{"paper":{"title":"Revisiting the Longitudinal Development of Electromagnetic Air Showers: Analytical Improvements to the Greisen Formalism with Zenith Angle Dependence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-ph","hep-th"],"primary_cat":"astro-ph.HE","authors_text":"Barbara Guti\\'errez, Constanza Valdivieso, Nicol\\'as Viaux M., Raquel Pezoa R., Sebasti\\'an Mendizabal, Sebasti\\'an Tapia","submitted_at":"2025-04-12T22:38:46Z","abstract_excerpt":"We present a new analytical approach to the longitudinal development of electromagnetic air showers, offering improvements to the classical Greisen formalism. We introduce a novel profile for the slope function $\\lambda_1(s)$ that achieves an agreement less than $0.75\\%$ with the original $\\lambda_1$ for shower age parameter $s$ between $0.3 < s < 1.4$, where $s$ represents the stage of shower development. Our new formalism provides an improved representation of shower evolution, particularly near and beyond the shower maximum. In addition, we derive a complete expression for the number of par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.09359","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.09359/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}