The antiferromagnetic system on a rare-earth pyrochlore has been focused as a strong candidate of U(1) quantum spin liquid. Here, we study the phase transitions driven by external magnetic field and discuss the thermal Hall effect due to emergent spinon excitations with staggered gauge fields. Despite the spinons, the charge excitations of the effective action that carry spin-1/2 quantum number, do not couple to the external field, the emergent U(1) gauge field is influenced in the presence of external magnetic field. In particular, along the  and  directions, we discuss the possible phase transitions between U(1) spin liquids with different gauge fluxes are stabilized in fields. Beyond the cases where the gauge flux per plaquette is fixed to be either 0 or pi, there exists a regime where the staggered gauge fluxes are stabilized without time-reversal symmetry. In such a phase, the thermal Hall conductivity kappa(xy)/T similar to 4.6 x 10(-3) W/(K(2)m) is expected to be measurable below 1 K.