The Higgs boson obtains its mass through a mechanism known as electroweak symmetry breaking, which is a fundamental aspect of the Higgs mechanism. In the Standard Model of particle physics, the Higgs field permeates all of space, and particles interact with this field to acquire mass.
In quantum field theory (QFT), the Higgs field is described by a scalar field that has a non-zero vacuum expectation value. The Higgs field interacts with the electroweak gauge bosons (W and Z bosons) and fermions (such as quarks and leptons) through a process known as Yukawa coupling.
The Higgs field and the associated Higgs boson arise from the Higgs mechanism, which involves spontaneous symmetry breaking. At high energies, the electroweak symmetry is unbroken, and the W and Z bosons and the Higgs boson are massless. However, as the universe cools down after the Big Bang, the Higgs field settles into a non-zero vacuum expectation value, breaking the electroweak symmetry and giving mass to the W and Z bosons. The Higgs boson itself emerges as a quantum fluctuation or excitation of the Higgs field.
While QFT provides a theoretical framework to describe the Higgs mechanism and calculate various properties of the Higgs boson, it does not allow for an exact calculation of the Higgs boson's mass. The mass of the Higgs boson is an input parameter in the Standard Model and needs to be determined experimentally through particle collider experiments. The discovery of the Higgs boson at the Large Hadron Collider (LHC) in 2012 confirmed its existence and provided an experimental measurement of its mass, which is approximately 125 GeV/c².
It's important to note that while the Higgs boson mass can be experimentally determined, QFT itself cannot predict its value. Theoretical calculations in QFT involve a combination of perturbative techniques, approximations, and experimental input to make predictions about particle interactions and properties.