  We have evaluated the total carrier mass enhancement factor f_{t} for MgB_{2}
from two independent experiments (specific heat and upper critical field).
These experiments consistently show that f_{t} = 3.1\pm0.1. The unusually large
f_{t} is incompatible with the measured reduced gap (2\Delta (0)/k_{B}T_{c} =
4.1) and the total isotope-effect exponent (\alpha = 0.28\pm0.04) within the
conventional phonon-mediated model. We propose an unconventional
phonon-mediated mechanism, which is able to quantitatively explain the values
of T_{c}, f_{t}, \alpha, and the reduced energy gap in a consistent way.
