We analysed red giant branch stars in 16 Galactic globular clusters, computing their atmospheric parameters both from the photometry and from excitation and ionisation balances. The spectroscopic parameters are lower than the photometric ones and this discrepancy increases decreasing the metallicity, reaching, at [Fe/H]~-2.5 dex, differences of ~350 K in effective temperature and ~1 dex in surface gravity. We demonstrate that the spectroscopic parameters are inconsistent with the position of the stars in the colour-magnitude diagram, providing too low temperatures and gravities, and predicting that the stars are up to about 2.5 magnitudes brighter than the observed magnitudes. The parameter discrepancy is likely due to the inadequacies of the adopted physics, in particular the assumption of 1-dimensional geometry can be the origin of the observed slope between iron abundances and excitation potential that leads to low temperatures. However, the current modelling of 3D/NLTE radiative transfer for giant stars seems to be not able to totally erase this slope. We conclude that the spectroscopic parameters are wrong for metallicity lower than -1.5 dex and for these red giant stars photometric temperatures and gravities should be adopted. We provide a simple relation to correct the spectroscopic temperatures in order to put them onto a photometric scale.
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