Classification of effective operators for interactions between the Standard Model and dark matter

Open Access
Regular Article - Theoretical Physics

Abstract

We construct a basis for effective operators responsible for interactions between the Standard Model and a dark sector composed of particles with spin ≤ 1. Redundant operators are eliminated using dim-4 equations of motion. We consider simple scenarios where the dark matter components are stabilized against decay by ℤ2 symmetries. We determine operators which are loop-generated within an underlying theory and those that are potentially tree-level generated.

Keywords

Beyond Standard Model Cosmology of Theories beyond the SM Effective field theories 

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]
    S. Bhattacharya, A. Drozd, B. Grzadkowski and J. Wudka, Two-component dark matter, JHEP 10 (2013) 158 [arXiv:1309.2986] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    S. Bhattacharya, A. Drozd, B. Grzadkowski and J. Wudka, Constraints on two-component dark matter, Acta Phys. Polon. B 44 (2013) 2373 [arXiv:1310.7901] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    H.D. Politzer, Power corrections at short distances, Nucl. Phys. B 172 (1980) 349 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    H. Kluberg-Stern and J.B. Zuber, Renormalization of non-Abelian gauge theories in a background-field gauge. II. Gauge-invariant operators, Phys. Rev. D 12 (1975) 3159 [INSPIRE].ADSGoogle Scholar
  5. [5]
    C. Grosse-Knetter, Effective Lagrangians with higher derivatives and equations of motion, Phys. Rev. D 49 (1994) 6709 [hep-ph/9306321] [INSPIRE].ADSMathSciNetGoogle Scholar
  6. [6]
    C. Arzt, Reduced effective Lagrangians, Phys. Lett. B 342 (1995) 189 [hep-ph/9304230] [INSPIRE].ADSMathSciNetGoogle Scholar
  7. [7]
    H. Simma, Equations of motion for effective Lagrangians and Penguins in rare B decays, Z. Phys. C 61 (1994) 67 [hep-ph/9307274] [INSPIRE].ADSGoogle Scholar
  8. [8]
    J. Wudka, Electroweak effective Lagrangians, Int. J. Mod. Phys. A 9 (1994) 2301 [hep-ph/9406205] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    J. Hisano, D. Kobayashi, N. Mori and E. Senaha, Effective interaction of electroweak-interacting dark matter with Higgs boson and its phenomenology, Phys. Lett. B 742 (2015) 80 [arXiv:1410.3569] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    R.J. Hill and M.P. Solon, Standard model anatomy of WIMP dark matter direct detection. II. QCD analysis and hadronic matrix elements, Phys. Rev. D 91 (2015) 043505 [arXiv:1409.8290] [INSPIRE].ADSGoogle Scholar
  11. [11]
    S. Matsumoto, S. Mukhopadhyay and Y.-L.S. Tsai, Singlet Majorana fermion dark matter: a comprehensive analysis in effective field theory, JHEP 10 (2014) 155 [arXiv:1407.1859] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    M.B. Krauss, S. Morisi, W. Porod and W. Winter, Higher dimensional effective operators for direct dark matter detection, JHEP 02 (2014) 056 [arXiv:1312.0009] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    N.F. Bell, Y. Cai and A.D. Medina, Co-annihilating dark matter: effective operator analysis and collider phenomenology, Phys. Rev. D 89 (2014) 115001 [arXiv:1311.6169] [INSPIRE].ADSGoogle Scholar
  14. [14]
    E. Dudas, L. Heurtier, Y. Mambrini and B. Zaldivar, Extra U(1), effective operators, anomalies and dark matter, JHEP 11 (2013) 083 [arXiv:1307.0005] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    M.R. Buckley, Using effective operators to understand CoGeNT and CDMS-Si signals, Phys. Rev. D 88 (2013) 055028 [arXiv:1308.4146] [INSPIRE].ADSGoogle Scholar
  16. [16]
    A. De Simone, A. Monin, A. Thamm and A. Urbano, On the effective operators for dark matter annihilations, JCAP 02 (2013) 039 [arXiv:1301.1486] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  17. [17]
    J.-Y. Chen, E.W. Kolb and L.-T. Wang, Dark matter coupling to electroweak gauge and Higgs bosons: an effective field theory approach, Phys. Dark Univ. 2 (2013) 200 [arXiv:1305.0021] [INSPIRE].CrossRefGoogle Scholar
  18. [18]
    R. Ding, Y. Liao, J.-Y. Liu and K. Wang, Comprehensive constraints on a spin-3/2 singlet particle as a dark matter candidate, JCAP 05 (2013) 028 [arXiv:1302.4034] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    A. Greljo, J. Julio, J.F. Kamenik, C. Smith and J. Zupan, Constraining Higgs mediated dark matter interactions, JHEP 11 (2013) 190 [arXiv:1309.3561] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    Y.J. Chae and M. Perelstein, Dark matter search at a linear collider: effective operator approach, JHEP 05 (2013) 138 [arXiv:1211.4008] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    J.-M. Zheng et al., Constraining the interaction strength between dark matter and visible matter: I. Fermionic dark matter, Nucl. Phys. B 854 (2012) 350 [arXiv:1012.2022] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  22. [22]
    Z.-H. Yu et al., Constraining the interaction strength between dark matter and visible matter: II. Scalar, vector and spin-3/2 dark matter, Nucl. Phys. B 860 (2012) 115 [arXiv:1112.6052] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  23. [23]
    R. Ding and Y. Liao, Spin 3/2 particle as a dark matter candidate: an effective field theory approach, JHEP 04 (2012) 054 [arXiv:1201.0506] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    K. Cheung, P.-Y. Tseng, Y.-L.S. Tsai and T.-C. Yuan, Global constraints on effective dark matter interactions: relic density, direct detection, indirect detection and collider, JCAP 05 (2012) 001 [arXiv:1201.3402] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    Q.-H. Cao, C.-R. Chen, C.S. Li and H. Zhang, Effective dark matter model: relic density, CDMS II, Fermi LAT and LHC, JHEP 08 (2011) 018 [arXiv:0912.4511] [INSPIRE].Google Scholar
  26. [26]
    J. Goodman et al., Constraints on light Majorana dark matter from colliders, Phys. Lett. B 695 (2011) 185 [arXiv:1005.1286] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    M. Beltrán, D. Hooper, E.W. Kolb, Z.A.C. Krusberg and T.M.P. Tait, Maverick dark matter at colliders, JHEP 09 (2010) 037 [arXiv:1002.4137] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    J. Goodman et al., Constraints on dark matter from colliders, Phys. Rev. D 82 (2010) 116010 [arXiv:1008.1783] [INSPIRE].ADSGoogle Scholar
  29. [29]
    M. Duch, Effective operators for dark matter interactions, MSc Thesis, University of Warsaw, Warsaw Poland (2014) [arXiv:1410.4427] [INSPIRE].
  30. [30]
    W. Buchmüller and D. Wyler, Effective Lagrangian analysis of new interactions and flavor conservation, Nucl. Phys. B 268 (1986) 621 [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-six terms in the standard model Lagrangian, JHEP 10 (2010) 085 [arXiv:1008.4884] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  32. [32]
    M.B. Einhorn and J. Wudka, The bases of effective field theories, Nucl. Phys. B 876 (2013) 556 [arXiv:1307.0478] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  33. [33]
    B. Grzadkowski and J. Wudka, Pragmatic approach to the little hierarchy problem: the case for dark matter and neutrino physics, Phys. Rev. Lett. 103 (2009) 091802 [arXiv:0902.0628] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    B. Grzadkowski and J. Wudka, Naive solution of the little hierarchy problem and its physical consequences, Acta Phys. Polon. B 40 (2009) 3007 [arXiv:0910.4829] [INSPIRE].ADSGoogle Scholar
  35. [35]
    O. Lebedev, H.M. Lee and Y. Mambrini, Vector Higgs-portal dark matter and the invisible Higgs, Phys. Lett. B 707 (2012) 570 [arXiv:1111.4482] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    S. Kanemura, S. Matsumoto, T. Nabeshima and N. Okada, Can WIMP dark matter overcome the nightmare scenario?, Phys. Rev. D 82 (2010) 055026 [arXiv:1005.5651] [INSPIRE].ADSGoogle Scholar
  37. [37]
    H. Ruegg and M. Ruiz-Altaba, The Stueckelberg field, Int. J. Mod. Phys. A 19 (2004) 3265 [hep-th/0304245] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  38. [38]
    H. van Hees, The renormalizability for massive Abelian gauge field theories revisited, hep-th/0305076 [INSPIRE].
  39. [39]
    J.F. Kamenik and C. Smith, FCNC portals to the dark sector, JHEP 03 (2012) 090 [arXiv:1111.6402] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  40. [40]
    J.F. Kamenik and C. Smith, Could a light Higgs boson illuminate the dark sector?, Phys. Rev. D 85 (2012) 093017 [arXiv:1201.4814] [INSPIRE].ADSGoogle Scholar
  41. [41]
    C. Arzt, M.B. Einhorn and J. Wudka, Patterns of deviation from the standard model, Nucl. Phys. B 433 (1995) 41 [hep-ph/9405214] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Faculty of PhysicsUniversity of WarsawWarsawPoland
  2. 2.Department of Physics and AstronomyUC RiversideRiversideU.S.A.

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