A weaker coupling sets the particles free

A weaker coupling sets the particles free

For a long time physicists believed that it would be impossible to find a theory by which the effects of the strong interaction between quarks could be calculated in the same way as for the electromagnetic or the weak interaction. If, for example, the interaction between two protons in a nucleus is studied, quite good results can be obtained by describing it as an exchange of pi-mesons — an idea that gave Hideki Yukawa the Nobel Prize in 1949. A coupling constant larger than 1 is needed, however, which means that Feynman’s perturbation calculations (see above) cannot be used. Unfortunately, even today there is no satisfactory method for calculating such strong interaction effects.

The situation seemed to be even worse for higher energies; if the beta function is positive (the way the coupling constant changes with energy) the interaction will be even stronger and the calculations become increasingly absurd.

The German theoretical physicist, Kurt Symanzik (now deceased), realised that the only way to achieve a reasonable theory was to find one with a negative beta function. That would also explain why quarks could sometimes appear as free particles, grains, inside the proton — an effect that had been seen in scattering experiments between electrons and protons.

Unfortunately, Symanzik himself did not find such a theory, and although Gerardus’t Hooft was very close to discovering it during the summer of 1972, physicists started to despair. “Evidence” was even presented that all realistic theories had a positive beta function. We now know it was incorrect because in June 1973 this year’s Laureates entered the arena. In two publications back-to-back in the journal Physical Review Letters, one by Gross and Wilczek and one by Politzer, the amazing discovery was announced that the beta function can be negative. When their discovery was made, these physicists were quite young — Wilczek and Politzer were still graduate students, in fact.

According to their theories, the force carriers, the gluons, have a unique and highly unexpected property, namely that they interact not only with quarks but also with each other. This property means that the closer quarks come to each other, the weaker the quark colour charge and the weaker the interaction. Quarks come closer to each other when the energy increases, so the interaction strength decreases with energy. This property, called asymptotic freedom, means that the beta function is negative. On the other hand, the interaction strength increases with increasing distance, which means that a quark cannot be removed from an atomic nucleus. The theory confirmed the experiments: quarks are confined, in groups of three, inside the proton and the neutron but can be visualized as “grains” in suitable experiments.

Asymptotic freedom makes it possible to calculate the small distance interaction for quarks and gluons, assuming that they are free particles. By colliding the particles at very high energies it is possible to bring them close enough together. When asymptotic freedom had been discovered and a theory, Quantum ChromoDynamics, QCD, that was asymptomatically free, had been formulated, calculations could be made for the first time that showed excellent agreement with experiments (fig. 2).

Fig. 2. The value of the “running” coupling constant, as, as a function of the energy scale E. The curve that slopes downwards (negative beta function) is a prediction of the asymptomatic freedom in QCD and, as can be seen, it agrees very closely with the measurements that have been made

The showers of particles reveal the truth

An important proof of the QCD theory is provided by the collisions between electrons and their antiparticles, positrons, with very high kinetic energy, when they annihilate each other. According to Einstein’s equation E= mc², kinetic energy can be transformed into new particles, for example, quarks with mass and kinetic energy. These quarks are created very deep within the process, very close to each other but moving away from each other at an extremely high speed. Thanks to the asymptotic freedom in QCD it is now possible to calculate this process.

Admittedly, when the quarks have moved away from each other, they are influenced by increasingly strong forces that eventually lead to the creation of new quark-antiquark particles, and a shower of particles arises in the direction of the original quarks and antiquarks respectively. But the process retains a “memory” of the first asymptomatically free part which can be calculated, giving a value for the probability of the occurrence of these two-shower events that agrees with observations.

Even more convincing, perhaps, are the three-shower occurrences discovered at the DESY accelerator in Hamburg in the late 1970s. These occurrences can be successfully interpreted as a gluon radiating away from a quark or an antiquark (fig. 3).

Fig. 3. Occurrences of two or three showers of particles observed in collisions between electrons and positrons. The enlarged portion displays the QCD interpretation, that also allows detailed calculations of the probability for these occurrences. These probabilities agree very well with measured data (e–= electron,         e+= positron, q= quark, q with overscore= antiquark, g= gluon)

The QCD asymptotic freedom that this year's Laureates discovered also provided physicists with an explanation of a phenomenon that had been observed several years earlier at the Stanford accelerator (Friedman, Kendall and Taylor; Nobel Prize in 1990). The electrically-charged constituents of the proton behave as free particles when they are hit so hard that they get a high energy. By adding together the amount of the proton’s momentum that comprised the charged constituents (the quarks) it also became evident that about half of the proton momentum was something else — gluons!