Here is the KATRIN experiment:
The KArlsruhe TRItium Neutrino (KATRIN) experiment, which is presently being assembled at Tritium Laboratory Karlsruhe on the KIT Campus North site, will investigate the most important open issue in neutrino physics:
What is the absolute mass scale of neutrinos?
Predecessor experiments at Mainz and Troitsk were able to appoint an upper limit to the electron anti-neutrino mass of 2.3 eV/c^2. KATRIN, using the same measurement technique, will either improve this limit by one order of magnitude down to 0.2 eV/c^2 (90% CL) or discover the actual mass, if it is larger than 0.35 eV/c^2. This requires an improvement by two orders of magnitude with respect to key experimental parameters.KATRIN measures the neutrino mass in a model-independant way via ultrahigh precision measurements of the kinematics of electrons from beta-decay. To detect the subtle effects of a massive neutrino on the kinematics of the beta electrons requires on one hand the provision of a strong gaseous windowless Tritium source with well-known properties and precision control. On the other hand it requires a high resolution spectrometer (MAC-E filter) with large diameter (10 m) to analyze precisely the electron energies from the source. All major components are under construction or already in place and in the commissioning phase.
Like many ultra-precision experiments KATRIN pushes state of the art technologies to its borders. Its wide spectrum of involved physics and engineering, varying for example from molecular physics to nuclear physics, or from cryogenics over vacuum engineering to material science, makes the special touch and fascination of such an experiment.
from the wikipedia article
The experiment began running tests in October 2016, with measurements scheduled in 2017.
Update, from the abstract
A fit of the integrated electron spectrum over a narrow interval around the kinematic endpoint at 18.57 keV gives gives an effective neutrino mass square value of $(−1.0) +0.9−1.1 eV^2$. From this we derive an upper limit of $1.1 eV$ (90% confidence level) on the absolute mass scale of neutrinos. This value coincides with the KATRIN sensitivity. It improves upon previous mass limits from kinematic measurements by almost a factor of two and provides model-independent input to cosmological studies of structure formation.