New methods to reconstruct $$X_{\mathrm{max}}$$ X 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 ( $$X_{\mathrm{max}}$$ ) 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 $$X_{\mathrm{max}}$$ 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 $$X_{\mathrm{max}}$$ . Resolutions about $$40 \, (20)\,\mathrm{g/cm^2}$$ and about $$30 \, (20)\%$$ for, respectively, $$X_{\mathrm{max}}$$ and $$E_0$$ at $$1 \, (10) \ \mathrm {TeV}$$ 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.