A group of physicists from the UK, Spain, USA and Canada have calculated the exact mass values ​​of the lightest up (u) and down (d) quarks.

The first proofs of the existence of quarks were obtained more than 40 years ago, but it was not possible for a long time to measure their mass in the experiment, or at least give its theoretical estimate. The reason is simple: the property of confinement prevents the observation of quarks in a free state, and physicists have to work with hadrons – elementary particles that contain quarks. It should be understood that the basic physical properties of a particle are determined by a limited number of valence quarks that interact and bond with each other through gluons. In addition to them, hadrons contain constantly emerging and disappearing virtual pairs of particles (the so-called sea quarks). In the case of the proton, which is believed to be made up of two up quarks and one down quark, these three valence particles account for less than two percent of its mass.

The masses of the four lightest quarks given by scientists in the article under consideration. The errors of the values ​​that are given in the documents of the international collaboration Particle Data Group are shown in color. (Illustration from Physical Review Letters.)

Scientists use lattice quantum chromodynamics (QCD) methods to calculate the characteristics of hadrons. In this popular interpretation of quantum chromodynamics – a theory describing strong interactions involving quarks and gluons – time is assumed to be discrete. In the space of a virtual hadron, a lattice is constructed, at the nodes of which the fields corresponding to quarks are determined, and in the links connecting neighboring sites, the fields corresponding to gluons. The simulation accuracy, as you might guess, is determined by the size of the links, which gradually decrease with increasing power of supercomputers.

In calculations within the framework of QCD on a lattice, the quark masses are selected in such a way that the properties of the resulting hadrons correspond to the experimental data. The masses of heavy quarks have already been determined with a fairly high accuracy, but the error in the values ​​established for light fundamental particles was as much as 30%.

The authors did not calculate the masses of the quarks directly, but determined the ratio of the masses of the charmed (c) and strange (s) quarks by performing simulations for lattices with intervals between sites from 0.15 to 0.05 fm. The exact value obtained – 11.85 ± 0.16 – was used in combination with the mass of the charmed quark established in 2008 and calculations by another scientific group, which found out the ratio of the masses of the strange, up and down quarks. As a result, the researchers came to the conclusion that the mass of the u-quark should be (2.01 ± 0.14) MeV / s², and the d-quark – (4.79 ± 0.16). These values, the error of which, as we can see, is much less than 30%, are only 0.214 and 0.510 percent of the mass of the proton.

Determining the exact parameters of quarks will allow theorists to predict and interpret the results of experiments with particle accelerators with greater confidence. Scientists also hope to build a theory that will develop the provisions of the Standard Model and clearly explain why quarks have this or that mass; obviously, for this physicists need to know its numerical value.

According to Norman Christ, an employee of Columbia University (USA), the presented values ​​require additional verification: in their calculations, the authors make several assumptions that can influence the result. “Most of all I would like to see confirmation of this data from a competing group that will do their best to find the error in the calculations,” says Mr Christ.

Source: science.compulenta.ru