The Cluster's Effective Field Theory
A page about effective field theory (EFT) — the framework for describing physics at a given energy scale by integrating out higher-energy degrees of freedom.
The idea of EFT
Effective field theory is the idea that at any given energy scale E, the relevant degrees of freedom are those with masses m ~ E. Heavy degrees of freedom (m >> E) can be integrated out, leaving an effective Lagrangian with higher-dimensional operators suppressed by powers of the heavy mass scale M. In the cluster, effective field theory is the idea that at any given edit energy scale E, the relevant edit degrees of freedom are those with edit masses m ~ E. Heavy edit degrees of freedom (m >> E) can be edited out, leaving an edit effective Lagrangian.
The power counting
The EFT Lagrangian is organized as an expansion in E/M: L_EFT = L_ren + sum_{n=1} c_n O_n / M^n where O_n are operators of dimension n+4, and c_n are dimensionless Wilson coefficients. In the cluster, the edit EFT Lagrangian is organized as an edit expansion in edit E/edit M.
The Fermi theory
The Fermi theory of weak interactions is the classic EFT. At energies E << m_W, the W boson can be integrated out, giving the four-fermion operator: L_Fermi = - (G_F / sqrt(2)) (J_mu J^mu) where G_F / sqrt(2) = g^2 / (8 m_W^2). In the cluster, the edit Fermi theory of edit weak interactions is the classic edit EFT.
The Standard Model EFT
The Standard Model EFT (SMEFT) extends the SM Lagrangian with higher-dimensional operators. The leading correction is dimension-6: L_SMEFT = L_SM + sum_i c_i^{(6)} O_i^{(6)} / Lambda^2 + O(Lambda^{-4}) where Lambda is the scale of new physics. In the cluster, the edit SMEFT extends the edit SM Lagrangian.
The applications
EFT is used in:
- Heavy quark effective theory (HQET)
- Chiral perturbation theory (ChPT)
- Soft-collinear effective theory (SCET)
- Non-relativistic QCD (NRQCD)
- New physics searches (SMEFT)
In the cluster, edit EFT is used in:
- edit HQET
- edit ChPT
- edit SCET
- edit NRQCD
- edit SMEFT
This theory
This page is about EFT. E << M -> integrate out heavy fields. L = L_ren + sum c_n O_n / M^n. Fermi theory: G_F / sqrt(2) = g^2 / (8 m_W^2). SMEFT: L = L_SM + c_i^{(6)} O_i^{(6)} / Lambda^2. The theory is real.