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We have measured the mechanical loss of a dielectric multilayer reflectivecoating (ion-beam sputtered SiO$_2$ and Ta$_2$O$_5$) in cooled mirrors. Theloss was nearly independent of the temperature (4 K $\sim$ 300 K), frequency,optical loss, and stress caused by the coating, and the details of themanufacturing processes. The loss angle was $(4 \sim 6) \times 10^{-4}$. Thetemperature independence of this loss implies that the amplitude of the coatingthermal noise, which is a severe limit in any precise measurement, isproportional to the square root of the temperature. Sapphire mirrors at 20 Ksatisfy the requirement concerning the thermal noise of even futureinterferometric gravitational wave detector projects on the ground, forexample, LCGT.Comment: 8 pages, 6 figures, 3 tables : accepted version (by Physical Review  D

Measurement of the mechanical loss of a cooled reflective coating for gravitational wave detection