The mechanism by which particles gain mass through the Higgs field is known as the Higgs mechanism. According to the theory, the Higgs field permeates all of space, and particles interact with it to varying degrees, resulting in different masses.
The Higgs field has a non-zero vacuum expectation value (v.e.v), which means that even in its lowest energy state (vacuum), it has a non-zero value everywhere. This breaks a fundamental symmetry in the universe, known as electroweak symmetry, and gives rise to the masses of certain particles.
In the Standard Model of particle physics, particles are classified into two categories: fermions (such as quarks and leptons) and bosons (such as photons and W and Z bosons). Fermions gain mass through their interaction with the Higgs field, while bosons acquire mass due to their interaction with the Higgs field fluctuations.
To gain mass, fermions must couple with the Higgs field. The strength of this coupling determines the mass of the fermion. The more strongly a fermion interacts with the Higgs field, the greater its mass. This interaction happens regardless of the fermion's speed or motion. It is important to note that the mass of a particle is a fundamental property and is not dependent on its speed or state of motion.
For bosons, the Higgs field fluctuations affect their mass. The W and Z bosons, which mediate the weak nuclear force, acquire mass through their interaction with the Higgs field. In this case, the non-zero vacuum expectation value of the Higgs field affects the masses of the bosons, making them relatively heavy compared to the massless photon, which does not couple with the Higgs field.
In summary, particles gain mass through their interaction with the Higgs field. The strength of this interaction determines the mass of the particle, regardless of its speed or motion. The Higgs mechanism, involving symmetry breaking and the non-zero vacuum expectation value of the Higgs field, is responsible for giving mass to particles in the Standard Model of particle physics.