The RR Lyrae Period - K Luminosity relation for Globular Clusters: an   observational approach
  The Period - metallicity - K band luminosity (PLK) relation for RR Lyrae stars in 15 Galactic globular clusters and in the LMC globular cluster Reticulum has been derived. It is based on accurate near infrared (K) photometry combined with 2MASS and other literature data. The PLK relation has been calibrated and compared with the previous empirical and theoretical determinations in literature. The zero point of the absolute calibration has been obtained from the K magnitude of RR Lyr whose distance modulus has been measured via trigonometric parallax with HST. Using this relation we obtain a distance modulus to the LMC of (m-M)_0 = 18.54 \pm 0.15 mag, in good agreement with recent determinations based on the analysis of Cepheid variable stars. 
A. Sollima, C. Cacciari, E. Valenti