Unconventional phonon-mediated superconductivity in MgB2

We have evaluated the total carrier mass enhancement factor f(t) for MgB2 from two independent experiments (specific heat and upper critical field). These experiments consistently show that f(t) = 3.1 +/- 0.1. The unusually large f(t) is incompatible with the measured reduced gap (2Delta(0)/k(B)T(c) = 4.1) and the total isotope-effect exponent (alpha = 0.28 +/- 0.04) 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.