Yukawa interaction

In particle physics, Yukawa's interaction or Yukawa coupling, named after Hideki Yukawa, is an interaction between a scalar field ϕ and a Dirac field ψ of the type

The Yukawa interaction can be used to describe the nuclear force between nucleons (which are fermions), mediated by pions (which are pseudoscalar mesons). The Yukawa interaction is also used in the Standard Model to describe the coupling between the Higgs field and massless quark and lepton fields (i.e., the fundamental fermion particles). Through spontaneous symmetry breaking, these fermions acquire a mass proportional to the vacuum expectation value of the Higgs field.

The action for a meson field φ interacting with a Dirac baryon field ψ is

where the integration is performed over d dimensions (typically 4 for four-dimensional spacetime). The meson Lagrangian is given by

Here, ${\displaystyle V(\phi )}$ is a self-interaction term. For a free-field massive meson, one would have ${\displaystyle V(\phi )={\frac {1}{2}}\mu ^{2}\phi ^{2}}$ where ${\displaystyle \mu }$ is the mass for the meson. For a (renormalizable, polynomial) self-interacting field, one will have ${\displaystyle V(\phi )={\frac {1}{2}}\mu ^{2}\phi ^{2}+\lambda \phi ^{4}}$ where λ is a coupling constant. This potential is explored in detail in the article on the quartic interaction.

...
Wikipedia