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Build and match effective field theories
Organize low-energy predictions through symmetries, scale separation, operator bases, matching, and transparent estimates of truncation uncertainty.
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Inside this module
Module 01 research
Build and match effective field theories
Organize low-energy predictions through symmetries, scale separation, operator bases, matching, and transparent estimates of truncation uncertainty.
- 01
Separation of scales and local expansions
Identify which heavy contributions can be replaced by local operators and test a derivative expansion against a known pole.
38 min - 02
Operator dimensions and EFT power counting
Build dimensionally consistent interactions and translate canonical dimensions into a qualified amplitude expansion.
38 min - 03
Redundant operators and field redefinitions
Reduce an EFT operator basis while preserving on-shell observables and tracking induced coefficient shifts.
38 min - 04
Tree-level matching by heavy-field elimination
Eliminate a specified heavy scalar and match local operators, keeping sign, factorial, and crossed-channel cancellations explicit.
38 min - 05
One-loop matching and regulator consistency
Subtract common infrared physics to identify a local one-loop coefficient and keep UV renormalization distinct from IR cancellation.
38 min - 06
Wilson-coefficient running and operator mixing
Evolve matched coefficients between scales and track the compensating operator evolution with a declared transpose convention.
38 min - 07
Nonrelativistic effective field theories
Separate rest energy from residual motion and explain how a large scattering length changes the organization of contact interactions.
38 min - 08
Chiral effective theory and low-energy constants
Organize pion interactions by soft momenta and quark masses, with loop order and low-energy constants counted together.
38 min - 09
The Standard Model effective operator expansion
State the SMEFT field and symmetry assumptions, count operator orders, and connect a normalized dimension-five interaction to an illustrative neutrino scale.
38 min - 10
EFT truncation errors and validity tests
Construct transparent truncation estimates, separate them from other uncertainties, and test their coefficient and breakdown assumptions.
38 min