How many quarks would a charm quark charm if a charm quark could charm quarks?

Fundamental physics is having quite a spectacular season.  In mid-March, the collaborators of the BICEP2 telescope announced the first direct evidence of cosmic inflation, answering a long-standing question about the beginnings of the universe.

Now, on the heels of that discovery, the LHCb (Large Hadron Collider beauty) collaboration at CERN has announced the discovery of a new particle — an exotic hadron that has four quarks in it, instead of the usual three quarks or quark-antiquark pair.  Such a beast lies outside our current understanding of particle physics, opening the door to even more revelations about our universe.  Matthew Francis has another nice summary of the discovery at Ars Technica.

The details of this discovery, and its long-term implications for physics, are out of my depth these days (I haven’t been a particle physicist for a while).  However, the press releases assumes a lot from the reader — do they know what quarks are, and why they only come in threes or quark-antiquark pairs?  With this in mind, I thought I could write a short post giving some background for those who aren’t familiar with the details — the “Cliff Notes” of quarks, so to speak! As I tend to do, I’ll approach this from a historical perspective, though this history will be simplified for the sake of brevity.

The discovery of quarks can be thought of the result of humankind’s desire to understand what we’re made of, and our instinct that a theory of matter must be quite simple.   For instance, as far back as ancient Greece, philosophers broke down all of nature into the four classical elements earth, water, air and fire.  They were wrong, of course, but that desire to simplify nature, specifically matter, has been a large part of science ever since.

Most everyone is familiar with one of the greatest accomplishments in this effort: the periodic table, introduced by Dmitri Mendeleev in 1869, which arranges chemical elements in order of atomic number and chemical properties.  From the structure of the periodic table, Mendeleev was able to predict as yet undiscovered elements from gaps in the existing table.

The modern periodic table, via Wikipedia.

The modern periodic table, via Wikipedia.

When I say “chemical elements,” of course, I’m referring to different types of atoms.  The regular behavior of the periodic table hinted that atoms are built of more fundamental particles, though it took quite some time to figure out exactly what.  The first piece of the new puzzle was the discovery* of the negatively-charged electron by J.J. Thompson in 1896, which was immediately recognized to be a part of the atom.  The next important piece was the discovery of the positively-charged atomic nucleus by Ernest Rutherford in 1911, based on experiments done by his assistants in 1909.  This observation gave us the most familiar picture of the atom seen today, with electrons orbiting a tiny nucleus**.


But what is the nucleus made of?  In 1917, Rutherford managed to show that the hydrogen nucleus (the smallest one, with a positive charge equal in magnitude to the negative charge of the electron) is present in other, heavier elements.  This was the first evidence that all nuclei are built from these single positive charges, now called protons.

Something else was missing, however, as the mass of the heavier nuclei is greater than could be explained by just protons alone.  The mystery was solved in 1932, when James Chadwick discovered the neutron, an almost “twin” of the proton with roughly the same mass but no charge.

So ordinary matter, in the form of atoms, consists of a small nucleus of protons and neutrons, with electrons “orbiting.”

A simple model of a helium atom.

A simple model of a helium atom.

Even in 1932, however, this was not the entire story: in 1928, Paul Dirac predicted theoretically the existence of antimatter, negative twins of ordinary matter with opposite electric charge that annihilate with ordinary matter.  The anti-electron (positron) was discovered in 1932 by Carl D. Anderson.  In 1933, one seemingly final piece of the puzzle of matter was proposed, the neutrino, a (nearly) massless, chargeless particle that is closely related to the electron.

So, in the early 1930s, there was a seemingly quite complete picture of matter: electrons, protons, neutrons, neutrinos, and their antiparticle compliments.  However, things would quickly change: in 1936, a new negatively-charged particle was discovered, the muon, that would later turn out to be in essence a heavier version of the electron.  Seemingly serving no real purpose in nature, the muon was a new puzzle.  Muons are created all the time by collisions of high-energy particles in the upper atmosphere, and they decay into an electron and neutrinos.  The existence of the muon was baffling, famously leading physicist I.I. Rabi to remark, “Who ordered that?”

Things got worse — or better, depending on one’s view of scientific mysteries!  To discover the nucleus, Rutherford smashed alpha particles (helium nuclei) against gold atoms.  To probe inside the nucleus required higher-energy collisions of atoms and particles, and this set the stage for a century of particle physics experiments that are still going on today.  However, as collisions of higher and higher energies were generated, new heavy particles were created that were distinct from the protons, neutrons and electrons already known!  These particles were broadly grouped into baryons (including protons and neutrons) and mesons (something new), and suddenly the “fundamental” set of particles had grown to a set of dozens.

Clearly something else was missing, and it took until 1964 for the answer to come.  In that year, physicists Murray Gell-Mann and George Zweig independently proposed that all of the “fundamental” particles — baryons and mesons — were composed of a much smaller set of even more fundamental particles, labeled “quarks.”

Over the course of several decades, six distinct quarks — and their antiquarks — were predicted and/or discovered experimentally, the last — and heaviest — being the top quark, discovered in 1995.  A picture of all known fundamental particles is illustrated below.

The standard model of particle physics, showing all fundamental particles (but not their antiparticles).

The standard model of particle physics, showing all fundamental particles (but not their antiparticles).

A few things to note here.  The “leptons” include the electron (e), the muon (μ), and the electron and muon neutrinos (the ν’s), as well as an even heavier cousin of the electron, the tau (τ).  The “gauge bosons” are particles that “mediate,” or create, the fundamental forces of nature, including the photon γ, or “particle of light.”  Also on the list is the Higgs boson, a particle that, loosely speaking, “gives” mass to other massive particles.  The Higgs was originally hypothesized in 1964, but it was not until 2012 that it was officially discovered at the Large Hadron Collider.  The Higgs is the heaviest fundamental particle known, and so it was the last to be discovered, requiring collisions at energies that only the LHC could provide.

You may note that even this list seems like a really large number of supposedly “fundamental” particles!  This somewhat paradoxical situation is the motivation for string theory, which speculates that all of the particles in the standard model are really just different excitation/vibrations of a single fundamental string-like particle.  There is no way to experimentally test this theory for the foreseeable future, however.

Putting all of that aside, however, let’s focus on the quarks!  The six quarks, in order of increasing heaviness, are listed below.

  • up quark: mass 2.3 MeV, charge +2/3e
  • down quark: mass 4.8 MeV, charge -1/3e
  • strange quark: mass 95 MeV, charge -1/3e
  • charm quark: mass 1.275 GeV, charge +2/3e
  • bottom quark: mass 4.18 GeV, charge -1/3e
  • top quark: mass 173 Gev, charge +2/3e

The masses are given in units of energy; MeV = million electron-volts, and GeV = billion electron-volts.  The charges of the quarks are given as fractions of the fundamental charge of the electron, e.  This in itself raises an odd question, though: how can the quarks have a smaller charge than the fundamental unit of charge?

The answer is that quarks are never seen alone: they only appear in trios or in quark-antiquark pairs.  The strong nuclear force that holds quarks together never allows them to exist in isolation.  Smash two protons together with a tremendous collision energy, and that energy will result in additional quark-antiquark pairs being created, not in the separation of individual quarks.  The output of such a high-energy collision is a huge zoo of particles traveling in all directions, as illustrated below.

Simulation of a Higgs boson detection at the CMS detector as CERN, via CERN.

Simulation of a Higgs boson detection at the CMS detector as CERN, via CERN.

This is where things get interesting, and even beautiful!  The theory of strong nuclear interactions — quantum chromodynamics — indicates that quarks in fact come in three “colors” — call them red, green, and blue — and their corresponding “anti-colors.”  The nuclear force only allows “colorless” combinations of quarks to exist, either in three quarks of different colors — one red, one green, one blue — or in a quark/anti-quark pair of opposing colors, for instance red and anti-red.  The implication of this is that quarks can only be combined in ways that produce a non-fractional total charge!  For instance, a proton consists of two up quarks and one down quark, which has a total charge:

+2/3e (up, red) + 2/3e (up, green) -1/3e (down, blue) = e.

A neutron consists of two down quarks and one up quark, with a total charge:

-1/3e (down, red) – 1/3e(down, green) +2/3e (up, blue) = 0.

A simple meson, the pi+ meson, consists of an up quark and an anti-down quark:

+2/3e (up, red) +1/3e (anti-down, anti-red) = e.

Additional rules apply for the more exotic quarks.  It turns out that “strangeness,” “charmness,” “bottomness” and “topness” are all conserved quantities, as well.  That is, charm quarks can only be produced in charm/anti-charm pairs, where the total “charm” is zero, with similar considerations for the other heavy quarks.

This simple model of quantum chromodynamics (which of course in practice is much more complicated) allows the construction of all the mundane and exotic baryons and mesons.  With quarks, then, we have a wonderful and complex hierarchy of matter, from the smallest (quarks) to the largest aggregates, such as a beaker of water.


At long last, we can come back to the new discovery at CERN!  As we’ve alluded throughout this post, new discoveries come at increasingly more advanced accelerators that can (a) smash things together harder and (b) do so at a faster rate, to build up enough statistics to see exceedingly rare events.  In particular the LHCb collaboration sifted through 180 trillion proton-proton collisions at the LHC, investigated 25,000 promising meson decays among thetse, and found unambiguous evidence that a new particle was being formed from a collection of four quarks.  This result confirms earlier tantalizing evidence of this particle that was seen in 2008 by the Belle collaboration.

The new object, dubbed Z(4430) because of its mass of 4.43 GeV, does not last long before decaying into lighter particles.  However, the collaboration was able to determine the quark composition of this new transient particle: a charm quark, a charm antiquark, a down quark, and an up antiquark.

Quark content of Z(4430).  The overlines indicate the antiquarks.

Quark content of Z(4430). The overlines indicate the antiquarks.

This new particle does not break any of the rules we have set out previously.  The total amount of “charm” is zero, thanks to the present of the charm quark and the charm antiquark, so charm is conserved.  Also, the total charge is -e, an integer amount of fundamental charges.  The total color can still be zero, since we could have a red down quark, an antired up antiquark, a blue charm quark, and an antiblue anticharm quark.

However, the theory of quantum chromodynamics does not predict that this combination of quarks will form a distinct particle, which means it is new physics of some sort.  As Matthew Francis notes at Ars Technica, this could be some sort of unusual fusion of two mesons (down/anti-up plus charm/anti-charm), or it could be a new type of particle entirely — a tetraquark!

These results are a bit of a relief, I imagine, for the particle physics community.  After the discovery of the Higgs boson, there was at least some worry that there might not be anything else to discover, at least in the short-term!  The discovery of this unusual particle resonance indicates that there is new physics to be found at the LHC, and this work will give experimentalists and theorists something to ponder and study for a while.


* By “discovery,” I should really say “proof that the electron is a distinct particle and not an atom or wave.”  So-called cathode rays had been observed years earlier, but their precise nature was unclear.

** This picture of an atom is oversimplified, as the electron has wavelike properties and is more aptly described as being a sort of blur around the nucleus.

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