  In the 1980s Branner and Douady discovered a surgery relating various limbs
of the Mandelbrot set. We put this surgery in the framework of "Pacman
Renormalization Theory" that combines features of quadratic-like and Siegel
renormalizations. We show that Siegel renormalization periodic points
(constructed by McMullen in the 1990s) can be promoted to pacman
renormalization periodic points. Then we prove that these periodic points are
hyperbolic with one-dimensional unstable manifold. As a consequence, we obtain
the scaling laws for the centers of satellite components of the Mandelbrot set
near the corresponding Siegel parameters.
