Skip to main content
Download PDF

Continuum-mediated self-interacting dark matter

Journal of High Energy Physics volume 2021, Article number: 8 (2021) Cite this article

A preprint version of the article is available at arXiv.

Abstract

Dark matter may self-interact through a continuum of low-mass states. This happens if dark matter couples to a strongly-coupled nearly-conformal hidden sector. This type of theory is holographically described by brane-localized dark matter interacting with bulk fields in a slice of 5D anti-de Sitter space. The long-range potential in this scenario depends on a non-integer power of the spatial separation, in contrast to the Yukawa potential generated by the exchange of a single 4D mediator. The resulting self-interaction cross section scales like a non-integer power of velocity. We identify the Born, classical and resonant regimes and investigate them using state-of-the-art numerical methods. We demonstrate the viability of our continuum-mediated framework to address the astrophysical small-scale structure anomalies. Investigating the continuum-mediated Sommerfeld enhancement, we demonstrate that a pattern of resonances can occur depending on the non-integer power. We conclude that continuum mediators introduce novel power-law scalings which open new possibilities for dark matter self-interaction phenomenology.

References

  1. M. Pospelov, Secluded U(1) below the weak scale, Phys. Rev. D 80 (2009) 095002 [arXiv:0811.1030] [INSPIRE].

    Article  ADS  Google Scholar 

  2. 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 

  3. 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 

  4. R. Essig et al., Working Group Report: New Light Weakly Coupled Particles, in proceedings of the Community Summer Study 2013: Snowmass on the Mississippi, Minneapolis, MN, U.S.A., 29 July–6 August 2013, arXiv:1311.0029 [INSPIRE].

  5. J. Alexander et al., Dark Sectors 2016 Workshop: Community Report, arXiv:1608.08632 [INSPIRE].

  6. M. Battaglieri et al., U.S. Cosmic Visions: New Ideas in Dark Matter 2017: Community Report, in proceedings of the U.S. Cosmic Visions: New Ideas in Dark Matter, College Park, MD, U.S.A., 23–25 March 2017, arXiv:1707.04591 [INSPIRE].

  7. E. D. Carlson, M. E. Machacek and L. J. Hall, Self-interacting dark matter, Astrophys. J. 398 (1992) 43 [INSPIRE].

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. S. Tulin, H.-B. Yu and K. M. Zurek, Beyond Collisionless Dark Matter: Particle Physics Dynamics for Dark Matter Halo Structure, Phys. Rev. D 87 (2013) 115007 [arXiv:1302.3898] [INSPIRE].

    Article  ADS  Google Scholar 

  10. S. Tulin and H.-B. Yu, Dark Matter Self-interactions and Small Scale Structure, Phys. Rept. 730 (2018) 1 [arXiv:1705.02358] [INSPIRE].

    MathSciNet  MATH  Article  ADS  Google Scholar 

  11. T. Gherghetta and B. von Harling, A Warped Model of Dark Matter, JHEP 04 (2010) 039 [arXiv:1002.2967] [INSPIRE].

    MATH  Article  ADS  Google Scholar 

  12. B. von Harling and K. L. McDonald, Secluded Dark Matter Coupled to a Hidden CFT, JHEP 08 (2012) 048 [arXiv:1203.6646] [INSPIRE].

    Article  Google Scholar 

  13. M. J. Strassler, Why Unparticle Models with Mass Gaps are Examples of Hidden Valleys, arXiv:0801.0629 [INSPIRE].

  14. C.-H. Chen and C. S. Kim, Sommerfeld Enhancement from Unparticle Exchange for Dark Matter Annihilation, Phys. Lett. B 687 (2010) 232 [arXiv:0909.1878] [INSPIRE].

    Article  ADS  Google Scholar 

  15. A. Friedland, M. Giannotti and M. Graesser, On the RS2 realization of unparticles, Phys. Lett. B 678 (2009) 149 [arXiv:0902.3676] [INSPIRE].

    Article  ADS  Google Scholar 

  16. A. Friedland, M. Giannotti and M. L. Graesser, Vector Bosons in the Randall-Sundrum 2 and Lykken-Randall models and unparticles, JHEP 09 (2009) 033 [arXiv:0905.2607] [INSPIRE].

    MathSciNet  Article  ADS  Google Scholar 

  17. H. M. Lee, Gauged U(1) clockwork theory, Phys. Lett. B 778 (2018) 79 [arXiv:1708.03564] [INSPIRE].

    MATH  Article  ADS  Google Scholar 

  18. P. Brax, S. Fichet and P. Tanedo, The Warped Dark Sector, Phys. Lett. B 798 (2019) 135012 [arXiv:1906.02199] [INSPIRE].

    MathSciNet  Article  Google Scholar 

  19. A. Costantino, S. Fichet and P. Tanedo, Effective Field Theory in AdS: Continuum Regime, Soft Bombs, and IR Emergence, Phys. Rev. D 102 (2020) 115038 [arXiv:2002.12335] [INSPIRE].

    MathSciNet  Article  ADS  Google Scholar 

  20. J. S. Bullock and M. Boylan-Kolchin, Small-Scale Challenges to the ΛCDM Paradigm, Ann. Rev. Astron. Astrophys. 55 (2017) 343 [arXiv:1707.04256] [INSPIRE].

    Article  ADS  Google Scholar 

  21. P. Fadeev, Y. V. Stadnik, F. Ficek, M. G. Kozlov, V. V. Flambaum and D. Budker, Revisiting spin-dependent forces mediated by new bosons: Potentials in the coordinate-space representation for macroscopic- and atomic-scale experiments, Phys. Rev. A 99 (2019) 022113 [arXiv:1810.10364] [INSPIRE].

    Article  ADS  Google Scholar 

  22. S. Fichet, Quantum Forces from Dark Matter and Where to Find Them, Phys. Rev. Lett. 120 (2018) 131801 [arXiv:1705.10331] [INSPIRE].

    Article  ADS  Google Scholar 

  23. A. Costantino, S. Fichet and P. Tanedo, Exotic Spin-Dependent Forces from a Hidden Sector, JHEP 03 (2020) 148 [arXiv:1910.02972] [INSPIRE].

    MathSciNet  Article  ADS  Google Scholar 

  24. A. Katz, M. Reece and A. Sajjad, Continuum-mediated dark matter-baryon scattering, Phys. Dark Univ. 12 (2016) 24 [arXiv:1509.03628] [INSPIRE].

    Article  Google Scholar 

  25. L. Randall and R. Sundrum, An Alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].

    MathSciNet  MATH  Article  ADS  Google Scholar 

  26. W. D. Goldberger and M. B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett. 83 (1999) 4922 [hep-ph/9907447] [INSPIRE].

    Article  ADS  Google Scholar 

  27. A. Manohar and H. Georgi, Chiral Quarks and the Nonrelativistic Quark Model, Nucl. Phys. B 234 (1984) 189 [INSPIRE].

    Article  ADS  Google Scholar 

  28. H. Georgi and L. Randall, Flavor Conserving CP-violation in Invisible Axion Models, Nucl. Phys. B 276 (1986) 241 [INSPIRE].

    Article  ADS  Google Scholar 

  29. H. Georgi, Generalized dimensional analysis, Phys. Lett. B 298 (1993) 187 [hep-ph/9207278] [INSPIRE].

    Article  ADS  Google Scholar 

  30. M. A. Luty, Naive dimensional analysis and supersymmetry, Phys. Rev. D 57 (1998) 1531 [hep-ph/9706235] [INSPIRE].

    Article  ADS  Google Scholar 

  31. E. E. Jenkins, A. V. Manohar and M. Trott, Naive Dimensional Analysis Counting of Gauge Theory Amplitudes and Anomalous Dimensions, Phys. Lett. B 726 (2013) 697 [arXiv:1309.0819] [INSPIRE].

    MATH  Article  ADS  Google Scholar 

  32. G. Dvali and C. Gomez, Quantum Information and Gravity Cutoff in Theories with Species, Phys. Lett. B 674 (2009) 303 [arXiv:0812.1940] [INSPIRE].

    MathSciNet  Article  ADS  Google Scholar 

  33. S. Fichet, Braneworld effective field theories — holography, consistency and conformal effects, JHEP 04 (2020) 016 [arXiv:1912.12316] [INSPIRE].

    MathSciNet  MATH  Article  ADS  Google Scholar 

  34. H. Davoudiasl, G. Perez and A. Soni, The Little Randall-Sundrum Model at the Large Hadron Collider, Phys. Lett. B 665 (2008) 67 [arXiv:0802.0203] [INSPIRE].

    Article  ADS  Google Scholar 

  35. P. Breitenlohner and D. Z. Freedman, Positive Energy in anti-de Sitter Backgrounds and Gauged Extended Supergravity, Phys. Lett. B 115 (1982) 197 [INSPIRE].

    MathSciNet  Article  ADS  Google Scholar 

  36. P. Breitenlohner and D. Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].

    MathSciNet  MATH  Article  ADS  Google Scholar 

  37. J. M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].

  38. S. S. Gubser, I. R. Klebanov and A. M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].

    MathSciNet  MATH  Article  ADS  Google Scholar 

  39. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    MathSciNet  MATH  Article  ADS  Google Scholar 

  40. D. Z. Freedman, S. D. Mathur, A. Matusis and L. Rastelli, Comments on 4 point functions in the CFT/AdS correspondence, Phys. Lett. B 452 (1999) 61 [hep-th/9808006] [INSPIRE].

    MathSciNet  MATH  Article  ADS  Google Scholar 

  41. H. Liu and A. A. Tseytlin, On four point functions in the CFT/AdS correspondence, Phys. Rev. D 59 (1999) 086002 [hep-th/9807097] [INSPIRE].

    MathSciNet  Article  ADS  Google Scholar 

  42. D. Z. Freedman, S. D. Mathur, A. Matusis and L. Rastelli, Correlation functions in the CFTd/AdSd+1 correspondence, Nucl. Phys. B 546 (1999) 96 [hep-th/9804058] [INSPIRE].

    MathSciNet  MATH  Article  ADS  Google Scholar 

  43. E. D’Hoker, D.Z. Freedman and L. Rastelli, AdS/CFT four point functions: How to succeed at z integrals without really trying, Nucl. Phys. B 562 (1999) 395 [hep-th/9905049] [INSPIRE].

    MathSciNet  MATH  Article  ADS  Google Scholar 

  44. E. D’Hoker, D. Z. Freedman, S. D. Mathur, A. Matusis and L. Rastelli, Graviton exchange and complete four point functions in the AdS/CFT correspondence, Nucl. Phys. B 562 (1999) 353 [hep-th/9903196] [INSPIRE].

    MathSciNet  MATH  Article  ADS  Google Scholar 

  45. O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].

    MathSciNet  MATH  Article  ADS  Google Scholar 

  46. A. Zaffaroni, Introduction to the AdS-CFT correspondence, Class. Quant. Grav. 17 (2000) 3571 [INSPIRE].

    MathSciNet  MATH  Article  ADS  Google Scholar 

  47. H. Nastase, Introduction to AdS-CFT, arXiv:0712.0689 [INSPIRE].

  48. J. Kaplan, Lectures on AdS/CFT from the Bottom Up, (2015).

  49. N. Arkani-Hamed, M. Porrati and L. Randall, Holography and phenomenology, JHEP 08 (2001) 017 [hep-th/0012148] [INSPIRE].

    MathSciNet  Article  ADS  Google Scholar 

  50. P. Creminelli, A. Nicolis and R. Rattazzi, Holography and the electroweak phase transition, JHEP 03 (2002) 051 [hep-th/0107141] [INSPIRE].

    Article  ADS  Google Scholar 

  51. A. Hebecker and J. March-Russell, Randall-Sundrum II cosmology, AdS/CFT, and the bulk black hole, Nucl. Phys. B 608 (2001) 375 [hep-ph/0103214] [INSPIRE].

  52. D. Langlois, L. Sorbo and M. Rodriguez-Martinez, Cosmology of a brane radiating gravitons into the extra dimension, Phys. Rev. Lett. 89 (2002) 171301 [hep-th/0206146] [INSPIRE].

    MathSciNet  MATH  Article  ADS  Google Scholar 

  53. D. Langlois and L. Sorbo, Bulk gravitons from a cosmological brane, Phys. Rev. D 68 (2003) 084006 [hep-th/0306281] [INSPIRE].

    Article  ADS  Google Scholar 

  54. A. Costantino, S. Fichet and F. Tanedo, Dark Radiation from a Cold Conformal Sector, work in progress.

  55. S. B. Giddings, E. Katz and L. Randall, Linearized gravity in brane backgrounds, JHEP 03 (2000) 023 [hep-th/0002091] [INSPIRE].

    MathSciNet  MATH  Article  ADS  Google Scholar 

  56. J. G. Lee, E. G. Adelberger, T. S. Cook, S. M. Fleischer and B. R. Heckel, New Test of the Gravitational 1/r2 Law at Separations down to 52 μm, Phys. Rev. Lett. 124 (2020) 101101 [arXiv:2002.11761] [INSPIRE].

    Article  ADS  Google Scholar 

  57. P. Brax, S. Fichet and G. Pignol, Bounding Quantum Dark Forces, Phys. Rev. D 97 (2018) 115034 [arXiv:1710.00850] [INSPIRE].

    Article  ADS  Google Scholar 

  58. F. Kahlhoefer, K. Schmidt-Hoberg and S. Wild, Dark matter self-interactions from a general spin-0 mediator, JCAP 08 (2017) 003 [arXiv:1704.02149] [INSPIRE].

    Article  ADS  Google Scholar 

  59. R. Zwicky, A brief Introduction to Dispersion Relations and Analyticity, in proceedings of the Quantum Field Theory at the Limits: from Strong Fields to Heavy Quarks, Dubna, Russian Federation, 18–30 July 2016, Verlag Deutsches Elektronen-Synchrotron, Hamburg Germany (2017), pp. 93–120 [https://doi.org/10.3204/DESY-PROC-2016-04/Zwicky] [arXiv:1610.06090] [INSPIRE].

  60. S. Fichet, Opacity and effective field theory in anti-de Sitter backgrounds, Phys. Rev. D 100 (2019) 095002 [arXiv:1905.05779] [INSPIRE].

    MathSciNet  Article  ADS  Google Scholar 

  61. A. Costantino and S. Fichet, Opacity from Loops in AdS, JHEP 02 (2021) 089 [arXiv:2011.06603] [INSPIRE].

    MathSciNet  MATH  Article  ADS  Google Scholar 

  62. M. Kaplinghat, S. Tulin and H.-B. Yu, Dark Matter Halos as Particle Colliders: Unified Solution to Small-Scale Structure Puzzles from Dwarfs to Clusters, Phys. Rev. Lett. 116 (2016) 041302 [arXiv:1508.03339] [INSPIRE].

    Article  ADS  Google Scholar 

  63. R. Dave, D. N. Spergel, P. J. Steinhardt and B. D. Wandelt, Halo properties in cosmological simulations of selfinteracting cold dark matter, Astrophys. J. 547 (2001) 574 [astro-ph/0006218] [INSPIRE].

    Article  ADS  Google Scholar 

  64. J. J. Sakurai, Modern quantum mechanics, revised edition, Addison-Wesley, Reading MA U.S.A. (1994).

    Google Scholar 

  65. D. Chiron and B. Marcos, Classical particle scattering for power-law two-body potentials, arXiv:1601.00064 [INSPIRE].

  66. S. A. Khrapak, A. V. Ivlev, G. E. Morfill and S. K. Zhdanov, Scattering in the Attractive Yukawa Potential in the Limit of Strong Interaction, Phys. Rev. Lett. 90 (2003) 225002 [INSPIRE].

    Article  ADS  Google Scholar 

  67. B. Colquhoun, S. Heeba, F. Kahlhoefer, L. Sagunski and S. Tulin, Semiclassical regime for dark matter self-interactions, Phys. Rev. D 103 (2021) 035006 [arXiv:2011.04679] [INSPIRE].

    MathSciNet  Article  ADS  Google Scholar 

  68. R. H. Cyburt, B. D. Fields, K. A. Olive and T.-H. Yeh, Big Bang Nucleosynthesis: Present status, Rev. Mod. Phys. 88 (2016) 015004 [arXiv:1505.01076] [INSPIRE].

    Article  ADS  Google Scholar 

  69. J. Hisano, S. Matsumoto, M. M. Nojiri and O. Saito, Non-perturbative effect on dark matter annihilation and gamma ray signature from galactic center, Phys. Rev. D 71 (2005) 063528 [hep-ph/0412403] [INSPIRE].

    Article  ADS  Google Scholar 

  70. 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].

    Article  ADS  Google Scholar 

  71. M. Lattanzi and J. I. Silk, Can the WIMP annihilation boost factor be boosted by the Sommerfeld enhancement?, Phys. Rev. D 79 (2009) 083523 [arXiv:0812.0360] [INSPIRE].

    Article  ADS  Google Scholar 

  72. R. Iengo, Sommerfeld enhancement: General results from field theory diagrams, JHEP 05 (2009) 024 [arXiv:0902.0688] [INSPIRE].

    MathSciNet  Article  ADS  Google Scholar 

  73. R. Iengo, Sommerfeld enhancement for a Yukawa potential, arXiv:0903.0317 [INSPIRE].

  74. S. Cassel, Sommerfeld factor for arbitrary partial wave processes, J. Phys. G 37 (2010) 105009 [arXiv:0903.5307] [INSPIRE].

    Article  ADS  Google Scholar 

  75. S. Hannestad and T. Tram, Sommerfeld Enhancement of DM Annihilation: Resonance Structure, Freeze-Out and CMB Spectral Bound, JCAP 01 (2011) 016 [arXiv:1008.1511] [INSPIRE].

    Article  ADS  Google Scholar 

  76. B. Bellazzini, M. Cliche and P. Tanedo, Effective theory of self-interacting dark matter, Phys. Rev. D 88 (2013) 083506 [arXiv:1307.1129] [INSPIRE].

    Article  ADS  Google Scholar 

  77. I. R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].

    MathSciNet  MATH  Article  ADS  Google Scholar 

  78. F. Gross, Relativistic Quantum Mechanics and Field Theory, Wiley (1999).

  79. 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].

    MATH  Article  ADS  Google Scholar 

  80. L. D. Landau and E. M. Lifshitz, Mechanics. Course of Theoretical Physics. Volume 1, third edition, Butterworth-Heinemann (1976).

  81. M. R. Buckley and P. J. Fox, Dark Matter Self-Interactions and Light Force Carriers, Phys. Rev. D 81 (2010) 083522 [arXiv:0911.3898] [INSPIRE].

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics & Astronomy, University of California, 900 University Avenue, Riverside, CA, 92521, USA

    Ian Chaffey & Philip Tanedo

  2. ICTP SAIFR & IFT-UNESP, R. Dr. Bento Teobaldo Ferraz, São Paulo, 271, Brazil

    Sylvain Fichet

Authors
  1. Ian Chaffey
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sylvain Fichet
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Philip Tanedo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ian Chaffey.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

ArXiv ePrint: 2102.05674

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.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chaffey, I., Fichet, S. & Tanedo, P. Continuum-mediated self-interacting dark matter. J. High Energ. Phys. 2021, 8 (2021). https://doi.org/10.1007/JHEP06(2021)008

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP06(2021)008

Keywords

  • Phenomenology of Field Theories in Higher Dimensions
  • Strings and branes phenomenology