Multi-color photometry of the Galactic globular cluster M 75=NGC 6864.: A new sensitive metallicity indicator and the position of the horizontal branch in UV

Aims. We carry out and analyze new multi-color photometry of the Galactic globular cluster ( GC) M 75 in UBVI and focus on the brighter sequences of the color - magnitude diagram (CMD), with particular emphasis on their location in U-based CMD. Specifically, we study the level both of the horizontal (HB) and red giant branches (RGB) relative to the main-sequence turnoff (TO) in the U magnitude. Methods. Along with the presented photometry of M 75, we use our collection of photometric data on GCs belonging to the metal-poor range, [Fe/H](ZW) < - 1.1 dex, obtained from observations with different equipment, but calibrated by standard stars situated in the observed cluster fields. Results. We confirm our earlier finding, and extend it to a larger magnitude range. We demonstrate that. UBHB TO expressing the difference in U magnitude between the TO point and the level of the blue HB, near its red boundary, of the metal-poor GCs observed with the EMMI camera of the NTT/ESO telescope is about 0.4 - 0.5 mag smaller as compared to GCs observed with the 100 '' telescope and 1.3 m Warsaw telescope of the Las Campanas Observatory. At the same time, Delta U-TO(RGB), the difference in U magnitude between the TO and RGB inflection ( brightest) points, does not show such an apparent dependence on the characteristics of U filters used, but it depends on cluster metallicity. We have shown, for the first time, the dependence of the parameter Delta U-TO(RGB) on [Fe/H] and have estimated its analytical expression, by assuming a linear relation between the parameter and metallicity. Its slope, Delta U-TO(RGB)/Delta[Fe/H] similar to 1.2 mag/dex, is approximately a factor of two steeper than that of the dependence of the RGB bump position in the V magnitude on metallicity. The asymptotic giant branch (AGB) clump and features of the RGB luminosity function (LF) of M 75 are also discussed.