  We study the two-alpha-particle (alpha-alpha) system in an Effective Field
Theory (EFT) for halo-like systems. We propose a power counting that
incorporates the subtle interplay of strong and electromagnetic forces leading
to a narrow resonance at an energy of about 0.1 MeV. We investigate the EFT
expansion in detail, and compare its results with existing low-energy
alpha-alpha phase shifts and previously determined effective-range parameters.
Good description of the data is obtained with a surprising amount of
fine-tuning. This scenario can be viewed as an expansion around the limit
where, when electromagnetic interactions are turned off, the Be-8 ground state
is at threshold and exhibits conformal invariance. We also discuss possible
extensions to systems with more than two alpha particles.
