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Motivated by recent experimental indications of preformed electron-hole pairsin $\nu_T=1$ quantum Hall bilayers at relatively large separation, we formulatea Chern-Simons (CS) theory of the coupled composite electron liquid (CEL) andcomposite hole liquid (CHL). We show that the effective action of the CS gaugefield fluctuations around the saddle-point leads to stable pairing between CELand CHL. We find that the CEL-CHL pairing theory leads to a dominant $s$-wavechannel in contrast to the dominant $p$-wave channel found in the CEL-CELpairing theory. Moreover, the CEL-CHL pairing is generally stronger than theCEL-CEL pairing across the whole frequency spectrum. Finally, we discusspossible differences between the two pairing mechanisms that may be probed inexperiments.

Pairing of Composite-Electrons and Composite-Holes in $\nu_T=1$ Quantum Hall Bilayers