AbstractNear critical doping, high-temperature superconductors exhibit multiple anomalies associated with enhanced electronic correlations and quantum criticality. Quasiparticle mass enhancement approaching optimal doping has been reported in quantum oscillation measurements in both cuprate and pnictide superconductors. Although the data are suggestive of enhanced interactions, the microscopic theory of quantum oscillation measurements near a quantum critical point is not yet firmly established. It is therefore desirable to have a direct thermodynamic measurement of quasiparticle mass. Here we report high-magnetic field measurements of heat capacity in the doped pnictide superconductor BaFe₂(As_1−xP_x)₂. We observe saturation of the specific heat at high magnetic field in a broad doping range above optimal doping which enables a direct determination of the electronic density of states recovered when superconductivity is suppressed. Our measurements find a strong total mass enhancement in the Fermi pockets that superconduct. This mass enhancement extrapolates to a mass divergence at a critical doping of x = 0.28.