  Pnictides provide an opportunity to study the effects of quantum criticality
in a multi-band high temperature superconductor. Quasiparticle mass divergence
near optimal doping, observed in two major classes of high-temperature
superconductors, pnictides and cuprates, is a direct experimental indicator of
enhanced electronic interactions that accompany quantum criticality. Whether
quasiparticles on all Fermi surface pockets in BaFe2(As1-xPx)2 are affected by
quantum criticality is an open question, which specific heat measurements at
high magnetic fields can directly address. Here we report specific heat
measurements up to 35T in BaFe2(As1-xPx)2 over a broad doping range, 0.44 <= x
<= 0.6. We observe saturation of C/T in the normal state at all dopings where
superconductivity is fully suppressed. Our measurements demonstrate that
quasiparticle mass increases towards optimal doping in multiple pockets, some
of which exhibit even stronger mass enhancement than previously reported from
quantum oscillations of a single pocket.
