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Quarks bonding differently at LHCb

The strong force binds quarks together to form hadrons. Until last Monday, only two types of hadron were known, but the LHCb experiment at CERN has just proved there is a third way

The LHCb cavern at CERN, with some of the collaboration
The LHCb cavern at CERN, with some of the collaboration Photograph: CERN Photograph: Cern

While fundamental particles famously require the Higgs boson in order to acquire their masses¹, most of the visible mass in the universe is in the form of hadrons, which are not fundamental. Hadrons, such as the protons and neutrons that make up atomic nuclei, consist of quarks bound together by the strong force. The vast majority of the mass of these hadrons comes from the energy involved in binding the quarks together. You might think this was a good motivation to understand this binding energy. You’d be right, but it is not easy. This new LHCb result tells us something qualitatively new and interesting about it.

The strong force is rather special. Even though we have a theory for it – QCD – which is part of the Standard Model of particle physics, it is very hard to calculate how the binding of quarks works. This is mainly because the force is strong, and most of our techniques for calculating things in particle physics rely on perturbation theory, which only works for relatively weak forces².

Quarks have a property we call “color”, which plays the same role in QCD that electric charge plays in the theory of electromagnetism. Hadrons, however, do not have color. All the known hadrons are made of quarks combined in such a way that their colors cancel out. Color is nothing to do with the colour we see with our eyes, except by analogy. A quark and an antiquark have complementary colors, which cancel, and so we can make one type of hadron – called mesons – from them. Protons and neutrons, on the other hand, are made of three quarks, each with a different color. Three primary colors together also cancel, so protons and neutrons - and other particles made of three quarks, known collectively as baryons - are also colorless.

So until last week there were two known types of hadron. Two ways in which quarks can stick together. Either a quark and an antiquark (meson) or three quarks (baryon)³. And that was it.

LHCb has just confirmed what data from other experiments had already led us to suspect. There is a third way.

The LHCb experiment detects very large numbers of hadrons produced in proton-proton collisions at the Large Hadron Collider. It excels in determining not just the energy and direction of these hadrons, but what kind of hadron they are, and exactly how they decay into other particles. New bound states of quarks – new hadrons – show up in these decays as bumps at a particular mass, corresponding to the mass of the new hadron⁴.

A few years ago, the Belle experiment at the KEKB electron-positron collider in Japan noticed an interesting bump in a particular decay of B hadrons (which contain bottom quarks). The decay was B → ѱ'π⁻K, and the bump was in the ѱ'π⁻ mass distribution. Decoding the Greek there, ѱ' is a meson with a charm and an anticharm quark inside (whose charges cancel), and π⁻ is a meson made of a down quark (with charge -⅓) and an anti-up quark (with charge -⅔). So the resonance has a total charge of -1, and would seem to be made up of two different quarks and two different antiquarks – not fitting the pattern for either a meson or a baryon.

The Belle physicists were sure this bump was interesting, but did not have enough data to prove it was really a resonance – there was a small possibility that complications from other resonances could be conspiring to mislead the analysers. This may sound fussy, but for such a qualitatively new thing – the first hadron outside the meson/baryon pattern - you have a very high standard of evidence. LHCb, with ten times more data, have now shown that this bump really is a resonance.

They have done this by performing an "amplitude analysis". This involves taking all the known possible contributions to the distribution into account, with and without the addition of a bump for the new hadron. They find that they cannot describe the data without including a new resonance corresponding to the bump seen by Belle, and called a Z⁻, at a mass of about 4430 MeV. Once the Z⁻ is included, their fit describes the data very well.

An amplitude analysis is more than just adding bumps together though. Amplitudes describe quantum states, and they don't just have a size, they have a direction, or phase, as well. This allows amplitudes that have opposite phases to cancel out, while those with the same phases add up. Trying the fit out with different possibilities for the phase of the new Z⁻ contributions (as a function of the ѱ'π⁻ mass) shows that the way the phase changes is as would be expected for a new resonance. This rules out any of the other potential explanations, and confirms we really do have a new type of hadron - a Tetraquark - here.

This is no magic bullet that suddenly lays bare the binding equations of the strong interaction. But it is certainly a new and important piece of information. Here are two of the physicists involved giving their take on what it means:

The Large Hadron Collider beauty (LHCb) collaboration spokesperson Pierluigi Campana and LHCb physicist Richard Jacobsson discuss the results.


One of the main goals of the LHCb experiment is to try to understand the matter-antimatter asymmetry in the universe (as the 2008 Large Hadron Rap had it, "LHCb sees where the antimatter's gone"). A couple of weeks ago I wrote about how we learn a lot about physics by assuming there should be no privileged observers, and drew some parallels with social privilege. A couple of days ago this happened:

(Mum, dad, small daughter, older son at table. Son & daughter sitting opposite each other.)

Daughter (to son): No - left is that way!

Son: Haha not my left!

Daughter: (confused)

Dad: (explains. Daughter gets it.)

Dad: Cool. She's learning about symmetries and transformations!

Mum: She's learning how to see things from another person's point of view...

Reflection in a pub
Reflection in a pub Photograph: Jon Butterworth/JMB Photograph: Jon Butterworth/JMB

¹ Doing so via the Brout-Englert-Higgs mechanism, which involves interaction with a scalar field, of which the Higgs boson is an excitation, and which aforesaid boson is therefore required to be present, and is.

²We have confidence QCD is the right theory because at very high energies is becomes less strong, and then we can test its predictions.

³ In fact three antiquarks also works – antibaryons – but that’s pretty much the same mechanism as baryons.

⁴ Very much as the Higgs boson shows up as a bump at much higher masses in ATLAS and CMS.
