Abstract
The existence of a dark matter model with a rich dark sector could be the reason why WIMP dark matter has evaded its detection so far. For instance, colored coannihilation naturally leads to the prediction of heavier dark matter masses. Importantly, in such a scenario the Sommerfeld effect and bound state formation must be considered in order to accurately predict the relic abundance. Based on the example of the currently widely studied t-channel simplified model with a colored mediator, we demonstrate the importance of considering these non-perturbative effects for correctly inferring the viable model parameters. We emphasize that a flat correction factor on the relic abundance is not sufficient in this context. Moreover, we find that parameter space thought to be excluded by direct detection experiments and LHC searches remains still viable. Additionally, we illustrate that long-lived particle searches and bound-state searches at the LHC can play a crucial role in probing such a model. We demonstrate how future direct detection experiments will be able to close almost all of the remaining window for freeze-out production, making it a highly testable scenario.
Article PDF
Similar content being viewed by others
References
Planck collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641 (2020) A6 [Erratum ibid. 652 (2021) C4] [arXiv:1807.06209] [INSPIRE].
G. Arcadi et al., The waning of the WIMP? A review of models, searches, and constraints, Eur. Phys. J. C 78 (2018) 203 [arXiv:1703.07364] [INSPIRE].
ATLAS collaboration, Status of searches for dark matter at the LHC, ATL-PHYS-PROC-2022-003 (2022).
XENON collaboration, First Dark Matter Search Results from the XENON1T Experiment, Phys. Rev. Lett. 119 (2017) 181301 [arXiv:1705.06655] [INSPIRE].
PICO collaboration, Dark Matter Search Results from the PICO-60 C3 F8 Bubble Chamber, Phys. Rev. Lett. 118 (2017) 251301 [arXiv:1702.07666] [INSPIRE].
H. E. S. S. collaboration, Search for Photon-Linelike Signatures from Dark Matter Annihilations with H.E.S.S, Phys. Rev. Lett. 110 (2013) 041301 [arXiv:1301.1173] [INSPIRE].
J. Harz, B. Herrmann, M. Klasen, K. Kovarik and Q. L. Boulc’h, Neutralino-stop coannihilation into electroweak gauge and Higgs bosons at one loop, Phys. Rev. D 87 (2013) 054031 [arXiv:1212.5241] [INSPIRE].
J. Ellis, K.A. Olive and J. Zheng, The Extent of the Stop Coannihilation Strip, Eur. Phys. J. C 74 (2014) 2947 [arXiv:1404.5571] [INSPIRE].
J. Harz, B. Herrmann, M. Klasen, K. Kovařík and M. Meinecke, SUSY-QCD corrections to stop annihilation into electroweak final states including Coulomb enhancement effects, Phys. Rev. D 91 (2015) 034012 [arXiv:1410.8063] [INSPIRE].
A. Ibarra, A. Pierce, N. R. Shah and S. Vogl, Anatomy of Coannihilation with a Scalar Top Partner, Phys. Rev. D 91 (2015) 095018 [arXiv:1501.03164] [INSPIRE].
M. J. Baker et al., The Coannihilation Codex, JHEP 12 (2015) 120 [arXiv:1510.03434] [INSPIRE].
J. Harz, B. Herrmann, M. Klasen, K. Kovarik and P. Steppeler, Theoretical uncertainty of the supersymmetric dark matter relic density from scheme and scale variations, Phys. Rev. D 93 (2016) 114023 [arXiv:1602.08103] [INSPIRE].
S. El Hedri and M. de Vries, Cornering Colored Coannihilation, JHEP 10 (2018) 102 [arXiv:1806.03325] [INSPIRE].
S. Schmiemann, J. Harz, B. Herrmann, M. Klasen and K. Kovařík, Squark-pair annihilation into quarks at next-to-leading order, Phys. Rev. D 99 (2019) 095015 [arXiv:1903.10998] [INSPIRE].
J. Branahl, J. Harz, B. Herrmann, M. Klasen, K. Kovařík and S. Schmiemann, SUSY-QCD corrected and Sommerfeld enhanced stau annihilation into heavy quarks with scheme and scale uncertainties, Phys. Rev. D 100 (2019) 115003 [arXiv:1909.09527] [INSPIRE].
C. Arina, B. Fuks, L. Mantani, H. Mies, L. Panizzi and J. Salko, Closing in on t-channel simplified dark matter models, Phys. Lett. B 813 (2021) 136038 [arXiv:2010.07559] [INSPIRE].
C. Arina, B. Fuks and L. Mantani, A universal framework for t-channel dark matter models, Eur. Phys. J. C 80 (2020) 409 [arXiv:2001.05024] [INSPIRE].
J. Abdallah et al., Simplified Models for Dark Matter Searches at the LHC, Phys. Dark Univ. 9-10 (2015) 8 [arXiv:1506.03116] [INSPIRE].
A. Sommerfeld, Über die Beugung und Bremsung der Elektronen, Annalen Phys. 403 (1931) 257 [INSPIRE].
A. D. Sakharov, Interaction of an Electron and Positron in Pair Production, Zh. Eksp. Teor. Fiz. 18 (1948) 631 [INSPIRE].
J. Hisano, S. Matsumoto and M. M. Nojiri, Unitarity and higher order corrections in neutralino dark matter annihilation into two photons, Phys. Rev. D 67 (2003) 075014 [hep-ph/0212022] [INSPIRE].
M. Drees, J. M. Kim and K. I. Nagao, Potentially Large One-loop Corrections to WIMP Annihilation, Phys. Rev. D 81 (2010) 105004 [arXiv:0911.3795] [INSPIRE].
M. Beneke, C. Hellmann and P. Ruiz-Femenia, Heavy neutralino relic abundance with Sommerfeld enhancements — a study of pMSSM scenarios, JHEP 03 (2015) 162 [arXiv:1411.6930] [INSPIRE].
M. Beneke, R. Szafron and K. Urban, Wino potential and Sommerfeld effect at NLO, Phys. Lett. B 800 (2020) 135112 [arXiv:1909.04584] [INSPIRE].
J. Hisano, S. Matsumoto, M. Nagai, O. Saito and M. Senami, Non-perturbative effect on thermal relic abundance of dark matter, Phys. Lett. B 646 (2007) 34 [hep-ph/0610249] [INSPIRE].
B. von Harling and K. Petraki, Bound-state formation for thermal relic dark matter and unitarity, JCAP 12 (2014) 033 [arXiv:1407.7874] [INSPIRE].
J. Ellis, F. Luo and K. A. Olive, Gluino Coannihilation Revisited, JHEP 09 (2015) 127 [arXiv:1503.07142] [INSPIRE].
H. An, M. B. Wise and Y. Zhang, Effects of Bound States on Dark Matter Annihilation, Phys. Rev. D 93 (2016) 115020 [arXiv:1604.01776] [INSPIRE].
P. Asadi, M. Baumgart, P. J. Fitzpatrick, E. Krupczak and T. R. Slatyer, Capture and Decay of Electroweak WIMPonium, JCAP 02 (2017) 005 [arXiv:1610.07617] [INSPIRE].
K. Petraki, M. Postma and J. de Vries, Radiative bound-state-formation cross-sections for dark matter interacting via a Yukawa potential, JHEP 04 (2017) 077 [arXiv:1611.01394] [INSPIRE].
S. P. Liew and F. Luo, Effects of QCD bound states on dark matter relic abundance, JHEP 02 (2017) 091 [arXiv:1611.08133] [INSPIRE].
T. Binder, B. Blobel, J. Harz and K. Mukaida, Dark matter bound-state formation at higher order: a non-equilibrium quantum field theory approach, JHEP 09 (2020) 086 [arXiv:2002.07145] [INSPIRE].
K. Petraki, M. Postma and M. Wiechers, Dark-matter bound states from Feynman diagrams, JHEP 06 (2015) 128 [arXiv:1505.00109] [INSPIRE].
J. Harz and K. Petraki, Radiative bound-state formation in unbroken perturbative non-Abelian theories and implications for dark matter, JHEP 07 (2018) 096 [arXiv:1805.01200] [INSPIRE].
S. El Hedri, A. Kaminska and M. de Vries, A Sommerfeld Toolbox for Colored Dark Sectors, Eur. Phys. J. C 77 (2017) 622 [arXiv:1612.02825] [INSPIRE].
S. El Hedri, A. Kaminska, M. de Vries and J. Zurita, Simplified Phenomenology for Colored Dark Sectors, JHEP 04 (2017) 118 [arXiv:1703.00452] [INSPIRE].
K. A. Mohan, D. Sengupta, T. M. P. Tait, B. Yan and C. P. Yuan, Direct detection and LHC constraints on a t-channel simplified model of Majorana dark matter at one loop, JHEP 05 (2019) 115 [arXiv:1903.05650] [INSPIRE].
M. Garny and J. Heisig, Bound-state effects on dark matter coannihilation: Pushing the boundaries of conversion-driven freeze-out, Phys. Rev. D 105 (2022) 055004 [arXiv:2112.01499] [INSPIRE].
J. Bollig and S. Vogl, Impact of bound states on non-thermal dark matter production, arXiv:2112.01491 [INSPIRE].
A. DiFranzo, K. I. Nagao, A. Rajaraman and T. M. P. Tait, Simplified Models for Dark Matter Interacting with Quarks, JHEP 11 (2013) 014 [Erratum ibid. 01 (2014) 162] [arXiv:1308.2679] [INSPIRE].
Y. Liu, B. Yan and R. Zhang, Loop induced top quark FCNC through top quark and dark matter interactions, Phys. Lett. B 827 (2022) 136964 [arXiv:2103.07859] [INSPIRE].
J. Harz and K. Petraki, Higgs Enhancement for the Dark Matter Relic Density, Phys. Rev. D 97 (2018) 075041 [arXiv:1711.03552] [INSPIRE].
J. Harz and K. Petraki, Higgs-mediated bound states in dark-matter models, JHEP 04 (2019) 130 [arXiv:1901.10030] [INSPIRE].
S. Biondini, Bound-state effects for dark matter with Higgs-like mediators, JHEP 06 (2018) 104 [arXiv:1805.00353] [INSPIRE].
M. Becker, E. Copello and J. Harz, in preparation.
J. Edsjo and P. Gondolo, Neutralino relic density including coannihilations, Phys. Rev. D 56 (1997) 1879 [hep-ph/9704361] [INSPIRE].
M. Garny, J. Heisig, B. Lülf and S. Vogl, Coannihilation without chemical equilibrium, Phys. Rev. D 96 (2017) 103521 [arXiv:1705.09292] [INSPIRE].
M. Garny, J. Heisig, M. Hufnagel and B. Lülf, Top-philic dark matter within and beyond the WIMP paradigm, Phys. Rev. D 97 (2018) 075002 [arXiv:1802.00814] [INSPIRE].
R. T. D’Agnolo, D. Pappadopulo and J. T. Ruderman, Fourth Exception in the Calculation of Relic Abundances, Phys. Rev. Lett. 119 (2017) 061102 [arXiv:1705.08450] [INSPIRE].
O. Just, The partial wave formalism and its application to neutralino dark matter, MSc Thesis, Technische Universität München, Munich Germany (2008).
Particle Data Group collaboration, Review of Particle Physics, PTEP 2020 (2020) 083C01 [INSPIRE].
G. Bélanger, F. Boudjema, A. Pukhov and A. Semenov, MicrOMEGAs 2.0: A Program to calculate the relic density of dark matter in a generic model, Comput. Phys. Commun. 176 (2007) 367 [hep-ph/0607059] [INSPIRE].
M. Beneke, P. Falgari and C. Schwinn, Soft radiation in heavy-particle pair production: All-order colour structure and two-loop anomalous dimension, Nucl. Phys. B 828 (2010) 69 [arXiv:0907.1443] [INSPIRE].
R. Oncala and K. Petraki, Bound states of WIMP dark matter in Higgs-portal models. Part I. Cross-sections and transition rates, JHEP 06 (2021) 124 [arXiv:2101.08666] [INSPIRE].
S. Cassel, Sommerfeld factor for arbitrary partial wave processes, J. Phys. G 37 (2010) 105009 [arXiv:0903.5307] [INSPIRE].
R. Iengo, Sommerfeld enhancement: General results from field theory diagrams, JHEP 05 (2009) 024 [arXiv:0902.0688] [INSPIRE].
S. Biondini and M. Laine, Thermal dark matter co-annihilating with a strongly interacting scalar, JHEP 04 (2018) 072 [arXiv:1801.05821] [INSPIRE].
S. Biondini and S. Vogl, Coloured coannihilations: Dark matter phenomenology meets non-relativistic EFTs, JHEP 02 (2019) 016 [arXiv:1811.02581] [INSPIRE].
S. Biondini and S. Vogl, Scalar dark matter coannihilating with a coloured fermion, JHEP 11 (2019) 147 [arXiv:1907.05766] [INSPIRE].
T. Binder, L. Covi and K. Mukaida, Dark Matter Sommerfeld-enhanced annihilation and Bound-state decay at finite temperature, Phys. Rev. D 98 (2018) 115023 [arXiv:1808.06472] [INSPIRE].
T. Binder, K. Mukaida and K. Petraki, Rapid bound-state formation of Dark Matter in the Early Universe, Phys. Rev. Lett. 124 (2020) 161102 [arXiv:1910.11288] [INSPIRE].
T. Binder, K. Mukaida, B. Scheihing-Hitschfeld and X. Yao, Non-Abelian electric field correlator at NLO for dark matter relic abundance and quarkonium transport, JHEP 01 (2022) 137 [arXiv:2107.03945] [INSPIRE].
T. Binder, A. Filimonova, K. Petraki and G. White, Saha equilibrium for metastable bound states and dark matter freeze-out, arXiv:2112.00042 [INSPIRE].
A. Belyaev, N. D. Christensen and A. Pukhov, CalcHEP 3.4 for collider physics within and beyond the Standard Model, Comput. Phys. Commun. 184 (2013) 1729 [arXiv:1207.6082] [INSPIRE].
M. Garny and J. Heisig, Interplay of super-WIMP and freeze-in production of dark matter, Phys. Rev. D 98 (2018) 095031 [arXiv:1809.10135] [INSPIRE].
G. Bélanger et al., Leptoquark manoeuvres in the dark: a simultaneous solution of the dark matter problem and the \( {R}_{D^{\left({}^{\ast}\right)}} \) anomalies, JHEP 02 (2022) 042 [arXiv:2111.08027] [INSPIRE].
DARWIN collaboration, DARWIN: towards the ultimate dark matter detector, JCAP 11 (2016) 017 [arXiv:1606.07001] [INSPIRE].
J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations, JHEP 07 (2014) 079 [arXiv:1405.0301] [INSPIRE].
S. Dulat et al., New parton distribution functions from a global analysis of quantum chromodynamics, Phys. Rev. D 93 (2016) 033006 [arXiv:1506.07443] [INSPIRE].
ATLAS collaboration, Search for squarks and gluinos in final states with jets and missing transverse momentum using 139 fb−1 of \( \sqrt{s} \) = 13 TeV pp collision data with the ATLAS detector, JHEP 02 (2021) 143 [arXiv:2010.14293] [INSPIRE].
B. Dumont et al., Toward a public analysis database for LHC new physics searches using MADANALYSIS 5, Eur. Phys. J. C 75 (2015) 56 [arXiv:1407.3278] [INSPIRE].
ATLAS collaboration, Search for new phenomena in events with an energetic jet and missing transverse momentum in pp collisions at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, Phys. Rev. D 103 (2021) 112006 [arXiv:2102.10874] [INSPIRE].
https://madanalysis.irmp.ucl.ac.be/wiki/PublicAnalysisDatabase.
M. Cacciari, G. P. Salam and G. Soyez, FastJet User Manual, Eur. Phys. J. C 72 (2012) 1896 [arXiv:1111.6097] [INSPIRE].
Y. L. Dokshitzer, G. D. Leder, S. Moretti and B. R. Webber, Better jet clustering algorithms, JHEP 08 (1997) 001 [hep-ph/9707323] [INSPIRE].
DELPHES 3 collaboration, DELPHES 3, A modular framework for fast simulation of a generic collider experiment, JHEP 02 (2014) 057 [arXiv:1307.6346] [INSPIRE].
T. Sjöstrand et al., An introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159 [arXiv:1410.3012] [INSPIRE].
S. Hoeche et al., Matching parton showers and matrix elements, hep-ph/0602031 [INSPIRE].
A. L. Read, Presentation of search results: The CL(s) technique, J. Phys. G 28 (2002) 2693 [INSPIRE].
I. Zurbano Fernandez et al., High-Luminosity Large Hadron Collider (HL-LHC): Technical design report, CERN-2020-010 (2020).
ATLAS collaboration, Search for new phenomena in high-mass diphoton final states using 37 fb−1 of proton–proton collisions collected at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, Phys. Lett. B 775 (2017) 105 [arXiv:1707.04147] [INSPIRE].
ATLAS collaboration, Search for resonances in diphoton events at \( \sqrt{s} \) = 13 TeV with the ATLAS detector, JHEP 09 (2016) 001 [arXiv:1606.03833] [INSPIRE].
S. P. Martin, Diphoton decays of stoponium at the Large Hadron Collider, Phys. Rev. D 77 (2008) 075002 [arXiv:0801.0237] [INSPIRE].
B. Batell and S. Jung, Probing Light Stops with Stoponium, JHEP 07 (2015) 061 [arXiv:1504.01740] [INSPIRE].
CMS collaboration, Searches for Long-Lived Charged Particles in pp Collisions at \( \sqrt{s} \) = 7 and 8 TeV, JHEP 07 (2013) 122 [arXiv:1305.0491] [INSPIRE].
G. Bélanger et al., LHC-friendly minimal freeze-in models, JHEP 02 (2019) 186 [arXiv:1811.05478] [INSPIRE].
CMS collaboration, Search for heavy stable charged particles with 12.9 fb−1 of 2016 data, CMS-PAS-EXO-16-036 (2017).
CMS collaboration, Constraints on the pMSSM, AMSB model and on other models from the search for long-lived charged particles in proton-proton collisions at \( \sqrt{s} \) = 8 TeV, Eur. Phys. J. C 75 (2015) 325 [arXiv:1502.02522] [INSPIRE].
M. Cahill-Rowley, S. El Hedri, W. Shepherd and D. G. E. Walker, Perturbative Unitarity Constraints on Charged/Colored Portals, Phys. Dark Univ. 22 (2018) 48 [arXiv:1501.03153] [INSPIRE].
A. Schuessler and D. Zeppenfeld, Unitarity constraints on MSSM trilinear couplings, in 15th International Conference on Supersymmetry and the Unification of Fundamental Interactions (SUSY07), Karlsruhe, Germany (2007), pg. 236 [arXiv:0710.5175] [INSPIRE].
Y. Kats and M. D. Schwartz, Annihilation decays of bound states at the LHC, JHEP 04 (2010) 016 [arXiv:0912.0526] [INSPIRE].
FCC collaboration, FCC-hh: The Hadron Collider: Future Circular Collider Conceptual Design Report Volume 3, Eur. Phys. J. ST 228 (2019) 755 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2203.04326
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Becker, M., Copello, E., Harz, J. et al. Impact of Sommerfeld effect and bound state formation in simplified t-channel dark matter models. J. High Energ. Phys. 2022, 145 (2022). https://doi.org/10.1007/JHEP08(2022)145
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2022)145