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Journal of High Energy Physics

, 2015:23 | Cite as

Yukawa bound states of a large number of fermions

  • Mark B. Wise
  • Yue ZhangEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We consider the bound state problem for a field theory that contains a Dirac fermion χ that Yukawa couples to a (light) scalar field ϕ. We are interested in bound states with a large number N of χ particles. A Fermi gas model is used to numerically determine the dependence of the radius R of these bound states on N and also the dependence of the binding energy on N. Since scalar interactions with relativistic χ’s are suppressed two regimes emerge. For modest values of N the state is composed of non-relativistic χ particles. In this regime as N increases R decreases. Eventually the core region becomes relativistic and the size of the state starts to increase as N increases. As a result, for fixed Yukawa coupling and χ mass, there is a minimum sized state that occurs roughly at the value of N where the core region first becomes relativistic. We also compute an elastic scattering form factor that can be relevant for direct detection if the dark matter is composed of such χ particles.

Keywords

Beyond Standard Model Cosmology of Theories beyond the SM Statistical Methods 

Notes

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.

References

  1. [1]
    A. Djouadi, O. Lebedev, Y. Mambrini and J. Quevillon, Implications of LHC searches for Higgs-portal dark matter, Phys. Lett. B 709 (2012) 65 [arXiv:1112.3299] [INSPIRE].CrossRefADSGoogle Scholar
  2. [2]
    S. Baek, P. Ko and W.-I. Park, Search for the Higgs portal to a singlet fermionic dark matter at the LHC, JHEP 02 (2012) 047 [arXiv:1112.1847] [INSPIRE].CrossRefADSGoogle Scholar
  3. [3]
    I. Low, P. Schwaller, G. Shaughnessy and C.E.M. Wagner, The dark side of the Higgs boson, Phys. Rev. D 85 (2012) 015009 [arXiv:1110.4405] [INSPIRE].ADSGoogle Scholar
  4. [4]
    D.N. Spergel and P.J. Steinhardt, Observational evidence for selfinteracting cold dark matter, Phys. Rev. Lett. 84 (2000) 3760 [astro-ph/9909386] [INSPIRE].CrossRefADSGoogle Scholar
  5. [5]
    M. Rocha et al., Cosmological simulations with self-interacting dark matter I: constant density cores and substructure, Mon. Not. Roy. Astron. Soc. 430 (2013) 81 [arXiv:1208.3025] [INSPIRE].CrossRefADSGoogle Scholar
  6. [6]
    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].ADSGoogle Scholar
  7. [7]
    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].ADSGoogle Scholar
  8. [8]
    K.K. Boddy, J.L. Feng, M. Kaplinghat and T.M.P. Tait, Self-interacting dark matter from a non-Abelian hidden sector, Phys. Rev. D 89 (2014) 115017 [arXiv:1402.3629] [INSPIRE].ADSGoogle Scholar
  9. [9]
    F.J. Rogers, H.C. Graboske Jr. and D.J. Harwood, Bound eigenstates of the static screened Coulomb potential, Phys. Rev. A 1 (1970) 1577.CrossRefADSGoogle Scholar
  10. [10]
    M.B. Wise and Y. Zhang, Stable bound states of asymmetric dark matter, Phys. Rev. D 90 (2014) 055030 [arXiv:1407.4121] [INSPIRE].ADSGoogle Scholar
  11. [11]
    S.L. Shapiro and S.A. Teukolsky, Black holes, white dwarfs and neutron stars: the physics of compact objects, Wiley, U.S.A. (2008).Google Scholar
  12. [12]
    G. Krnjaic and K. Sigurdson, Big bang darkleosynthesis, arXiv:1406.1171 [INSPIRE].
  13. [13]
    W. Detmold, M. McCullough and A. Pochinsky, Dark nuclei I: cosmology and indirect detection, Phys. Rev. D 90 (2014) 115013 [arXiv:1406.2276] [INSPIRE].ADSGoogle Scholar

Copyright information

© The Author(s) 2015

Open AccessThis 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.

Authors and Affiliations

  1. 1.Walter Burke Institute for Theoretical PhysicsCalifornia Institute of TechnologyPasadenaU.S.A.

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