Distance to the Large Magellanic Cloud: the RR Lyrae stars
(abridged) New photometry and spectroscopy for more than a hundred RR Lyrae stars in two fields located close to the bar of the Large Magellanic Cloud (LMC) are used to derive new accurate estimates of the average magnitude, the local reddening, the luminosity-metallicity relation, and of the distance to the LMC. Metallicities from low resolution spectra obtained with the VLT have been derived for 101 RR Lyr's; the average value is [Fe/H]=-1.48+/-0.03 (sigma=0.29). An estimate of the reddening was obtained with 2 different methods, and we found: E(B-V)=0.116+/-0.017, and 0.086+/-0.017 mag in field A and B, respectively. The dereddened apparent average luminosity of the RR Lyrae's defined by the present photometry is _0=19.064+/-0.064 at [Fe/H]=-1.5. We determine the slope of the luminosity-metallicity relation for the RR Lyrae stars: Delta[M_V(RR)]/ Delta[Fe/H]=0.214+/-0.047, with no clear evidence for a change in slope at [Fe/H]=-1.5. When coupled with the absolute magnitude derived from the Baade-Wesselink and the statistical parallaxes methods, both methods known to favour the short distance scale, this value leads mod(LMC)=18.38+/- 0.16 and 18.30+/-0.14, respectively. If we use instead the absolute magnitude from the new Main Sequence Fitting of Galactic globular clusters [M_V(RR)=0.61+/-0.07 mag at [Fe/H]=-1.5] we derive mod(LMC)=18.45+/-0.09. The average I luminosity of the clump stars is I_0=18.12+/-0.06, and moves the clump distance modulus to the LMC to mod(LMC)=18.42+/-0.07 and 18.45+/-0.07 when two metallicity-I relations are used. All these values are only 1 sigma shorter than provided by the Pop I distance indicators, and allow to reconcile the short and long distance scale on a common value for the distance modulus of the LMC of 18.515+/-0.085 mag.