New methods to reconstruct $X_{\rm max}$ and the energy of gamma-ray air showers with high accuracy in large wide-field observatories

Novel methods to reconstruct the slant depth of the maximum of the longitudinal profile (\Xmax) of high-energy showers initiated by gamma-rays as well as their energy ($E_0$) are presented. The methods were developed for gamma rays with energies ranging from a few hundred GeV to $\sim 10$ TeV. An estimator of \Xmax is obtained, event-by-event, from its correlation with the distribution of the arrival time of the particles at the ground, or the signal at the ground for lower energies. An estimator of $E_0$ is obtained, event-by-event, using a parametrization that has as inputs the total measured energy at the ground, the amount of energy contained in a region near to the shower core and the estimated \Xmax. Resolutions about $40 \, (20)\,{\rm g/cm^2}$ and about $30 \, (20)\%$ for, respectively, \Xmax and $E_0$ at $1 \, (10) \ \rm{TeV}$ energies are obtained, considering vertical showers. The obtained results are auspicious and can lead to the opening of new physics avenues for large wide field-of-view gamma-ray observatories. The dependence of the resolutions with experimental conditions is discussed.