  Motivated by the recent experimental observation of quantum oscillations in
the underdoped cuprates, we study the cyclotron and infrared Hall effective
masses in an anisotropic Fermi liquid characterized by an angle-dependent
quasiparticle residue Z_q, which models an arc-shaped Fermi surface. Our
primary motivation is to explain the relatively large value of the cyclotron
effective mass observed experimentally and its relation with the effective Hall
mass. In the framework of a phenomenological model of an anisotropic Fermi
liquid, we find that the cyclotron mass is enhanced by a factor <1/Z_q>, while
the effective Hall mass is proportional to <Z_q> / <Z_q^2>, where <...> implies
an averaging over the Fermi surface. We conclude that if the Z-factor becomes
small in some part of the Fermi surface (e.g., in the case of a Fermi arc), the
cyclotron mass is enhanced sharply while the infrared Hall mass may remain
small. Possible future experiments are discussed.
