Heavy particles, which physicists call baryons, are like tiny families of three quarks. The common baryons are protons and neutrons, which make up everything around us. But there are also exotic relatives: instead of light quarks, they harbor charm or bottom quarks — heavy and short-lived. Such particles are born only in accelerator collisions and live for infinitesimal fractions of a second.

To determine their masses, scientists cannot simply weigh a particle on a scale. Instead, they use lattice computer simulations — an imaginary grid that divides space and time. On this grid, they calculate how quarks and the gluons that bind them behave. The main challenge is to correctly account for the motion of the heavy bottom quark. Previously, it was described approximately, as if it were stationary. In the new work, a fully relativistic approach was applied for the first time: the quark moves at speeds close to the speed of light, and this is taken into account exactly.

The calculation results matched experimental data for known particles and provided predictions for yet undiscovered ones. It's like building an accurate model of a family from photographs of a few members, and learning the height and weight of those never seen. Such calculations help physicists prepare future experiments at the Large Hadron Collider and other accelerators.

Now that the method is validated, masses of entire families of heavy particles can be calculated. This is an important step toward understanding how quarks assemble into matter — from the lightest to the heaviest combinations.