nLab Symanzik effective field theory

Idea

In the field of quantum chromodynamics, what is known as Symanzik’s effective field theory (Symanzik 82, Symanzik 83) is a type of effective field theory used in lattice QCD in order to deal with lattice-spacing effects.

In lattice QCD, the extraction of hadronic observables involves setting a scale for a particular lattice action functional with given sea-quark configurations. This involves the extrapolation of the dimensionless product of various quantities, such as gradient-flow scales and the omega baryon mass, to the continuum and infinite volume limit. This is in turn, interpolated to quark mass points in the isospin limit. These extrapolation functions must incorporate:

1. Light and Strange Quark Mass Dependence

2. Finite Volume Corrections

3. Discretization Corrections

Symanzik’s effective field theory is constructed by expanding the discretized action about the continuum limit.

Related concepts

effective field theories of nuclear physics, hence for confined-phase quantum chromodynamics:

• with effective ligh meson fields:

  • chiral perturbation theory

    • vector meson dominance

    • hidden local symmetry

  • with emergent (solitonic) baryon fields:

    • quark bag model

    • Skyrme model

    • Witten-Sakai-Sugimoto model

  • with explicit effective baryon fields:

    • baryon chiral perturbation theory

    • quantum hadrodynamics

      • Walecka model

  • with explicit quark fields:

    • quark-meson coupling model

References

Original articles:

• Kurt Symanzik, Section 3 of: Some topics in quantum field theory In: Schrader R., Seiler R., Uhlenbrock D.A. (eds.) Mathematical Problems in Theoretical Physics Lecture Notes in Physics, vol 153, Springer 1982 (doi:10.1007/3-540-11192-1_11)

• Kurt Symanzik, Continuum limit and improved action in lattice theories: (I). Principles and $\phi^4$ theory, Nuclear Physics B Volume 226, Issue 1, 26 September 1983, Pages 187-204 Nuclear Physics B (doi:10.1016/0550-3213(83)90468-6)

Review:

• Andreas S. Kronfeld, Section 4 in: Uses of Effective Field Theory in Lattice QCD, in: At the Frontier of Particle Physics pp. 2412-2477, World Scientific 2002 (arXiv:hep-lat/0205021, doi:10.1142/9789812777270_0004)

See also:

• Stephen R. Sharpe, Robert L. Singleton,Jr, Spontaneous flavor and parity breaking with Wilson fermions Phys. Rev.D58, 074501 (1998), ([arXiv:hep-lat/9804028])

• Scale setting the Möbius Domain Wall Fermion on gradient-flowed HISQ action using the omega baryon mass and the gradient-flow scales $t_0$ and $w_0$ (arXiv:hep-lat/2011.12166)