In physics, an effective field theory is an approximate theory (usually a quantum field theory) that contains the appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale, but ignores the substructure and the degrees of freedom at shorter distances (or, equivalently, higher energies).

Nevertheless, this approximation is often good enough to understand all processes whose typical distance scale is longer than the scale of the effective field theory or whose exchanged energy is smaller than the chosen bound.

For example, an effective field theory describes the nuclear interactions in terms of protons, neutrons, and mesons, even though all these objects are bound states of quarks. More generally, the transition between different effective field theories and the dependence of its parameters on the length scale in particular is described by the renormalization group.

One of the most widely used effective theories is chiral perturbation theory . The degrees of freedom are Goldstone bosons, identified with the lightest pseudoscalar mesons, (the pions, kaons and the eta) interacting with themselves and with heavier hadrons such as nucleons. The interactions in this theory are organized in an expansion in powers of the Goldstone boson momenta. The theory is most predictive for soft Goldstone bosons, but more unknown parameters need to be added to increase the precision at higher orders.

The special case of hadrons containing very heavy quarks (for example bottom and charm quarks) is described by another effective theory called heavy quark effective theory . Here the small expansion parameter is the inverse of the heavy quark mass.

Another limit of the theory of the strong interactions involves processes with very energetic mesons and baryons. The effective theory appropriate to this situation is the soft-collinear effective theory .

External Links

• Cliff P. Burgess, "Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory"