  We report precision measurements of the effective mass m* in high-quality
bilayer graphene using the temperature dependence of the Shubnikov-de Haas
oscillations. In the density range of 0.7 x 10^12/cm^2 < n < 4.1 x 10^12 /cm^2,
both the hole mass m*_h and the electron mass m*_e increase with increasing
density, demonstrating the hyperbolic nature of the bands. The hole mass m*_h
is approximately 20-30% larger than the electron mass m*_e. Tight-binding
calculations provide a good description of the electron-hole asymmetry and
yield an accurate measure of the inter-layer hopping parameter v_4 = 0.063.
Both m*_h and m*_e are substantially suppressed compared to single-particle
values, providing clear and unprecedented evidence for the strong
renormalization effect of electron-electron interaction in the band structure
of bilayer graphene.
