Vertex renormalization of weak interactions in compact stars: beyond leading order

Neutrino emission rate from baryonic matter in neutron stars via weak neutral vector interaction is computed up to order O(v_F^6), where v_F is the Fermi velocity in units of speed of light. The vector current polarization tensors are evaluated with full vertices which include resummed series in the particle-hole channel. The neutrino emissivity is enhanced compared to the O(v_F^4) order up of 10% for values v_F< 0.4 characteristic to baryons in compact stars.