physics - Yukawa interaction

In particle physics, Yukawa interaction, named after Hideki Yukawa, is an interaction between a scalar field $h$ and a Dirac field $Ψ$ of the type

$V \approx h\cdot\bar\Psi \Psi$

In the Standard Model, this interaction is responsible for the fermion masses after the Higgs field acquires a VEV.

It's also possible to have a Yukawa interaction between a scalar and a Majorana field. In fact, the Yukawa interaction involving a scalar and a Dirac spinor can be thought of as a Yukawa interaction involving a scalar with two Majorana spinors of the same mass.

$S[\phi,\psi]=\int d^dx \left[\frac{1}{2}\partial^\mu \phi \partial_\mu \phi -V(\phi) +\bar{\psi}(i\partial\!\!\!/-m-\lambda \phi)\psi\right]$

where λ is the (real) coupling constant.

$S[\phi,\chi]=\int d^dx \left[\frac{1}{2}\partial^\mu\phi \partial_\mu \phi -V(\phi)+\chi^\dagger i\bar{\sigma}\cdot\partial\chi+\frac{i}{2}(m+\lambda \phi)\chi^T \sigma^2 \chi-\frac{i}{2}(m+\lambda \phi)^* \chi^\dagger \sigma^2 \chi^*\right]$

where λ is complex coupling constant and m is a complex number.

Yukawa interaction

See also