The period-luminosity relation of Mira variables in NGC 6388 and NGC 6441

We report a result of our near-infrared repeated observations of Mira variables in the globular clusters NGC 6388 and 6441. These two clusters are known as peculiar clusters with blue horizontal branch stars and RR Lyr variables which are unexpected for their relatively high metallicities. We derive their distance moduli by fitting the Mira variables in the period-luminosity relation. They are the first distance estimates, for these clusters, which were observationally obtained in an independent way from the horizontal branch stars. The obtained distances revealed that the absolute magnitudes of the peculiar RR Lyr variables are similar to the metal-poor ones of [Fe/H]=-2 dex. It is suggested that the constraint we found should be reproduced by any theories to explain the horizontal morphology of these peculiar clusters.