 in particle physics, yukawa's interaction, named after hideki yukawa, is an interaction between a scalar field Ï and a dirac field Ï of the type :v \approx g\bar\psi \phi \psi (scalar) or g \bar \psi i\gamma^5 \phi \psi (pseudoscalar). the yukawa interaction can be used to describe the strong 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== the action for a meson field Ï interacting with a dirac baryon field Ï is :s[\phi,\psi]=\int d^dx \;\left[ \mathcal{l}_\mathrm{meson}(\phi) + \mathcal{l}_\mathrm{dirac}(\psi) + \mathcal{l}_\mathrm{yukawa}(\phi,\psi) \right] where the integration is performed over d dimensions (typically 4 for four-dimensional spacetime). the meson lagrangian is given by :\mathcal{l}_\mathrm{meson}(\phi) = \frac{1}{2}\partial^\mu \phi \partial_\mu \phi -v(\phi). here, v(\phi) is a self-interaction term. for a free-field massive meson, one would have v(\phi)=\frac{1}{2}\mu^2\phi^2 where \mu is the mass for the meson. for a (renormalizable) self-interacting field, one will have v(\phi)=\frac{1}{2}\mu^2\phi^2 + \lambda\phi^4 where Î» is a coupling constant. this potential is explored in detail in the article on the quartic interaction. the free-field dirac lagrangian is given by :\mathcal{l}_\mathrm{dirac}(\psi) = \bar{\psi}(i\partial\!\!\!/-m)\psi where m is the positive, real mass of the fermion. the yukawa interaction term is :\mathcal{l}_\mathrm{yukawa}(\phi,\psi) = -g\bar\psi \phi \psi where g is the (real) coupling constant for scalar mesons and :\mathcal{l}_\mathrm{yukawa}(\phi,\psi) = -g\bar\psi i\gamma^5 \phi \psi for pseudoscalar mesons. putting it all together one can write the above more explicitly as :s[\phi,\psi]=\int d^dx \left[\frac{1}{2}\partial^\mu \phi \partial_\mu \phi -v(\phi) + \bar{\psi}(i\partial\!\!\!/-m)\psi -g \bar{\psi}\phi\psi \right]. ==classical potential== if two fermions interact through a yukawa interaction with yukawa particle mass \mu, the potential between the two particles, known as the yukawa potential, will be: :v(r)=-\frac{g^2}{4\pi} \frac{1}{r} e^{-\mu r} which is the same as a coulomb potential except for the sign and the exponential factor. the sign will make the interaction attractive between all particles (the electromagnetic interaction is repulsive for identical particles). this is explained by the fact that the yukawa particle has spin zero and even spin always
Electroweak_theory Particle_physics Quantum_field_theory Standard_Model