In elementaryparticle physics andmathematical physics, in particular ineffective field theory, aform factor is afunction that encapsulates the properties of a certainparticle interaction without including all of the underlyingphysics, but instead, providing the momentum dependence of suitable matrix elements. It is further measured experimentally in confirmation or specification of a theory—seeexperimental particle physics.

For example, at low energies the interaction of aphoton with anucleon is a very complicated calculation involving interactions between the photon and a sea ofquarks andgluons, 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 thematrix element for the electromagnetic current interaction is known,

${\displaystyle {\epsilon }_{\mu }\overline{N}\left(\alpha (q^2){\gamma }^{\mu }+\beta (q^2)q^{\mu }+\kappa (q^2){\sigma }^{\mu \nu }{q}_{\nu }\right)N}$

where${\displaystyle q^{\mu }}$ represents the photonmomentum (equal in magnitude toE/c, whereE is the energy of the photon). The three functions:${\displaystyle \alpha ,\beta ,\kappa }$ are associated to theelectric andmagnetic 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 general, theFourier transforms of form factor components correspond toelectric charge or magnetic profile space distributions (such as thecharge radius) of thehadron involved. The analogousQCDstructure functions are a probe of thequark andgluon distributions ofnucleons.

• Structure function
• Atomic form factor
• Electric form factor
• Magnetic form factor
• Photon structure function
• Quantum field theory
• Standard Model
• Quantum mechanics
• Special relativity
• Charge radius

• Brown, Lowell S. (1994).Quantum Field Theory.Cambridge University Press.ISBN 978-0-521-46946-3. p 400
• Gasiorowicz, Stephen (1966),Elementary Particle Physics, John Wiley & Sons,ISBN 978-0471292876

• Wilson, R. (1969). "Form factors of elementary particles",Physics today22 p 47,doi:10.1063/1.3035356
• Charles Perdrisat and Vina Punjabi (2010). "Nucleon Form factors",Scholarpedia5(8): 10204.online article

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