  Motivated by the strong, low temperature damping of nodal quasiparticles
observed in some cuprate superconductors, we study quantum phase transitions in
d_{x^2-y^2} superconductors with a spin-singlet, zero momentum, fermion
bilinear order parameter. We present a complete, group-theoretic classification
of such transitions into 7 distinct cases (including cases with nematic order)
and analyze fluctuations by the renormalization group. We find that only 2, the
transitions to d_{x^2-y^2}+is and d_{x^2-y^2} + i d_{xy} pairing, possess
stable fixed points with universal damping of nodal quasiparticles; the latter
leaves the gapped quasiparticles along (1,0), (0,1) essentially undamped.
