Galactic extinction laws: I. A global NIR analysis with 2MASS photometry
  We have started an ambitious program to determine if the full diversity of
extinction laws is real or if some of it is due to calibration or
methodological issues. Here we start by analyzing the information on NIR
extinction in a 2MASS stellar sample with good quality photometry and very red
colours. We calculate the extinction at 1 $\mu$m, $A_1$, and the power-law
exponent, $\alpha$ ($A_\lambda = A_1 \lambda^{-\alpha}$), for the 2MASS stars
located in the extinction trajectory in the $H-K$ vs. $J-H$ plane expected for
red giants with $A_1 > 5$ mag. We test the validity of the assumption about the
nature of those stars, whether a single or multiple values of $\alpha$ are
needed, and the spatial variations of the results. Most ($\sim$83%) of those
stars can indeed be explained by high-extinction red giants and the rest is
composed of extinguished AGB stars (mostly O-rich), blended sources, and
smaller numbers of other objects, a contaminant fraction that can be reduced
with the help of Gaia} DR2 data. Galactic red giants experience a NIR
extinction with $\alpha\sim 2.27$ and an uncertainty of a few hundredths of a
magnitude. There is no significant spread in $\alpha$ even though our sample is
widely distributed and has a broad range of extinctions. Differences with
previous results are ascribed to the treatment of non-linear photometric
effects and/or the contaminant correction. Future research should concentrate
in finding the correct functional form for the NIR extinction law. In the
appendix we detail the treatment of non-linear photometric effects in the 2MASS
bands.
