Five lectures on effective field theory

Abstract

Lectures delivered at the 17th National Nuclear Physics Summer School 2005, Berkeley, CA, June 6-17, 2005.

Figures (15)

• Figure 1: A sample configuration contributing to the path integral for the scalar field theory in eq. (\ref{['eq:scalar']}). Its amplitude is $\phi_k$ and has wave number $\sim k$ and spatial extent $\sim 2\pi/k$.
• Figure 2: (a) Tree level $W$ and $Z$ exchange between four fermions. (b) The effective vertex in the low energy effective theory (Fermi interaction).
• Figure 3: $\Delta B=1$ and $\Delta B=2$ vertices in the effective theory.
• Figure 4: At tree level one matches the $\Delta B=1$ diagram from the standard model onto the $\Delta B=1$ contact interaction of the effective theory. At one loop level one determines the $\Delta B=2$ contact term of the effective theory by matching the $\Delta B=2$ box diagram from the standard model onto the one-loop graph involving the two $\Delta B=1$ vertices in the effective theory, plus the $\Delta B=2$ contact term. The calculation requires specification of renormalization scale, conveniently taken to be $\mu=M_W$.
• Figure 5: The bubble chain arising from local operators. The vertex is given by the tree level amplitude, eq. (\ref{['eq:tree']}).