Revisiting the Longitudinal Development of Electromagnetic Air Showers: Analytical Improvements to the Greisen Formalism with Zenith Angle Dependence
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913799152336896 |
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| author | Mendizabal, Sebastián M., Nicolás Viaux Tapia, Sebastián R., Raquel Pezoa Gutiérrez, Barbara Valdivieso, Constanza |
| author_facet | Mendizabal, Sebastián M., Nicolás Viaux Tapia, Sebastián R., Raquel Pezoa Gutiérrez, Barbara Valdivieso, Constanza |
| contents | 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 $λ_1(s)$ that achieves an agreement less than $0.75\%$ with the original $λ_1$ 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 particles $N(t)$. Our implementation includes the zenithal angle dependence on the number of particles at the detector level at high altitudes, making it particularly useful for high-altitude observatories. This expression is suitable for implementing air shower simulation tool fitting procedures over a wide range of energies and geometries. Our analysis suggests that the proposed new formalism may provide better agreement with the expected evolution of particle numbers compared to the traditional Greisen formulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09359 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Revisiting the Longitudinal Development of Electromagnetic Air Showers: Analytical Improvements to the Greisen Formalism with Zenith Angle Dependence Mendizabal, Sebastián M., Nicolás Viaux Tapia, Sebastián R., Raquel Pezoa Gutiérrez, Barbara Valdivieso, Constanza High Energy Astrophysical Phenomena High Energy Physics - Phenomenology High Energy Physics - Theory 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 $λ_1(s)$ that achieves an agreement less than $0.75\%$ with the original $λ_1$ 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 particles $N(t)$. Our implementation includes the zenithal angle dependence on the number of particles at the detector level at high altitudes, making it particularly useful for high-altitude observatories. This expression is suitable for implementing air shower simulation tool fitting procedures over a wide range of energies and geometries. Our analysis suggests that the proposed new formalism may provide better agreement with the expected evolution of particle numbers compared to the traditional Greisen formulation. |
| title | Revisiting the Longitudinal Development of Electromagnetic Air Showers: Analytical Improvements to the Greisen Formalism with Zenith Angle Dependence |
| topic | High Energy Astrophysical Phenomena High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2504.09359 |