ADVANCED TOPICS IN THE THEORY OF THE FUNDAMENTAL INTERACTIONS

Part 1: INTRODUCTION AND EXAMPLES
- INTRODUCTION:
Characterization of a physical system:
degrees of freedom, relevant scale(s), symmetries.
- EXAMPLES OF EFT:
the Fermi theory of weak interactions;
derivation from the full electroweak theory.
beyond the tree-level: Euler-Heisenberg Lagrangian;
symmetry considerations and derivation from QED.
- THE SM AS AN EFT:
recap of SM non-anomalous global symmetries;
dimension 5 operators, violation of (B-L) and neutrino masses;
possible microscopic origin (seesaw mechanism).
dimension 6 operators, violation of B and proton decay;
possible microscopic origin (GUTs);
dimension 6 operators and flavour physics.
- EFT IN NON-PERTURBATIVE REGIME:
the chiral Lagrangian; chiral symmetry breaking in QCD;
EFT for light pseudoscalar mesons; breaking effects;
anomaly of iso-axial current and neutral pion decay.
- OTHER EXAMPLES

Part 2: FORMAL ASPECTS
- EFT AND POWER COUNTING.
- INTEGRATING OUT HEAVY MODES:
RGE flow and matching conditions;
revisitation of the Euler-Heisenberg Lagrangian;
other examples.
- APPELQUIST-CARAZZONE DECOUPLING THEOREM.
- EQUIVALENT EFFECTIVE LAGRANGIANS;
independence of S-matrix elements on local field redefinitions.
- OPERATOR MIXING;
anomalous dimensions; examples;
- EFT DESCRIBING A BROKEN PHASE:
CCWZ construction; revisitation of the chiral Lagrangian;
other examples.