In elementary particle physics and mathematical physics, in particular in effective field theory, a form factor is a function that encapsulates the properties of a certain particle interaction without including all of the underlying physics, but instead, providing the momentum dependence of suitable matrix elements. It is further measured experimentally in confirmation or specification of a theory—see experimental particle physics.
Photon-nucleon example
For example, at low energies the interaction of a photon with a nucleon is a very complicated calculation involving interactions between the photon and a sea of quarks and gluons, and often the calculation cannot be fully performed from first principles. Often in this context, form factors are also called "structure functions", since they can be used to describe the structure of the nucleon.
However, the generic Lorentz-invariant form of the matrix element for the electromagnetic current interaction is known,
where
In general, the Fourier transforms of form factor components correspond to electric charge or magnetic profile space distributions (such as the charge radius) of the hadron involved. The analogous QCD structure functions are a probe of the quark and gluon distributions of nucleons.