Particle physics

Weighty questions

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In an unprecedented feat of computation, particle theorists made the most precise prediction yet of the mass of the ‘charm–bottom’ particle. Days later, experimentalists dramatically confirmed that prediction.

The lofty endeavour of particle physicists — to understand the birth, evolution and ultimate fate of the Universe by studying its fundamental particles — has just received a significant boost. The fiendishly difficult equations of the strong nuclear force have yielded to a 30-year effort to allow the first precise prediction of a composite particle's mass1, a prediction promptly confirmed by experiment2. The computational technique responsible, lattice quantum chromodynamics, could also be used to estimate quark masses better, to shed light on the origin of mass, and to reveal how the Universe, originally made of matter and antimatter in equal proportions, ended up containing just matter.

The ‘standard model’ of particle physics describes the interaction of fundamental particles, such as quarks and electrons, as the exchange of other particles that convey force. In an atom, for example, electrons bind to protons by swapping massless photons — the familiar electromagnetic force encompassed by the theory of quantum electrodynamics (QED). Similarly, inside the proton, ‘up’ and ‘down’ quarks bind by exchanging massless particles called gluons — an interaction described by the so-called strong force and the theory of quantum chromodynamics (QCD). Without this strong force, which not only binds quarks to form protons, but also keeps protons together in the nucleus, matter would simply fall apart.

The fundamental particles possess a wide range of masses: an electron is about 360,000 times lighter than the heaviest, or ‘top’, quark. In the standard model, the origin of the mass of fundamental particles is the yet-to-be-discovered Higgs force field. The reason electrons and quarks have the exact masses that they do must, however, come from a deeper theory of nature. Physicists hope that gaining knowledge of the quark masses will guide them to that theory.

As quarks are permanently bound into composite particles (Fig. 1), it is not possible to determine their masses directly. Theorists instead solve the equations of QCD for a composite particle made up of quarks (protons and neutrons are examples) with the quark masses and strength of the strong force as unknowns. The most likely value of a quark mass is that which best reproduces the measured mass of the composite particle. As energy is related to mass through E=mc2, where m is the mass of the particle and c the speed of light, this mass depends not only on the mass of the constituent quarks, but also on the bonds between them (potential energy) and their motion (kinetic energy).

Figure 1: Gregarious quarks.

a, Free quarks do not exist. In a proton, for example, the three principal quarks — two ‘up’ (u) and one ‘down’ (d) — are bound with a force of more than 10 tonnes by the exchange of gluons (curly lines). Additional gluons and quark pairs are constantly emitted, only to be reabsorbed; just a fraction of this swarm of particles is shown here, and for clarity the gluons that pass between the d quark and u quark in the proton are not shown. b, Tug on one of the three quarks in a proton, and c, by the time the separation is a proton radius (about 10−15 m), enough work has been done to produce a quark and an antiquark. d, The antiquark latches on to the quark to form a quark–antiquark state called a π-meson; the new quark replaces the original in the proton. The ‘charm–bottom’ particle, the mass of which was predicted by Allison et al.1, is a heavier variant of the π-meson, containing a ‘charm’ quark and a ‘bottom’ antiquark.

The mass of a hydrogen atom is less than the mass of its constituents by the electromagnetic binding energy (−13.6 electronvolts) — an effect of 1 part in 100 million. The effect of the strong force is greater: the mass of a nitrogen nucleus, with seven protons and seven neutrons, is less than the mass of its constituents by a binding energy of −105 megaelectronvolts (MeV), 0.7% of the total mass. This is the formidable energy that is released in nuclear fission and fusion reactions.

The binding effects between quarks are fundamentally different from those in atoms and atomic nuclei: they are positive, and so increase the mass of the composite particle. They are also two orders of magnitude larger than the quark masses themselves. In other words, nearly all the mass of protons and neutrons — of ordinary matter in the Universe, including stars, planets and humans — is due to the strong force's binding energy.

A precise calculation of the electromagnetic binding energy for hydrogen must include the possibilities that photons can be emitted and reabsorbed by the electron, and that pairs of electrons and positrons (the antimatter counterpart of the electron) can pop briefly into existence. Because the electromagnetic force is weak, these quantum corrections are small; a calculation involves just adding up a sufficient number of them. Consequently, the theory of QED has been verified to the tenth decimal place.

QCD is more complicated: not only do pairs of quarks and antiquarks make fleeting appearances and quarks constantly exchange gluons, but those gluons can constantly exchange other gluons as well. The quantum corrections are so large that adding them all up is not feasible. So the strong-force properties of composite particles are instead calculated using powerful computers to keep track of the most probable arrangements of the quarks and gluons inside them. No computer in existence can follow every quark and gluon, so the problem is simplified by imagining space and time not as a continuum, but as a lattice — a four-dimensional grid of discrete points in space-time. Quarks reside at these points and gluons on the links between them, reducing an infinite number of variables to a finite (though very large) number — an approach known as lattice QCD.

In the 1980s, lattice QCD was used to explain why quarks are bound inside protons. But the first realistic calculation of particle properties, rather than prediction of qualitative features, came only in 2003. Then, a significant breakthrough3 in the lattice technique — and teraflop-scale computers running for two years — allowed the inclusion of all pairs of light quarks (up, down and a third, slightly heavier variety, ‘strange’) and antiquarks that fluctuate into brief existence inside a composite particle. These quark–antiquark pairs had usually been left out of the calculations because their simulation — much more difficult than that of gluons — had demanded prohibitively large amounts of computer time.

After first obtaining the quark masses by ‘tuning’ the lattice to reproduce the masses of some well-known composite particles, ten further strong-force properties of composite particles were calculated3. The deviation of the calculated values from the accepted experimental values was never more than a few per cent. But the first prediction of an unknown quantity was still wanting; it is this that a team of lattice QCD experts from Glasgow University in Scotland and Ohio State University and Fermilab in the United States, writing in Physical Review Letters1, has now supplied.

The composite particle Bc or ‘charmed B-meson’, a bound state of a charm quark and a bottom antiquark, is known as the ‘last meson’ because it was the final such quark–antiquark pairing that physicists expected to find. The Bc was discovered in 1998, but its mass could not be determined accurately. Here was thus a rare opportunity for the lattice theorists to predict the mass before better measurements were made. Only days after their prediction1 of 6,304±22 MeV appeared on a preprint server, the CDF experiment2, picking through the pieces of trillions of particle collisions at Fermilab's Tevatron accelerator in Illinois, isolated 19 examples of the last meson with a mass of 6,287±4.9 MeV. The agreement between theory and experiment (Fig. 2) is a powerful validation of the lattice technique, especially for bottom and charm quarks.

Figure 2: Perfect harmony.

A comparison of the new lattice QCD calculation of Allison et al.1 (central point) for the mass of the Bc meson compared with an earlier calculation7 (left) and the experimental measurement of Acosta et al.2 (right). The uncertainty in the new calculation is five times smaller than the previous one and is validated by the experimental measurement.

An even stiffer test is imminent. Quarks also experience radioactive decays through the so-called weak force, the third fundamental force of the standard model. The pattern of these decay rates would be, especially for bottom quarks, sensitive to phenomena beyond the standard model4. The binding effect of the strong force between quarks modifies the decay rates, and so correction factors are needed to allow a full interpretation of new data.

These correction factors are even more difficult to predict than the composite particle masses. But their first calculation5 for mesons containing charm quarks has just been performed. Almost simultaneously, the CLEO experiment at Cornell University in New York has announced the result6 of the first measurement. The agreement is again good, although the accuracy of both the prediction and the experimental value is only around 10% (this should improve to under 5% within a year). If the agreement persists, similar calculations can be confidently applied to correct measurements of the disintegration rates of bottom quark mesons, whose correction factors are not measurable. If the corrected rates do not conform to standard-model predictions, they could provide hints about the deeper theory that gives quarks their mass — and, ultimately, why only matter exists in the Universe.


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    Allison, I. et al. Phys. Rev. Lett. 94, 172001 (2005).

  2. 2

    Acosta, D. et al. Phys. Rev. Lett. (submitted); preprint at

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    Davies, C. T. H. et al. Phys. Rev. Lett. 92 022001 (2004).

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    Shipsey, I. et al. Nature 427 591–592 (2004).

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    Aubin, C. et al. Phys. Rev. Lett. (submitted); preprint at (2005).

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    Bonvicini, G. et al. 22nd Symp. Lepton–Photon Interactions at High Energy, Uppsala 1–5 July 2005 (submitted).

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    Shanahan, H. P. et al. Phys. Lett. B 453, 289–294 (1999).

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Shipsey, I. Weighty questions. Nature 436, 186–187 (2005) doi:10.1038/436186a

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