source varies the apparent size of the surface (the solid angle) as the force also follows the dependence. This is equivalent to the part of the potential. In addition, the exchanged mesons are unstable and have a finite lifetime. The disappearance (radioactive decay) of the mesons causes a reduction of the flux through the surface that results in the additional exponential factor of the Yukawa potential. Massless particles such as photons are stable and thus yield only potentials. (Note however that other massless particles such as gluons or gravitons do not generally yield potentials because they interact with each other, distorting their field pattern. When this self-interaction is negligible, such as in weak-field gravity (Newtonian gravitation) or for very short distances for the strong interaction (asymptotic freedom), the potential is restored.) The action The Yukawa interaction is an interaction between a scalar field (or pseudoscalar field) and a Dirac field of the type (scalar) or (pseudoscalar). The action for a meson field interacting with a Dirac baryon field is where the integration is performed over dimensions; for typical four-dimensional spacetime , and The meson Lagrangian is given by Here, is a self-interaction term. For a free-field massive meson, one would have where is the mass for the meson. For a (renormalizable, polynomial) self-interacting field, one will have where 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 where is the real-valued, positive mass of the fermion. The Yukawa interaction term is where is the (real) coupling constant for scalar mesons and for pseudoscalar mesons. Putting it all together one can write the above more explicitly as Yukawa coupling to the Higgs in the Standard Model A Yukawa coupling term to the Higgs field effecting spontaneous symmetry breaking in the Standard Model is responsible for fermion masses in a symmetric manner. Suppose that the potential has its minimum, not at but at some non-zero value This can happen, for example, with a potential form such as with set to an imaginary number. In this case, the Lagrangian exhibits spontaneous symmetry breaking. This is because the non-zero value of the field, when operating on the vacuum, has a non-zero vacuum expectation value of In the Standard Model, this non-zero expectation is responsible for the fermion masses despite the chiral symmetry of the model apparently excluding them. To