Editing Effective field theory (section)

==Examples==
===Fermi theory of beta decay===
The best-known example of an effective field theory is the [[Fermi's interaction|Fermi theory of beta decay]]. This theory was developed during the early study of weak decays of [[Atomic nucleus|nuclei]] when only the [[hadron]]s and [[lepton]]s undergoing weak decay were known. The typical [[elementary particle reaction|reactions]] studied were:

::<math>
\begin{align}
n & \to p+e^-+\overline\nu_e \\
\mu^- & \to e^-+\overline\nu_e+\nu_\mu.
\end{align}
</math>

This theory posited a pointlike interaction between the four [[fermion]]s involved in these reactions. The theory had great [[phenomenology (particle physics)|phenomenological]] success and was eventually understood to arise from the [[gauge theory]] of [[electroweak interaction]]s, which forms a part of the [[standard model]] of particle physics. In this more fundamental theory, the interactions are mediated by a [[flavour (particle physics)|flavour]]-changing [[gauge boson]], the W<sup>±</sup>. The immense success of the Fermi theory was because the W particle has mass of about 80 [[GeV]], whereas the early experiments were all done at an energy scale of less than 10 [[MeV]]. Such a separation of scales, by over 3 orders of magnitude, has not been met in any other situation as yet.

===BCS theory of superconductivity===
Another famous example is the [[BCS theory]] of [[superconductivity]]. Here the underlying theory is the theory of [[electron]]s in a [[metal]] interacting with lattice vibrations called [[phonon]]s. The phonons cause attractive interactions between some electrons, causing them to form [[Cooper pair]]s. The length scale of these pairs is much larger than the wavelength of phonons, making it possible to neglect the dynamics of phonons and construct a theory in which two electrons effectively interact at a point. This theory has had remarkable success in describing and predicting the results of experiments on superconductivity.

===Gravitational field theories ===
[[General relativity]] (GR) itself is expected to be the low energy effective field theory of a full theory of [[quantum gravity]], such as [[string theory]] or [[loop quantum gravity]]. The expansion scale is the [[Planck mass]].
Effective field theories have also been used to simplify problems in general relativity, in particular in calculating the [[gravitational wave]] signature of inspiralling finite-sized objects.<ref>{{Cite journal |arxiv = hep-th/0409156|last1 = Goldberger|first1 = Walter|title = An Effective Field Theory of Gravity for Extended Objects|journal = Physical Review D|volume = 73|issue = 10|last2 = Rothstein|first2 = Ira|year = 2004| page=104029 |doi = 10.1103/PhysRevD.73.104029|s2cid = 54188791}}</ref> The most common EFT in GR is non-relativistic general relativity (NRGR),<ref>{{Cite web |last1=Porto |first1=Rafael A. |last2=Rothstein |first2=Ira |last3=Goldberger |first3=Walter |title=EFT meets GR |url=https://online.kitp.ucsb.edu/online/numrel-m08/buonanno/pdf1/Porto_NumRelData_KITP.pdf |access-date=3 November 2023 |website=online.kitp.ucsb.edu}}</ref><ref>{{Cite journal |arxiv = 0712.4116|last1 = Kol|first1 = Barak|title = Non-Relativistic Gravitation: From Newton to Einstein and Back|journal =  Classical and Quantum Gravity|volume = 25|issue = 14|pages = 145011|last2 = Smolkin|first2 = Lee|year = 2008|doi = 10.1088/0264-9381/25/14/145011|bibcode = 2008CQGra..25n5011K|s2cid = 119216835}}</ref><ref>{{Cite journal |arxiv = gr-qc/0511061|last1 = Porto|first1 = Rafael A|title = Post-Newtonian corrections to the motion of spinning bodies in NRGR|journal =  Physical Review D|volume = 73|issue = 104031|pages = 104031|year = 2006|doi = 10.1103/PhysRevD.73.104031|s2cid = 119377563}}</ref> which is similar to the [[post-Newtonian expansion]].<ref>{{Cite journal |doi = 10.1103/PhysRevD.88.104037|title = Theory of post-Newtonian radiation and reaction|journal = Physical Review D|volume = 88|issue = 10|pages = 104037|year = 2013|last1 = Birnholtz|first1 = Ofek|last2 = Hadar|first2 = Shahar|last3 = Kol|first3 = Barak|arxiv = 1305.6930|bibcode = 2013PhRvD..88j4037B|s2cid = 119170985}}</ref> Another common GR EFT is the extreme mass ratio (EMR), which in the context of the inspiralling problem is called [[extreme mass ratio inspiral]].

===Other examples===
Presently, effective field theories are written for many situations.
*One major branch of [[nuclear physics]] is [[quantum hadrodynamics]], where the interactions of [[hadron]]s are treated as a field theory, which should be derivable from the underlying theory of [[quantum chromodynamics]] (QCD). Quantum hadrodynamics is the theory of the [[nuclear force]], similarly to quantum chromodynamics being the theory of the [[strong interaction]] and quantum electrodynamics being the theory of the [[electromagnetic force]]. Due to the smaller separation of length scales here, this effective theory has some classificatory power, but not the spectacular success of the Fermi theory.
*In [[particle physics]] the effective field theory of QCD called [[chiral perturbation theory]] has had better success.<ref>{{Cite journal |arxiv = hep-ph/9311274|last1 = Leutwyler|first1 = H|title = On the Foundations of Chiral Perturbation Theory|journal =  Annals of Physics|volume = 235|pages = 165–203|year = 1994|issue = 1|doi = 10.1006/aphy.1994.1094|bibcode = 1994AnPhy.235..165L|s2cid = 16739698}}</ref> This theory deals with the interactions of [[hadron]]s with [[pion]]s or [[kaon]]s, which are the [[Goldstone boson]]s of [[spontaneous chiral symmetry breaking]]. The expansion parameter is the [[pion]] energy/momentum.
*For [[hadron]]s containing one heavy [[quark]] (such as the [[bottom quark|bottom]] or [[Charm quark|charm]]), an effective field theory which expands in powers of the quark mass, called the [[heavy quark effective theory]] (HQET), has been found useful.
*For [[hadron]]s containing two heavy quarks, an effective field theory which expands in powers of the [[relative velocity]] of the heavy quarks, called non-relativistic QCD (NRQCD), has been found useful, especially when used in conjunctions with [[lattice QCD]].
*For [[hadron]] reactions with light energetic ([[collinear]]) particles, the interactions with low-energetic (soft) degrees of freedom are described by the [[soft-collinear effective theory]] (SCET).
*Much of [[condensed matter physics]] consists of writing effective field theories for the particular property of matter being studied.
*Dissipationless [[hydrodynamics]] can also be treated using effective field theories.<ref>{{Cite journal |arxiv = 1211.6461|last1 = Endlich|first1 = Solomon|title = Dissipation in the effective field theory for hydrodynamics: First order effects|journal =  Physical Review D|volume = 88|issue = 10|pages = 105001|last2 = Nicolis|first2 = Alberto|last3 = Porto|first3 = Rafael|last4 = Wang|first4 = Junpu|year = 2013|doi = 10.1103/PhysRevD.88.105001|bibcode = 2013PhRvD..88j5001E|s2cid = 118441607}}</ref>