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C"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Novel methods to reconstruct the slant depth of the maximum of the longitudinal profile (<jats:inline-formula><jats:alternatives><jats:tex-math>$$X_{\\mathrm{max}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>X<\/mml:mi><mml:mi>max<\/mml:mi><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>) of high-energy showers initiated by gamma-rays as well as their energy (<jats:inline-formula><jats:alternatives><jats:tex-math>$$E_0$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>E<\/mml:mi><mml:mn>0<\/mml:mn><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>) are presented. The methods were developed for gamma rays with energies ranging from a few hundred GeV to<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\sim 10$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mo>\u223c<\/mml:mo><mml:mn>10<\/mml:mn><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>TeV. An estimator of<jats:inline-formula><jats:alternatives><jats:tex-math>$$X_{\\mathrm{max}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>X<\/mml:mi><mml:mi>max<\/mml:mi><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>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<jats:inline-formula><jats:alternatives><jats:tex-math>$$E_0$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>E<\/mml:mi><mml:mn>0<\/mml:mn><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>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<jats:inline-formula><jats:alternatives><jats:tex-math>$$X_{\\mathrm{max}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>X<\/mml:mi><mml:mi>max<\/mml:mi><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>. Resolutions about<jats:inline-formula><jats:alternatives><jats:tex-math>$$40 \\, (20)\\,\\mathrm{g\/cm^2}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mn>40<\/mml:mn><mml:mspace\/><mml:mrow><mml:mo>(<\/mml:mo><mml:mn>20<\/mml:mn><mml:mo>)<\/mml:mo><\/mml:mrow><mml:mspace\/><mml:mrow><mml:mi>g<\/mml:mi><mml:mo>\/<\/mml:mo><mml:msup><mml:mi>cm<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msup><\/mml:mrow><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>and about<jats:inline-formula><jats:alternatives><jats:tex-math>$$30 \\, (20)\\%$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mn>30<\/mml:mn><mml:mspace\/><mml:mo>(<\/mml:mo><mml:mn>20<\/mml:mn><mml:mo>)<\/mml:mo><mml:mo>%<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>for, respectively,<jats:inline-formula><jats:alternatives><jats:tex-math>$$X_{\\mathrm{max}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>X<\/mml:mi><mml:mi>max<\/mml:mi><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>and<jats:inline-formula><jats:alternatives><jats:tex-math>$$E_0$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>E<\/mml:mi><mml:mn>0<\/mml:mn><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>at<jats:inline-formula><jats:alternatives><jats:tex-math>$$1 \\, (10) \\ \\mathrm {TeV}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mn>1<\/mml:mn><mml:mspace\/><mml:mo>(<\/mml:mo><mml:mn>10<\/mml:mn><mml:mo>)<\/mml:mo><mml:mspace\/><mml:mi>TeV<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>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. 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