We report the discovery of HAT-P-26b, a transiting extrasolar planet orbiting the moderately bright V=11.744 K1 dwarf star GSC 0320-01027, with a period P = 4.234516 +- 0.000015 d, transit epoch Tc = 2455304.65122 +- 0.00035 (BJD), and transit duration 0.1023 +- 0.0010 d. The host star has a mass of 0.82 +- 0.03 Msun, radius of 0.79 + 0.10 - 0.04 Rsun, effective temperature 5079 +- 88 K, and metallicity [Fe/H] = -0.04 +- 0.08. The planetary companion has a mass of 0.059 +- 0.007 MJ, and radius of 0.565 + 0.072 - 0.032 RJ yielding a mean density of 0.40 +- 0.10 g cm-3. HAT-P-26b is the fourth Neptune-mass transiting planet discovered to date. It has a mass that is comparable to those of Neptune and Uranus, and slightly smaller than those of the other transiting Super-Neptunes, but a radius that is ~65% larger than those of Neptune and Uranus, and also larger than those of the other transiting Super-Neptunes. HAT-P-26b is consistent with theoretical models of an irradiated Neptune-mass planet with a 10 Mearth heavy element core that comprises >~ 50% of its mass with the remainder contained in a significant hydrogen-helium envelope, though the exact composition is uncertain as there are significant differences between various theoretical models at the Neptune-mass regime. The equatorial declination of the star makes it easily accessible to both Northern and Southern ground-based facilities for follow-up observations.
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