Mass–action equivalence with respect to Explicit Symmetry Breaking

The mass–action equivalence emerges naturally as the consequence of Relativistic Heisenberg Uncertainty (RHU). It changes the structure of relativistic energy–momentum equation that has been underpinning the chosen Lagrangian of the Standard Model, i.e., the Lagrangian which the Higgs mechanism works. The transition from the mass–energy to the mass–action equivalence zone occurs at a certain value of the particle’s wave group velocity $$v_{{\text{g}}}$$ indicating the crossing curve between relativistic energy and action. Due to this transition, particles in the Standard Model are not going to gain inertial mass coming from the Higgs mechanism and related Higgs field, but from another mechanism which can break the Lagrangian symmetry of the Standard Model. This mechanism corresponds to Explicit Symmetry Breaking by generating the new type of field, i.e., the X-Higgs-like field and works based on the mass–action equivalence. This field provides the mass for the X Matter as well as Higgs field for Ordinary Matter. The gaining mass of particles due to this mechanism is not related to the form of ordinary relativistic energy, but to the form of relativistic action. It leads us to the new dynamical equation instead of the ordinary Klein–Gordon and Dirac equation. There are two phenomena due to the increasing and decreasing of particle’s velocity in this mechanism. From the lower to the higher velocity, particle gains additional inertial mass from the X Matter, while conversely particle loses its inertial mass. It is reasonable for us to view that the missing inertial mass of particles in the Standard Model is compensated as the Dark Matter. The X-Higgs-like field breaking to be the Dark-Higgs-like and recognized Higgs field can be considered to explain the origin of the Dark and Ordinary Matter from the X Matter.