Eur. Phys. J. C (2024) 84: 1170
https://doi.org/10.1140/epjc/s10052-024-13472-4

Regular Article

Constraints on self-interaction cross-sections of dark matter in universal bound states from direct detection

¹ Max-Planck-Institut für Physik, 85748, Garching, Germany
² Institut für Hochenergiephysik der Österreichischen Akademie der Wissenschaften, 1010, Wien, Austria
³ Atominstitut, Technische Universität Wien, 1020, Wien, Austria
⁴ INFN, Laboratori Nazionali del Gran Sasso, 67100, Assergi, Italy
⁵ Faculty of Mathematics, Physics and Informatics, Comenius University, 84248, Bratislava, Slovakia
⁶ Physik-Department, TUM School of Natural Sciences, Technische Universität München, 85747, Garching, Germany
⁷ Eberhard-Karls-Universität Tübingen, 72076, Tübingen, Germany
⁸ Department of Physics, University of Oxford, OX1 3RH, Oxford, UK
⁹ LIBPhys-UC, Departamento de Fisica, Universidade de Coimbra, P3004 516, Coimbra, Portugal
¹⁰ Walther-Meißner-Institut für Tieftemperaturforschung, 85748, Garching, Germany
¹¹ GSSI-Gran Sasso Science Institute, 67100, L’Aquila, Italy
¹² Dipartimento di Ingegneria Civile e Meccanica, Università degli Studi di Cassino e del Lazio Meridionale, 03043, Cassino, Italy
¹³ Instituto de Física da Universidade de São Paulo, 05508-090, São Paulo, Brazil
¹⁴ Dipartimento di Fisica, Università di Milano Bicocca, 20126, Milan, Italy

^a shubham.gupta@oeaw.ac.at

Received: 8 July 2024
Accepted: 7 October 2024
Published online: 18 November 2024

Abstract

$\Lambda$-Cold Dark Matter ($\Lambda$CDM) has been successful at explaining the large-scale structures in the universe but faces severe issues on smaller scales when compared to observations. Introducing self-interactions between dark matter particles claims to provide a solution to the small-scale issues in the $\Lambda$CDM simulations while being consistent with the observations at large scales. The existence of the energy region in which these self-interactions between dark matter particles come close to saturating the S-wave unitarity bound can result in the formation of dark matter bound states called darkonium. In this scenario, all the low energy scattering properties are determined by a single parameter, the inverse scattering length $\gamma$. In this work, we set bounds on $\gamma$ by studying the impact of darkonium on the observations at direct detection experiments using data from CRESST-III and XENON1T. The exclusion limits on $\gamma$ are then subsequently converted to exclusion limits on the self-interaction cross-section and compared with the constraints from astrophysics and N-body simulations.