Skip to main content
Springer Nature Link
Account
Menu
Find a journal Publish with us Track your research
Search
Cart
  1. Home
  2. Journal of High Energy Physics
  3. Article

Radiative bound-state-formation cross-sections for dark matter interacting via a Yukawa potential

  • Regular Article - Theoretical Physics
  • Open access
  • Published: 13 April 2017
  • Volume 2017, article number 77, (2017)
  • Cite this article
Download PDF

You have full access to this open access article

Journal of High Energy Physics Aims and scope Submit manuscript
Radiative bound-state-formation cross-sections for dark matter interacting via a Yukawa potential
Download PDF
  • Kalliopi Petraki1,2,
  • Marieke Postma2 &
  • Jordy de Vries2 

  • 439 Accesses

  • 65 Citations

  • 1 Altmetric

  • Explore all metrics

A preprint version of the article is available at arXiv.

Abstract

We calculate the cross-sections for the radiative formation of bound states by dark matter whose interactions are described in the non-relativistic regime by a Yukawa potential. These cross-sections are important for cosmological and phenomenological studies of dark matter with long-range interactions, residing in a hidden sector, as well as for TeV-scale WIMP dark matter. We provide the leading-order contributions to the cross-sections for the dominant capture processes occurring via emission of a vector or a scalar boson. We offer a detailed inspection of their features, including their velocity dependence within and outside the Coulomb regime, and their resonance structure. For pairs of annihilating particles, we compare bound-state formation with annihilation.

Article PDF

Download to read the full article text

Similar content being viewed by others

Dark-matter bound states from Feynman diagrams

Article Open access 18 June 2015

Bound-state formation, dissociation and decays of darkonium with potential non-relativistic Yukawa theory for scalar and pseudoscalar mediators

Article Open access 25 March 2022

Radiative bound-state formation in unbroken perturbative non-Abelian theories and implications for dark matter

Article Open access 13 July 2018
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

References

  1. K. Petraki, M. Postma and M. Wiechers, Dark-matter bound states from Feynman diagrams, JHEP 06 (2015) 128 [arXiv:1505.00109] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  2. 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].

    ADS  Google Scholar 

  3. H. An, M.B. Wise and Y. Zhang, Strong CMB constraint on P-wave annihilating dark matter, arXiv:1606.02305 [INSPIRE].

  4. 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].

    Article  ADS  Google Scholar 

  5. A. Sommerfeld, Über die Beugung und Bremsung der Elektronen (in German), Ann. Phys. 403 (1931) 257.

  6. P. Hoyer, Bound states — from QED to QCD, arXiv:1402.5005 [INSPIRE].

  7. B. von Harling and K. Petraki, Bound-state formation for thermal relic dark matter and unitarity, JCAP 12 (2014) 033 [arXiv:1407.7874] [INSPIRE].

    Article  Google Scholar 

  8. I. Baldes and K. Petraki, Asymmetric thermal-relic dark matter: Sommerfeld-enhanced freeze-out, annihilation signals and unitarity bounds, arXiv:1703.00478 [INSPIRE].

  9. K.M. Belotsky, E.A. Esipova and A.A. Kirillov, On the classical description of the recombination of dark matter particles with a Coulomb-like interaction, Phys. Lett. B 761 (2016) 81 [arXiv:1506.03094] [INSPIRE].

  10. K. Petraki and R.R. Volkas, Review of asymmetric dark matter, Int. J. Mod. Phys. A 28 (2013) 1330028 [arXiv:1305.4939] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  11. F.-Y. Cyr-Racine and K. Sigurdson, Cosmology of atomic dark matter, Phys. Rev. D 87 (2013) 103515 [arXiv:1209.5752] [INSPIRE].

    ADS  Google Scholar 

  12. L. Pearce, K. Petraki and A. Kusenko, Signals from dark atom formation in halos, Phys. Rev. D 91 (2015) 083532 [arXiv:1502.01755] [INSPIRE].

    ADS  Google Scholar 

  13. L. Pearce and A. Kusenko, Indirect detection of self-interacting asymmetric dark matter, Phys. Rev. D 87 (2013) 123531 [arXiv:1303.7294] [INSPIRE].

    ADS  Google Scholar 

  14. J.M. Cline, Y. Farzan, Z. Liu, G.D. Moore and W. Xue, 3.5 keV X-rays as the “21 cm line” of dark atoms and a link to light sterile neutrinos, Phys. Rev. D 89 (2014) 121302 [arXiv:1404.3729] [INSPIRE].

  15. J.J. Sakurai, Modern quantum mechanics, (1985).

  16. M. Pospelov and A. Ritz, Astrophysical signatures of secluded dark matter, Phys. Lett. B 671 (2009) 391 [arXiv:0810.1502] [INSPIRE].

    Article  ADS  Google Scholar 

  17. C. Kouvaris, K. Langæble and N.G. Nielsen, The spectrum of darkonium in the sun, JCAP 10 (2016) 012 [arXiv:1607.00374] [INSPIRE].

    Article  ADS  Google Scholar 

  18. M. Cirelli, P. Panci, K. Petraki, F. Sala and M. Taoso, Dark matter’s secret liaisons: phenomenology of a dark U(1) sector with bound states, arXiv:1612.07295 [INSPIRE].

  19. K. Griest and M. Kamionkowski, Unitarity limits on the mass and radius of dark matter particles, Phys. Rev. Lett. 64 (1990) 615 [INSPIRE].

    Article  ADS  Google Scholar 

  20. X. Kong and F. Ravndal, Proton proton scattering lengths from effective field theory, Phys. Lett. B 450 (1999) 320 [Erratum ibid. B 458 (1999) 565] [nucl-th/9811076] [INSPIRE].

  21. X. Kong and F. Ravndal, Proton proton fusion in leading order of effective field theory, Nucl. Phys. A 656 (1999) 421 [nucl-th/9902064] [INSPIRE].

  22. K. Blum, R. Sato and T.R. Slatyer, Self-consistent calculation of the Sommerfeld enhancement, JCAP 06 (2016) 021 [arXiv:1603.01383] [INSPIRE].

    Article  ADS  Google Scholar 

  23. M. Cirelli, N. Fornengo and A. Strumia, Minimal dark matter, Nucl. Phys. B 753 (2006) 178 [hep-ph/0512090] [INSPIRE].

  24. M. Cirelli, A. Strumia and M. Tamburini, Cosmology and astrophysics of minimal dark matter, Nucl. Phys. B 787 (2007) 152 [arXiv:0706.4071] [INSPIRE].

    Article  ADS  Google Scholar 

  25. M. Cirelli and A. Strumia, Minimal dark matter: model and results, New J. Phys. 11 (2009) 105005 [arXiv:0903.3381] [INSPIRE].

    Article  ADS  Google Scholar 

  26. A. Hryczuk, R. Iengo and P. Ullio, Relic densities including Sommerfeld enhancements in the MSSM, JHEP 03 (2011) 069 [arXiv:1010.2172] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  27. A. Hryczuk, I. Cholis, R. Iengo, M. Tavakoli and P. Ullio, Indirect detection analysis: wino dark matter case study, JCAP 07 (2014) 031 [arXiv:1401.6212] [INSPIRE].

    Article  ADS  Google Scholar 

  28. 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].

    Article  Google Scholar 

  29. M. Cirelli, F. Sala and M. Taoso, Wino-like minimal dark matter and future colliders, JHEP 10 (2014) 033 [Erratum ibid. 01 (2015) 041] [arXiv:1407.7058] [INSPIRE].

  30. J. Ellis, F. Luo and K.A. Olive, Gluino coannihilation revisited, JHEP 09 (2015) 127 [arXiv:1503.07142] [INSPIRE].

    Article  ADS  Google Scholar 

  31. S. Kim and M. Laine, Rapid thermal co-annihilation through bound states in QCD, JHEP 07 (2016) 143 [arXiv:1602.08105] [INSPIRE].

    Article  ADS  Google Scholar 

  32. S. Kim and M. Laine, On thermal corrections to near-threshold annihilation, JCAP 01 (2017) 013 [arXiv:1609.00474] [INSPIRE].

    Article  ADS  Google Scholar 

  33. J.D. March-Russell and S.M. West, WIMPonium and boost factors for indirect dark matter detection, Phys. Lett. B 676 (2009) 133 [arXiv:0812.0559] [INSPIRE].

    Article  ADS  Google Scholar 

  34. B. Holdom, Two U(1)’s and ϵ charge shifts, Phys. Lett. B 166 (1986) 196 [INSPIRE].

    Article  ADS  Google Scholar 

  35. R. Foot and X.-G. He, Comment on ZZ′ mixing in extended gauge theories, Phys. Lett. B 267 (1991) 509 [INSPIRE].

    Article  ADS  Google Scholar 

  36. B. Körs and P. Nath, A Stückelberg extension of the Standard Model, Phys. Lett. B 586 (2004) 366 [hep-ph/0402047] [INSPIRE].

  37. D. Feldman, B. Körs and P. Nath, Extra-weakly interacting dark matter, Phys. Rev. D 75 (2007) 023503 [hep-ph/0610133] [INSPIRE].

  38. M. Pospelov, A. Ritz and M.B. Voloshin, Secluded WIMP dark matter, Phys. Lett. B 662 (2008) 53 [arXiv:0711.4866] [INSPIRE].

    Article  ADS  Google Scholar 

  39. P. Fayet, U-boson production in e + e − annihilations, ψ and Y decays and light dark matter, Phys. Rev. D 75 (2007) 115017 [hep-ph/0702176] [INSPIRE].

  40. M. Goodsell, J. Jaeckel, J. Redondo and A. Ringwald, Naturally light hidden photons in LARGE volume string compactifications, JHEP 11 (2009) 027 [arXiv:0909.0515] [INSPIRE].

    Article  ADS  Google Scholar 

  41. P. Fayet, The light U-boson as the mediator of a new force, coupled to a combination of Q, B, L and dark matter, Eur. Phys. J. C 77 (2017) 53 [arXiv:1611.05357] [INSPIRE].

    Article  ADS  Google Scholar 

  42. D.N. Spergel and P.J. Steinhardt, Observational evidence for selfinteracting cold dark matter, Phys. Rev. Lett. 84 (2000) 3760 [astro-ph/9909386] [INSPIRE].

  43. J.L. Feng, M. Kaplinghat, H. Tu and H.-B. Yu, Hidden charged dark matter, JCAP 07 (2009) 004 [arXiv:0905.3039] [INSPIRE].

    Article  ADS  Google Scholar 

  44. A. Loeb and N. Weiner, Cores in dwarf galaxies from dark matter with a Yukawa potential, Phys. Rev. Lett. 106 (2011) 171302 [arXiv:1011.6374] [INSPIRE].

    Article  ADS  Google Scholar 

  45. N. Arkani-Hamed, D.P. Finkbeiner, T.R. Slatyer and N. Weiner, A theory of dark matter, Phys. Rev. D 79 (2009) 015014 [arXiv:0810.0713] [INSPIRE].

    ADS  Google Scholar 

  46. I. Cholis, D.P. Finkbeiner, L. Goodenough and N. Weiner, The PAMELA positron excess from annihilations into a light boson, JCAP 12 (2009) 007 [arXiv:0810.5344] [INSPIRE].

    Article  ADS  Google Scholar 

  47. M. Abdullah, A. DiFranzo, A. Rajaraman, T.M.P. Tait, P. Tanedo and A.M. Wijangco, Hidden on-shell mediators for the galactic center γ-ray excess, Phys. Rev. D 90 (2014) 035004 [arXiv:1404.6528] [INSPIRE].

  48. A. Berlin, P. Gratia, D. Hooper and S.D. McDermott, Hidden sector dark matter models for the galactic center gamma-ray excess, Phys. Rev. D 90 (2014) 015032 [arXiv:1405.5204] [INSPIRE].

    ADS  Google Scholar 

  49. K.K. Boddy, J.L. Feng, M. Kaplinghat, Y. Shadmi and T.M.P. Tait, Strongly interacting dark matter: self-interactions and keV lines, Phys. Rev. D 90 (2014) 095016 [arXiv:1408.6532] [INSPIRE].

    ADS  Google Scholar 

  50. W. Detmold, M. McCullough and A. Pochinsky, Dark nuclei I: cosmology and indirect detection, Phys. Rev. D 90 (2014) 115013 [arXiv:1406.2276] [INSPIRE].

    ADS  Google Scholar 

  51. K. Petraki, L. Pearce and A. Kusenko, Self-interacting asymmetric dark matter coupled to a light massive dark photon, JCAP 07 (2014) 039 [arXiv:1403.1077] [INSPIRE].

    Article  ADS  Google Scholar 

  52. A. Kusenko and P.J. Steinhardt, Q ball candidates for selfinteracting dark matter, Phys. Rev. Lett. 87 (2001) 141301 [astro-ph/0106008] [INSPIRE].

  53. J.L. Feng, H. Tu and H.-B. Yu, Thermal relics in hidden sectors, JCAP 10 (2008) 043 [arXiv:0808.2318] [INSPIRE].

    Article  ADS  Google Scholar 

  54. R. Foot and Z.K. Silagadze, Thin disk of co-rotating dwarfs: a fingerprint of dissipative (mirror) dark matter?, Phys. Dark Univ. 2 (2013) 163 [arXiv:1306.1305] [INSPIRE].

    Article  Google Scholar 

  55. J. Fan, A. Katz, L. Randall and M. Reece, Dark-disk universe, Phys. Rev. Lett. 110 (2013) 211302 [arXiv:1303.3271] [INSPIRE].

    Article  ADS  Google Scholar 

  56. R. Foot, Tully-Fisher relation, galactic rotation curves and dissipative mirror dark matter, JCAP 12 (2014) 047 [arXiv:1307.1755] [INSPIRE].

    Article  ADS  Google Scholar 

  57. R. Foot, A dark matter scaling relation from mirror dark matter, Phys. Dark Univ. 5-6 (2014) 236 [arXiv:1303.1727] [INSPIRE].

    Article  Google Scholar 

  58. R. Foot and S. Vagnozzi, Dissipative hidden sector dark matter, Phys. Rev. D 91 (2015) 023512 [arXiv:1409.7174] [INSPIRE].

    ADS  MATH  Google Scholar 

  59. R. Foot and S. Vagnozzi, Diurnal modulation signal from dissipative hidden sector dark matter, Phys. Lett. B 748 (2015) 61 [arXiv:1412.0762] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  60. R. Foot, Dissipative dark matter and the rotation curves of dwarf galaxies, JCAP 07 (2016) 011 [arXiv:1506.01451] [INSPIRE].

    Article  ADS  Google Scholar 

  61. K.K. Boddy, M. Kaplinghat, A. Kwa and A.H.G. Peter, Hidden sector hydrogen as dark matter: small-scale structure formation predictions and the importance of hyperfine interactions, Phys. Rev. D 94 (2016) 123017 [arXiv:1609.03592] [INSPIRE].

    ADS  Google Scholar 

  62. R. Laha and E. Braaten, Direct detection of dark matter in universal bound states, Phys. Rev. D 89 (2014) 103510 [arXiv:1311.6386] [INSPIRE].

    ADS  Google Scholar 

  63. R. Laha, Directional detection of dark matter in universal bound states, Phys. Rev. D 92 (2015) 083509 [arXiv:1505.02772] [INSPIRE].

    ADS  Google Scholar 

  64. A. Butcher, R. Kirk, J. Monroe and S.M. West, Can tonne-scale direct detection experiments discover nuclear dark matter?, arXiv:1610.01840 [INSPIRE].

  65. W. Shepherd, T.M.P. Tait and G. Zaharijas, Bound states of weakly interacting dark matter, Phys. Rev. D 79 (2009) 055022 [arXiv:0901.2125] [INSPIRE].

    ADS  Google Scholar 

  66. H. An, B. Echenard, M. Pospelov and Y. Zhang, Probing the dark sector with dark matter bound states, Phys. Rev. Lett. 116 (2016) 151801 [arXiv:1510.05020] [INSPIRE].

    Article  ADS  Google Scholar 

  67. X.-J. Bi, Z. Kang, P. Ko, J. Li and T. Li, ADMonium: asymmetric dark matter bound state, Phys. Rev. D 95 (2017) 043540 [arXiv:1602.08816] [INSPIRE].

    ADS  Google Scholar 

  68. F. Nozzoli, A balance for dark matter bound states, Astropart. Phys. 91 (2017) 22 [arXiv:1608.00405] [INSPIRE].

    Article  ADS  Google Scholar 

  69. A.I. Akhiezer and N.P. Merenkov, The theory of lepton bound-state production, J. Phys. B 29 (1996) 2135.

    ADS  Google Scholar 

  70. J. de Vries, U.-G. Meißner, E. Epelbaum and N. Kaiser, Parity violation in proton-proton scattering from chiral effective field theory, Eur. Phys. J. A 49 (2013) 149 [arXiv:1309.4711] [INSPIRE].

    Article  ADS  Google Scholar 

  71. J. de Vries, N. Li, U.-G. Meißner, A. Nogga, E. Epelbaum and N. Kaiser, Parity violation in neutron capture on the proton: determining the weak pion-nucleon coupling, Phys. Lett. B 747 (2015) 299 [arXiv:1501.01832] [INSPIRE].

    Article  ADS  Google Scholar 

  72. W. Glöckle, The quantum mechanical few-body problem, Springer, Germany, (1983).

    Book  Google Scholar 

  73. E. Epelbaum, W. Glöckle and U.-G. Meißner, The two-nucleon system at next-to-next-to-next-to-leading order, Nucl. Phys. A 747 (2005) 362 [nucl-th/0405048] [INSPIRE].

  74. E. Anderson et al., LAPACK users’ guide, third ed., Society for Industrial and Applied Mathematics, Philadelphia PA U.S.A., (1999).

Download references

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.

Author information

Authors and Affiliations

  1. LPTHE, CNRS, UMR 7589, 4 Place Jussieu, F-75252, Paris, France

    Kalliopi Petraki

  2. Nikhef, Science Park 105, 1098 XG, Amsterdam, The Netherlands

    Kalliopi Petraki, Marieke Postma & Jordy de Vries

Authors
  1. Kalliopi Petraki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marieke Postma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jordy de Vries
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kalliopi Petraki.

Additional information

ArXiv ePrint: 1611.01394

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Petraki, K., Postma, M. & de Vries, J. Radiative bound-state-formation cross-sections for dark matter interacting via a Yukawa potential. J. High Energ. Phys. 2017, 77 (2017). https://doi.org/10.1007/JHEP04(2017)077

Download citation

  • Received: 14 November 2016

  • Revised: 31 January 2017

  • Accepted: 27 March 2017

  • Published: 13 April 2017

  • DOI: https://doi.org/10.1007/JHEP04(2017)077

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Beyond Standard Model
  • Cosmology of Theories beyond the SM
  • Nonperturbative Effects
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us
  • Track your research

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Journal finder
  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support
  • Cancel contracts here

Not affiliated

Springer Nature

© 2024 Springer Nature