In elementary particle physics and mathematical physics, in particular in effective field theory, a form factor is a

function Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-oriente ...

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 In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number (nucleon number). Until the 1960s, nucleons were ...

is a very complicated calculation involving interactions between the photon and a sea of

quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All commonly o ...

s and

gluon A gluon ( ) is an elementary particle that acts as the exchange particle (or gauge boson) for the strong force between quarks. It is analogous to the exchange of photons in the electromagnetic force between two charged particles. Gluons bind q ...

s, 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, :

\varepsilon_\mu \bar\left(\alpha(q^2) \gamma^\mu +  \beta(q^2) q^\mu + \kappa(q^2) \sigma^ q_\nu \right)N  \,

where

q^\mu

represents the photon momentum (equal in magnitude to ''E''/''c'', where ''E'' is the energy of the photon). The three functions:

\alpha, \beta , \kappa

are associated to the

electric Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described ...

and magnetic form factors for this interaction, and are routinely measured experimentally; these three effective vertices can then be used to check, or perform calculations that would otherwise be too difficult to perform from first principles. This matrix element then serves to determine the transition amplitude involved in the scattering interaction or the respective particle decay—cf.

Fermi's golden rule In quantum physics, Fermi's golden rule is a formula that describes the transition rate (the probability of a transition per unit time) from one energy eigenstate of a quantum system to a group of energy eigenstates in a continuum, as a result of ...

. 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 In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type o ...

structure functions are a probe of the

and

distributions of

References

* p 400 * *Wilson, R. (1969). "Form factors of elementary particles", ''Physics today'' 22 p 47, *Charles Perdrisat and Vina Punjabi (2010). "Nucleon Form factors", ''Scholarpedia'' 5(8): 10204.
online article

Photon–nucleon example

References

See also