  A free Fermi gas has, famously, a superconducting susceptibility that
diverges logarithmically at zero temperature. In this paper we ask whether this
is still true for a Fermi liquid and find that the answer is that it does {\it
not}. From the perspective of the renormalization group for interacting
fermions, the question arises because a repulsive interaction in the Cooper
channel is a marginally irrelevant operator at the Fermi liquid fixed point and
thus is also expected to infect various physical quantities with logarithms.
Somewhat surprisingly, at least from the renormalization group viewpoint, the
result for the superconducting susceptibility is that two logarithms are not
better than one. In the course of this investigation we derive a
Callan-Symanzik equation for the repulsive Fermi liquid using the
momentum-shell renormalization group, and use it to compute the long-wavelength
behavior of the superconducting correlation function in the emergent low-energy
theory. We expect this technique to be of broader interest.
