  Composite Fermi liquids (CFLs) are compressible states that can occur for 2D
interacting fermions confined in the lowest Landau level at certain Landau
level fillings. They have been understood as Fermi seas formed by composite
fermions which are bound states of electromagnetic fluxes and electrons as
reported by Halperin, Lee and Read [Phys. Rev. B 47, 7312 (1993)]. At half
filling, an explicitly particle-hole symmetric theory based on Dirac fermions
was proposed by Son [Phys. Rev. X 5, 031027 (2015)] as an alternative low
energy description. In this work, we investigate the Berry curvature of CFL
model wave functions at a filling fraction one-quarter, and observe that it is
uniformly distributed over the Fermi sea except at the center where an
additional $\pi$ phase was found. Motivated by this, we propose an effective
theory which generalizes Son's half filling theory, by internal gauge flux
attachment, to all filling fractions in which fermionic CFLs can occur. The
numerical results support the idea of internal gauge flux attachment.
