Metallicity of M dwarfs III. Planet-metallicity and planet-stellar mass correlations of the HARPS GTO M dwarf sample

Aims. The aim of this work is the study of the planet-metallicity and the planet-stellar mass correlations for M dwarfs from the HARPS GTO M dwarf subsample Methods. We use a new method that takes advantage of the HARPS high-resolution spectra to increase the precision of metallicity, using previous photometric calibrations of [Fe/H] and effective temperature as starting values. Results. In this work we use our new calibration (rms = 0.08 dex) to study the planet-metallicity relation of our sample. The well-known correlation for Giant planet FGKM hosts with metallicity is present. Regarding Neptunians and smaller hosts no correlation is found but there is a hint that an anti-correlation with [Fe/H] may exist. We combined our sample with the California Planet Survey late-K and M-type dwarf sample to increase our statistics but found no new trends. We fitted a power law to the frequency histogram of the Jovian hosts for our sample and for the combined sample, f_p = C10^\alpha[Fe/H], using two different approaches: a direct bin fitting and a bayesian fitting procedure. We obtained a value for C between 0.02 and 0.04 and for \alpha between 1.26 and 2.94. Regarding stellar mass, an hypothetical correlation with planets was discovered, but was found to be the result of a detection bias.