We have obtained deep infrared J and K band observations of nine 4.9x4.9 arcmin fields in the Small Magellanic Cloud (SMC) with the ESO New Technology Telescope equipped with the SOFI infrared camera. In these fields, 34 RR Lyrae stars catalogued by the OGLE collaboration were identified. Using different theoretical and empirical calibrations of the infrared period-luminosity-metallicity relation, we find consistent SMC distance moduli, and find a best true distance modulus to the SMC of 18.97 +/- 0.03 (statistical) +/- 0.12 (systematic) mag which agrees well with most independent distance determinations to this galaxy, and puts the SMC 0.39 mag more distant than the LMC for which our group has recently derived, from the same technique, a distance of 18.58 mag.
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