Contents

# Contents

## 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.

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

## 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:

• 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)