Gamma-ray measurements using the imaging atmospheric Cherenkov technique currently achieve
the highest angular resolution in astronomy at very high energies, reaching down to arcminute
scales at multi-TeV energies. High-resolution measurements provide the key to progress on many
of the central questions in high-energy astrophysics, including the sites and mechanisms of particle
acceleration up to PeV energies. The huge potential of the next-generation Cherenkov Telescope
Array Observatory (CTAO) in this regard can be maximized with the help of improved algorithms
for the reconstruction of the air-shower direction and energy.
Here, we present the FreePACT algorithm, a hybrid machine-learning maximum-likelihood re-
construction method for imaging atmospheric Cherenkov telescopes. It employs the neural ratio
estimation technique from the field of likelihood-free inference to replace the analytical likelihood
used in traditional image-likelihood fitting by a neural network that approximates the charge prob-
ability density function for each pixel in the camera.
The significant performance improvements provided by this algorithm are demonstrated using
simulations of the planned CTAO southern array. We also discuss implications of the improved
angular resolution for the science potential of CTAO using as an example the study of compact
X-ray Pulsar Wind Nebulae.