View source for Form factor (quantum field theory)

In elementary [[particle physics]] and [[mathematical physics]], in particular in [[effective field theory]], a '''form factor''' is a [[function (mathematics)|function]] that encapsulates the properties of a certain [[Fundamental interaction|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 [[quark]]s and [[gluon]]s, and often the calculation cannot be fully performed from first principles. Often in this context, form factors are also called "[[structure function]]s", since they can be used to describe the structure of the nucleon.

However, the generic Lorentz-invariant form of the [[Matrix element (physics)|matrix element]] for the electromagnetic current interaction is known,
: <math>\varepsilon_\mu \bar{N}\left(\alpha(q^2) \gamma^\mu +  \beta(q^2) q^\mu + \kappa(q^2) \sigma^{\mu \nu} q_\nu \right)N  \, </math> 
where <math>q^\mu</math> represents the photon [[momentum]] (equal in magnitude to ''E''/''c'', where ''E'' is the energy of the photon). The three functions: <math> \alpha, \beta , \kappa </math> are associated to the [[electric form factor|electric]] and [[magnetic form factor]]s 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, the [[Fourier transform]]s 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 function]]s are a probe of the [[quark]] and [[gluon]] distributions of [[nucleon]]s.

==References==

* {{cite book|ref=harv
 |last=Brown
 |first=Lowell S.
 |authorlink=Lowell S. Brown
 |title=Quantum Field Theory
 |publisher=[[Cambridge University Press]]
 |year=1994
 |isbn=978-0-521-46946-3 
}} p 400
*{{citation
 |title = Elementary Particle Physics
|last = Gasiorowicz 
|first = Stephen
|authorlink=Stephen Gasiorowicz
 |publisher = John Wiley & Sons
 |year = 1966
 |isbn = 978-0471292876
}}

*Wilson, R. (1969). "Form factors of elementary particles", ''Physics today'' '''22''' p 47, {{doi|10.1063/1.3035356}}
*Charles Perdrisat and Vina Punjabi (2010). "Nucleon Form factors", ''Scholarpedia'' '''5'''(8): 10204.  [http://www.scholarpedia.org/article/Nucleon_Form_factors online article]

==See also==
*[[Structure function]]
*[[Quantum field theory]]
*[[Standard model]]
*[[Quantum mechanics]]
*[[Special relativity]]
*[[Photon Structure Function]]
*[[Electric form factor]]
*[[Magnetic form factor]]
*[[Charge radius]]

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[[Category:Quantum field theory]]


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