Hazes are common in known planet atmospheres, and geochemical evidence suggests early Earth occasionally supported an organic haze with significant environmental and spectral consequences. The UV spectrum of the parent star drives organic haze formation through methane photochemistry. We use a 1D photochemical-climate model to examine production of fractal organic haze on Archean Earth-analogs in the habitable zonesof several stellar types: the modern and early Sun, AD Leo (M3.5V), GJ 876 (M4V), $epsilon$ Eridani (K2V), and $sigma$ Bootis (F2V). For Archean-like atmospheres, planets orbiting stars with the highest UV fluxes do not form haze due to the formation of photochemical oxygen radicals that destroy haze precursors. Organic hazes impact planetary habitability via UV shielding and surface cooling, but this cooling is minimized around M dwarfs whose energy is emitted at wavelengths where organic hazes are relatively transparent. We generate spectra to test the detectability of haze. For 10 transits of a planet orbiting GJ 876 observed by the James Webb Space Telescope, haze makes gaseous absorption features at wavelengths $<$ 2.5 $mu$m 2-10$sigma$ shallower compared to a haze-free planet, and methane and carbon dioxide are detectable at $>$5$sigma$. A haze absorption feature can be detected at 5$sigma$ near 6.3 $mu$m, but higher signal-to-noise is needed to distinguish haze from adjacent absorbers. For direct imaging of a planet at 10 parsecs using a coronagraphic 10-meter class ultraviolet-visible-near infrared telescope, a UV-blue haze absorption feature would be strongly detectable at $>$12$sigma$ in 200 hours.
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