Some of the exoplanets so far observed show featureless or flat transmission spectra, possibly indicating the existence of clouds and/or haze in their atmospheres. Thanks to its large aperture size and broad wavelength coverage, JWST is expected to enable detailed investigation of exoplanet atmospheres, which could provide important constraints on the atmospheric composition obscured by clouds/haze. Here, we use four warm ($lesssim 1000$ K) planets suitable for atmospheric characterization via transmission spectroscopy, GJ 1214b, GJ 436b, HD 97658b, and Kepler-51b, as examples to explore molecular absorption features detectable by JWST even in the existence of hydrocarbon haze in the atmospheres. We simulate photochemistry, the growth of hydrocarbon haze particles, and transmission spectra for the atmospheres of these four planets. Among the planetary parameters considered, super-Earths with hazy, relatively hydrogen-rich atmospheres are mostly expected to produce detectable molecular absorption features such as a quite prominent $mathrm{CH_4}$ feature at 3.3 ${rm mu}$m even for the extreme case of the most efficient production of photochemical haze. For a planet that has extremely low gravity, such as Kepler-51b, haze particles grow significantly large in the upper atmosphere due to the small sedimentation velocity, resulting in the featureless or flat transmission spectrum in a wide wavelength range. This investigation shows that the transmission spectra with muted features measured by HST in most cases do not preclude strong features at the longer wavelengths accessible by JWST.
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