars the imagination. A coincidence like this is simply unnatural.

Without some underlying (and currently unknown) physical principle that makes it obvious why this occurs, it is quite strange for the mass of the Higgs to be so low. That is why discovering the Higgs boson is not the end of the story. Theorists have come up with several different explanations for its low mass, and now it is up to the experimentalists to test them.

Don Lincoln


Now that we are on the verge of completing the Standard Model of Particle Physics, it’s time to look to the future of the field. Five physicists at CERN present their new state of the art* theory: The Substandard Model of Physics!

“It’s easy to understand but questionably accurate.” Mandy Baxter (Marine Biogeochemical Microbiologist, USCB)

Thanks to the actors.
The Substandard Model Task Force:
Androula Alekou (Neutrino Expert)
Katie Malone (Higgs Expert)
Stephen Ogilvy (Flavor Expert)
Aidan Randle-Conde (QCD Expert)
Lee Tomlinson (QFT Expert)

Steve Marsden (Standard Model Expert)
Helen Lambert (Environmental Sanitization Team)

You can find Steve and Aidan on youtube and twitter:



@sigsome @aidanatcern

Visit the US LHC Blogs at Quantum Diaries:


Music: Off to Osaka, Kevin Macleod, http://www.incompetech.com

Images taken from CKMFitter (http://ckmfitter.in2p3.fr), UTFit (http://www.utfit.org), Wikimedia.

This video does not reflect the views of CERN. It does not even reflect the views of the actors. In fact I’d be surprised if it reflected the views of anyone at all.

Thanks to Adam Davidson for inspiring the name. It was a off handed comment you made about 7 years ago that stuck with me ever since. Finally it has become a reality!

Apologies for the slightly out of focus footage and extra frame. Some small technical glitches always get through.

(*We’re just not sure what kind of a state, and what kind of art it is.)


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. :D

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

http://jovasquez.blogspot.com/2010_08_01_archive.htmlFigure 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.
  • 1911β-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).
  • 1934Enrio 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 (νe). [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 mZ = 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]