Measurement of the Inelastic Proton-Proton Cross-Section at $\sqrt{s} \geq 40$ TeV Using the Hybrid Data of the Pierre Auger Observatory
Measuring proton-proton interaction cross-sections at center-of-mass energies above 40 TeV remains a significant challenge in particle physics. The Pierre Auger Observatory provides a unique opportunity to study the interactions at the highest energies through the distribution of the depth of maximum shower development ($X_\mathrm{max}$) observed by its Fluorescence Detector. In previous studies, the determination of the interaction cross-section at ultrahigh energies has relied on the assumption that the tail of the $X_\mathrm{max}$ distribution is proton-dominated, which restricts the analysis to a limited energy range below the ankle and introduces related systematic uncertainties. In this contribution, we adopt a novel method for the simultaneous estimation of the proton-proton interaction cross-section and the primary cosmic-ray mass composition using data from the Pierre Auger Observatory, avoiding assumptions about one quantity to infer the other and thus improving the accuracy and robustness of our analysis. In addition, a systematic shift in the $X_\mathrm{max}$ scale is fitted to account for both experimental uncertainties and theoretical constraints on the modeling of particle interactions. The obtained results are consistent with previous analyses and provide additional constraints on hadronic interaction models. The measured proton-proton inelastic cross-section at ultra-high energies agrees well with extrapolations of accelerator data. The inferred cosmic-ray composition and the $X_\mathrm{max}$-scale shift are also compatible with previous estimates.
Authors
- Belén Andrada
- Pedro J. Costa (ORCID: https://orcid.org/0000-0002-7476-7875)
- Zbigniew Szadkowski (ORCID: https://orcid.org/0000-0002-2690-9912)
- Bruno L. Lago (ORCID: https://orcid.org/0000-0001-9672-0499)
- Marvin Gottowik (ORCID: https://orcid.org/0000-0001-7436-389X)
- Carla Taricco (ORCID: https://orcid.org/0000-0002-0129-5539)
- Giovanni Consolati (ORCID: https://orcid.org/0000-0003-3614-245X)
- Juan Manuel Gonzalez (ORCID: https://orcid.org/0000-0001-9193-0921)
- S. Petrera (ORCID: https://orcid.org/0000-0002-6029-1255)
- Varada Varma Kizakke Covilakam (ORCID: https://orcid.org/0000-0001-5278-3172)
- T. Pierog (ORCID: https://orcid.org/0000-0002-7472-8710)
- G. Sigl (ORCID: https://orcid.org/0000-0002-4396-645X)
- Mateo Fernandez
- T. Huege (ORCID: https://orcid.org/0000-0002-2783-4772)
- Nicolas Leal
- Carmina Pérez Bertolli (ORCID: https://orcid.org/0000-0002-9790-5732)
- Carlo Salvattore Cruz Sanchez (ORCID: https://orcid.org/0009-0002-6173-0974)
- Frank Schröder (ORCID: https://orcid.org/0000-0001-8495-7210)
- Gustavo Medina‐Tanco (ORCID: https://orcid.org/0000-0002-3202-319X)
- A. C. Fauth (ORCID: https://orcid.org/0000-0001-7239-0288)
- Enrico Arnone (ORCID: https://orcid.org/0000-0001-6740-5051)
- Enrique Varela (ORCID: https://orcid.org/0000-0003-0715-7513)
- O. Schölten (ORCID: https://orcid.org/0000-0003-3649-1254)
- Lorenzo Cazon (ORCID: https://orcid.org/0000-0001-6748-8395)
- B. R. Dawson (ORCID: https://orcid.org/0000-0002-4271-3055)
- Matteo Conte (ORCID: https://orcid.org/0000-0002-9932-224X)
- A. Haungs (ORCID: https://orcid.org/0000-0002-9638-7574)
- Dalibor Nosek (ORCID: https://orcid.org/0000-0001-6219-200X)
- G. Parente (ORCID: https://orcid.org/0000-0003-2847-0461)
- Paula Gina Isar (ORCID: https://orcid.org/0000-0002-1241-584X)
- Janning Meinert (ORCID: https://orcid.org/0000-0001-7582-3456)
- Emanuele De Vito (ORCID: https://orcid.org/0000-0003-2045-7588)
- Dušan Mandát (ORCID: https://orcid.org/0000-0001-7748-7468)
- Adila Abdul Halim (ORCID: https://orcid.org/0000-0003-1218-1737)
- Gonzalo Rodriguez Fernandez (ORCID: https://orcid.org/0000-0002-4683-230X)
- Jiří Blažek (ORCID: https://orcid.org/0000-0002-5870-8947)
- Therese Paulsen
- Adriel Bartz Mocellin
- Berenika Čermáková
- S. J. de Jong (ORCID: https://orcid.org/0000-0002-3120-3367)
- Alexey Yushkov (ORCID: https://orcid.org/0000-0001-5107-9116)
- K. Daumiller (ORCID: https://orcid.org/0000-0002-0527-4823)
- A. Insolia (ORCID: https://orcid.org/0000-0002-9040-1566)
- Lorenzo Caccianiga (ORCID: https://orcid.org/0000-0002-2245-5108)
- Darko Veberič (ORCID: https://orcid.org/0000-0003-2683-1526)
- María Isabel Micheletti (ORCID: https://orcid.org/0000-0002-1063-9938)
- A. Segreto (ORCID: https://orcid.org/0000-0001-7341-6603)
- L. Nellen (ORCID: https://orcid.org/0000-0003-1059-8731)
- Felicia Barbato (ORCID: https://orcid.org/0000-0003-0751-6731)
- Jan Pękala
- Alexandra Ramos Fernandes (ORCID: https://orcid.org/0000-0003-2054-4438)
- Gabriela Nicora (ORCID: https://orcid.org/0000-0001-7504-6423)
- Katarína Simkova (ORCID: https://orcid.org/0000-0003-2363-9846)
- R. Caruso (ORCID: https://orcid.org/0000-0003-1622-8731)
- I. Allekotte (ORCID: https://orcid.org/0000-0002-9624-3044)
- F. Sarazin (ORCID: https://orcid.org/0000-0001-5614-1986)
- Luis A. Núñez
- Chaitanya Priyadarshi (ORCID: https://orcid.org/0000-0002-9160-9617)
- M. Cristinziani (ORCID: https://orcid.org/0000-0003-3893-9171)
- E. Zas (ORCID: https://orcid.org/0000-0002-4430-8117)
- Clara Keiko Oliveira Watanabe
- Roberta Colalillo (ORCID: https://orcid.org/0000-0002-4179-9352)
- M. Hrabovský (ORCID: https://orcid.org/0000-0003-4223-7316)
- L. Miramonti (ORCID: https://orcid.org/0000-0002-2808-5363)
- F. Simon (ORCID: https://orcid.org/0000-0002-5978-0289)
- F. Salamida (ORCID: https://orcid.org/0000-0002-9306-8447)
- P. Trávnı́ček (ORCID: https://orcid.org/0000-0002-1655-9584)
- Benjamin Flaggs (ORCID: https://orcid.org/0000-0002-5549-1869)
- Michael Unger
- A. D. Supanitsky (ORCID: https://orcid.org/0000-0002-6942-6216)
- Maximilian Straub
- R. Mussa (ORCID: https://orcid.org/0000-0002-0294-9071)
- Camilla Petrucci
- Federico Maria Mariani
- Fiona H. Ellwanger
- J. Vícha (ORCID: https://orcid.org/0000-0002-7945-3605)
- Jaime Álvarez-Muñiz (ORCID: https://orcid.org/0000-0002-2367-0803)
- Олена Ткаченко (ORCID: https://orcid.org/0000-0002-6382-6390)
- Denise Boncioli (ORCID: https://orcid.org/0000-0003-1186-9353)
- L. Chytka (ORCID: https://orcid.org/0000-0001-5741-259X)
- Martin Vacula (ORCID: https://orcid.org/0000-0003-4844-3962)
- Miguel A. Martins (ORCID: https://orcid.org/0000-0002-7294-6204)
- F. Guarino (ORCID: https://orcid.org/0000-0003-1427-9885)
- M. Erdmann (ORCID: https://orcid.org/0000-0002-1653-1303)
- Jarosław Stasielak (ORCID: https://orcid.org/0000-0002-9284-7000)
- Shima Ujjani Shivashankara
- P. Abreu (ORCID: https://orcid.org/0000-0002-9973-7314)
- Tobias Schulz (ORCID: https://orcid.org/0000-0002-4208-2599)
- L. Nožka
- M. Palatka (ORCID: https://orcid.org/0000-0003-2061-6059)
- I. De Mitri (ORCID: https://orcid.org/0000-0002-8665-1730)
- Antoine Letessier-Selvon
- K. S. Caballero‐Mora (ORCID: https://orcid.org/0000-0002-4042-3855)
- Antonio Franco (ORCID: https://orcid.org/0000-0001-7707-4241)
- Roberto Aloisio (ORCID: https://orcid.org/0000-0003-0161-5923)
- Bjarni Pont (ORCID: https://orcid.org/0000-0002-2578-5364)
- Simone Rossoni
- S. Buitink (ORCID: https://orcid.org/0000-0002-6177-497X)
- Juan Ammerman Yebra (ORCID: https://orcid.org/0000-0002-2059-6206)
- Violet M. Harvey (ORCID: https://orcid.org/0000-0002-6764-4789)
- Hermann-Josef Mathes (ORCID: https://orcid.org/0000-0002-0680-040X)
- P. Mantsch (ORCID: https://orcid.org/0000-0002-8382-7745)
- Rukije Uzeiroska
- Nicolás Martín González (ORCID: https://orcid.org/0000-0001-6566-2222)
- Toshihiro Fujii (ORCID: https://orcid.org/0000-0003-2401-504X)
- Nicolas San Martin
- Corinne Bérat (ORCID: https://orcid.org/0000-0001-8294-6294)
- Zuzana Svozilikova (ORCID: https://orcid.org/0000-0001-5210-0781)
- Maximilian Stadelmaier (ORCID: https://orcid.org/0000-0002-7943-6012)
- P. Assis (ORCID: https://orcid.org/0000-0001-7765-3606)
- F. Montanet (ORCID: https://orcid.org/0000-0001-9787-596X)
- Mohit Saharan
- T. Hebbeker (ORCID: https://orcid.org/0000-0002-9736-266X)
- M. Mallamaci (ORCID: https://orcid.org/0000-0003-4068-0496)
- Alena Bakalová (ORCID: https://orcid.org/0000-0003-1001-4484)
- Peter L. Biermann (ORCID: https://orcid.org/0000-0003-3948-6143)
- Jan Ebr (ORCID: https://orcid.org/0000-0001-8807-6162)
- Anthony Bwembya (ORCID: https://orcid.org/0000-0002-6995-5978)
- J. A. Chinellato (ORCID: https://orcid.org/0000-0002-1236-0789)
- Luis A. Anchordoqui (ORCID: https://orcid.org/0000-0003-1463-7136)
- Jorge Caraça-Valente
- Agustín Cobos Cerutti
- David Schmidt (ORCID: https://orcid.org/0000-0003-2005-4244)
- Krzysztof Pytel (ORCID: https://orcid.org/0000-0002-2937-7886)
- R. Conceição (ORCID: https://orcid.org/0000-0003-4945-5340)
- C. Bonifazi (ORCID: https://orcid.org/0000-0002-3087-3609)
- Shefali Negi (ORCID: https://orcid.org/0000-0003-0891-0829)
- Jon Paul Lundquist (ORCID: https://orcid.org/0000-0002-4245-5092)
- Peter Mazur
- Edyvânia Emily Pereira Martins (ORCID: https://orcid.org/0000-0002-1167-8314)
- Fridtjof Feldbusch
- S. Vorobiov (ORCID: https://orcid.org/0000-0001-8679-3424)
- Alexander Novikov (ORCID: https://orcid.org/0000-0002-1086-7252)
- Emanuele Avocone (ORCID: https://orcid.org/0000-0003-3757-2718)
- H. Wilczyński (ORCID: https://orcid.org/0000-0003-2652-9685)
- Antonio Ambrosone (ORCID: https://orcid.org/0000-0002-9942-1029)
- Pranav Sampathkumar
- Patricia María Hansen
- A. Gorgi (ORCID: https://orcid.org/0000-0002-8085-2304)
- F. de Palma (ORCID: https://orcid.org/0000-0001-5898-2834)
- V. de Souza (ORCID: https://orcid.org/0000-0003-0865-233X)
- Esteban Roulet (ORCID: https://orcid.org/0000-0003-1478-9260)
- S. Dasso (ORCID: https://orcid.org/0000-0002-7680-4721)
- Italo Epicoco (ORCID: https://orcid.org/0000-0002-6408-1335)
- Leo Östman
- Fabio Convenga (ORCID: https://orcid.org/0000-0002-2841-1034)
- J. Matthews (ORCID: https://orcid.org/0000-0002-1832-4420)
- Fernando Catalani (ORCID: https://orcid.org/0000-0001-9332-1476)
- Adrian Sedoski (ORCID: https://orcid.org/0000-0002-4253-3361)
- Radomir Šmída (ORCID: https://orcid.org/0000-0003-0122-1123)
- Joaquín de Jesús (ORCID: https://orcid.org/0000-0002-4741-1769)
- Milton Freitas
- Jose A. Bellido (ORCID: https://orcid.org/0000-0002-0833-9194)
- Kathrin Bismark (ORCID: https://orcid.org/0000-0001-8637-7041)
- Adrián Rovero (ORCID: https://orcid.org/0000-0001-6979-5604)
- D. Góra (ORCID: https://orcid.org/0000-0002-4853-5974)
- J. Řídký (ORCID: https://orcid.org/0000-0001-6697-1393)
- B. Keilhauer (ORCID: https://orcid.org/0000-0003-4494-1155)
- Stef Verpoest (ORCID: https://orcid.org/0000-0002-3031-3206)
- Katharine Mulrey (ORCID: https://orcid.org/0000-0001-8026-8020)
- Mario Buscemi (ORCID: https://orcid.org/0000-0003-2123-5434)
- Wilson M. Namasaka
- Vincent Pelgrims (ORCID: https://orcid.org/0000-0002-5053-3847)
- Chloé Gaudu (ORCID: https://orcid.org/0000-0002-2803-4873)
- Yago Lema-Capeans
- Carmen Merx
- Mohsen Pourmohammad Shahvar
- Lukas Gülzow (ORCID: https://orcid.org/0009-0001-0620-3525)
- Shayoni Panja
- Nikolas Denner
- Simon Strähnz
- Sergio Cabana-Freire
- Alessandro Cermenati
- Beatriz de Errico (ORCID: https://orcid.org/0009-0002-4212-0708)
- João Vítor Reginatto Akim (ORCID: https://orcid.org/0000-0001-8179-9747)
- Fedor Tairli
- Alex Reuzki
- Tim Fehler
- Eric William Mayotte (ORCID: https://orcid.org/0000-0003-2618-9166)
- J. Chudoba (ORCID: https://orcid.org/0000-0002-6425-2579)
- Paolo Privitera (ORCID: https://orcid.org/0000-0002-0623-9261)
- Markus Roth (ORCID: https://orcid.org/0000-0002-9041-1414)
- A. De Roeck (ORCID: https://orcid.org/0000-0002-3234-6634)
- Jacco Vink (ORCID: https://orcid.org/0000-0002-0816-9949)
- Gioacchino Alex Anastasi (ORCID: https://orcid.org/0000-0003-0824-5283)
- José Ochoa (ORCID: https://orcid.org/0009-0001-1395-4159)
- Teresa Bister (ORCID: https://orcid.org/0000-0003-4005-0857)
- Tiina Suomijärvi (ORCID: https://orcid.org/0000-0003-1422-258X)
- Khoa Nguyen (ORCID: https://orcid.org/0000-0001-5763-650X)
- Jose Sanabria Gomez (ORCID: https://orcid.org/0000-0002-4217-3212)
- B. Garćıa (ORCID: https://orcid.org/0000-0003-0919-2734)
- Marcus Niechciol (ORCID: https://orcid.org/0000-0001-6823-8056)
- Leonel Morejón (ORCID: https://orcid.org/0000-0003-1494-2624)
- J. Brack (ORCID: https://orcid.org/0000-0003-4096-2063)
- Igor Vaiman (ORCID: https://orcid.org/0000-0002-8255-3631)
- Ralph Engel
- Juan Carlos D'Olivo
- Juan Pallotta
- Alberto Etchegoyen
- Humberto Ibarguen Salazar
- Rita Cassia dos Anjos
- Germano Guedes
- Analisa Mariazzi
- Ezequiel Rodriguez
- Luca Deval
- Stanislav Michal
- Johannes Blümer
- Jelena Köhler
- Eva Santos
- Antonino Del Popolo
- Dave Nitz
- Danilo Zavrtanik
- Fernando Gollan
- Luis Miguel Domingues Mendes
- Jaime de Oliveira
- Edivaldo Moura Santos
- Lukáš Vaclavek
- Isabelle Lhenry-Yvon
- Carlos Hojvat
- Qader Dorosti (ORCID: https://orcid.org/0000-0001-9711-0609)
- Bernardo Tomé
- Sara Martinelli
- Felix Riehn
- Charles Timmermans
- Paul Filip
- Antonio Bueno
- A. Filipčič (ORCID: https://orcid.org/0000-0001-5671-1555)
- Marco Aglietta
- Carlos J. Todero Peixoto (ORCID: https://orcid.org/0000-0003-3669-8212)
- Josina Schulte
- Luan Bonneau Arbeletche (ORCID: https://orcid.org/0000-0002-3087-3609)
- Thomas Fitoussi
- Carmelo Evoli
- Harm Schoorlemmer
- Mariano Gómez Berisso
- Roger W Clay
- Margita Kubátová
- Melanie Weitz (ORCID: https://orcid.org/0009-0001-9010-9610)
- A. A. Watson
- Primo F. Gómez Vitale
- Rogerio M. de Almeida
- Glennys R. Farrar
- Jonathan Biteau
- Martina Boháčová
- Niklas Langner
- R. Sarmento (ORCID: https://orcid.org/0000-0002-5018-5467)
- Pavel Horváth (ORCID: https://orcid.org/0000-0002-6710-5339)
- G. Marsella (ORCID: https://orcid.org/0000-0002-3152-8874)
- Nataliia Borodai (ORCID: https://orcid.org/0000-0003-1864-937X)
- Cristina Galea
- Kévin Almeida Cheminant (ORCID: https://orcid.org/0000-0001-6352-5339)
- Miroslav Pech
- Martin Schimassek (ORCID: https://orcid.org/0000-0003-4295-7719)
- Jose F. Valdés Galicia
- H. Schieler (ORCID: https://orcid.org/0000-0002-2637-4778)
- Andreas Weindl
- Sergio J Sciutto (ORCID: https://orcid.org/0000-0003-1148-3231)
- Petr Tobiska (ORCID: https://orcid.org/0000-0003-4017-2475)
- Lawrence Wiencke
- Jorge Rubén Rodriguez Rojo
- Daniele Martello
- Florian Lukas Briechle
- Marcelo Augusto Leigui de Oliveira
- Ioana Codrina Maris
- Giorgio Matthiae
- Michael Prouza
- Marcos Cerda
- Vincenzo Rizi
- Valerio Verzi
- Michael Schimp
- Brian Wundheiler
- Laura Valore
- Mário Pimenta
- Piera Luisa Ghia
- P. Gabriel Brichetto Orchera
- Gaetano Salina
- Markus Risse
- Ruben Squartini
- Achille Nucita
- Max Büsken
- Manuel Platino
- Antonella Castellina
- Corbin Covault
- Diego Correia dos Santos
- Brian Fick
- Hans Klages
- Silvia Mollerach
- Marko Zavrtanik
- Alan Fuster
- Vladimír Novotný
- Lorenzo Perrone
- Petr Janeček (ORCID: https://orcid.org/0000-0003-3501-7163)
- Virginia Binet
- Diego Ravignani
- Marina Scornavacche
- Alexander Menshikov
- C. Dobrigkeit
- Armando di Matteo
- Jörg Hörandel
- Indira D. Vergara Quispe
- Ricardo Sato
- Paul Sommers
- Cainã Oliveira
- Marta Bianciotto
- Steffen Hahn
- A. Săftoiu (ORCID: https://orcid.org/0000-0002-7903-6510)
- L. Lopes (ORCID: https://orcid.org/0000-0001-8571-0033)
- Patrick Stassi (ORCID: https://orcid.org/0000-0001-5584-8410)
- Abha Khakurdikar (ORCID: https://orcid.org/0000-0002-4857-5255)
- Sonja Mayotte (ORCID: https://orcid.org/0000-0001-8957-8033)
- F. Sánchez (ORCID: https://orcid.org/0000-0002-6861-6261)
- A. Almela (ORCID: https://orcid.org/0000-0003-1233-2670)
- Rodrigo Pelayo
- Fabian Gobbi
- Baobiao Yue
- Lorenzo Apollonio (ORCID: https://orcid.org/0009-0008-5625-5893)
- Carla Aramo
- Srijan Sehgal
- Joao dos Anjos
- Mario E. Bertaina
- Diego Melo
- Petr Hamal
- Pierpaolo Savina
- Vlastimil Jílek (ORCID: https://orcid.org/0000-0001-5774-7285)
- Matías Rolf Hampel
- Veronika Vašíčková
- Ugo GIACCARI
- J. Rautenberg
- Norbert Kunka
- Juan Carlos Arteaga Velázquez
- Viviana Scherini
- Luiz Augusto Pereira
- Adriana Vásquez-Ramírez
- Heino Falcke
- Geraldina Golup
- Petr Schovanek
- Jannis Pawlowsky
- Olivier Deligny
- Danelise de Oliveira Franco
- Juan Manuel Figueira
- Federico Campuzano
- Frederik Krieger
- Gael Flores Avila (ORCID: https://orcid.org/0000-0001-8375-6492)
- Sven Querchfeld
- Karl-Heinz Kampert
- Matthias Kleifges
- Sofia Andringa
- Samo Stanič
- Alex Tapia
- Gabriella Cataldi
- Luciana Andrade Dourado
- Tomáš Fodran (ORCID: https://orcid.org/0009-0000-9529-0853)
- Matias Jorge Tueros (ORCID: https://orcid.org/0000-0003-1570-1419)
- Megha Mogarkar
- Jhansi Bhavani Vuta
- Eric-Teunis de Boone
- Mohamed Ismaiel
- Karolina Syrokvas
- Matteo Tambone
- Pim van Dillen
Publication Details
- Published
- 2025-09-24
- DOI
- https://doi.org/10.22323/1.501.0416
- Primary Topic
- Particle physics theoretical and experimental studies
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Strong
- European Commission
- Agence Nationale de la Recherche
- Fundação de Amparo à Pesquisa do Estado de São Paulo
- Ministerstvo Školství, Mládeže a Tělovýchovy
- Grantová Agentura České Republiky
- Bundesministerium für Bildung und Forschung
- Fonds De La Recherche Scientifique - FNRS
- Consejo Nacional de Investigaciones Científicas y Técnicas
- Fonds Wetenschappelijk Onderzoek
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro
- Centre National de la Recherche Scientifique
- Financiadora de Estudos e Projetos
- Ministério da Ciência, Tecnologia, Inovações e Comunicações
- Vlaamse regering
- Agencia Nacional de Promoción Científica y Tecnológica
- Institut National de Physique Nucléaire et de Physique des Particules