Migdal effect in dark matter direct detection experiments

  • Masahiro Ibe
  • Wakutaka Nakano
  • Yutaro Shoji
  • Kazumine Suzuki
Open Access
Regular Article - Experimental Physics
  • 21 Downloads

Abstract

The elastic scattering of an atomic nucleus plays a central role in dark matter direct detection experiments. In those experiments, it is usually assumed that the atomic electrons around the nucleus of the target material immediately follow the motion of the recoil nucleus. In reality, however, it takes some time for the electrons to catch up, which results in ionization and excitation of the atoms. In previous studies, those effects are taken into account by using the so-called Migdal’s approach, in which the final state ionization/excitation are treated separately from the nuclear recoil. In this paper, we reformulate the Migdal’s approach so that the “atomic recoil” cross section is obtained coherently, where we make transparent the energy-momentum conservation and the probability conservation. We show that the final state ionization/excitation can enhance the detectability of rather light dark matter in the GeV mass range via the nuclear scattering. We also discuss the coherent neutrino-nucleus scattering, where the same effects are expected.

Keywords

Beyond Standard Model Dark matter Dark Matter and Double Beta Decay (experiments) Electroweak interaction 

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]
    G. Bertone, D. Hooper and J. Silk, Particle dark matter: Evidence, candidates and constraints, Phys. Rept. 405 (2005) 279 [hep-ph/0404175] [INSPIRE].
  2. [2]
    H. Murayama, Physics Beyond the Standard Model and Dark Matter, in Les Houches Summer School — Session 86: Particle Physics and Cosmology: The Fabric of Spacetime, Les Houches, France, July 31-August 25, 2006 (2007), arXiv:0704.2276 [INSPIRE].
  3. [3]
    J.L. Feng, Dark Matter Candidates from Particle Physics and Methods of Detection, Ann. Rev. Astron. Astrophys. 48 (2010) 495 [arXiv:1003.0904] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    B.W. Lee and S. Weinberg, Cosmological Lower Bound on Heavy Neutrino Masses, Phys. Rev. Lett. 39 (1977) 165 [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    G. Jungman, M. Kamionkowski and K. Griest, Supersymmetric dark matter, Phys. Rept. 267 (1996) 195 [hep-ph/9506380] [INSPIRE].
  6. [6]
    M.W. Goodman and E. Witten, Detectability of Certain Dark Matter Candidates, Phys. Rev. D 31 (1985) 3059 [INSPIRE].
  7. [7]
    F. Nesti and P. Salucci, The Dark Matter halo of the Milky Way, AD 2013, JCAP 07 (2013) 016 [arXiv:1304.5127] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    J.D. Lewin and P.F. Smith, Review of mathematics, numerical factors and corrections for dark matter experiments based on elastic nuclear recoil, Astropart. Phys. 6 (1996) 87 [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    R.J. Gaitskell, Direct detection of dark matter, Ann. Rev. Nucl. Part. Sci. 54 (2004) 315.ADSCrossRefGoogle Scholar
  10. [10]
    T. Marrodán Undagoitia and L. Rauch, Dark matter direct-detection experiments, J. Phys. G 43 (2016) 013001 [arXiv:1509.08767] [INSPIRE].
  11. [11]
    LUX collaboration, D.S. Akerib et al., Results from a search for dark matter in the complete LUX exposure, Phys. Rev. Lett. 118 (2017) 021303 [arXiv:1608.07648] [INSPIRE].
  12. [12]
    PandaX-II collaboration, A. Tan et al., Dark Matter Results from First 98.7 Days of Data from the PandaX-II Experiment, Phys. Rev. Lett. 117 (2016) 121303 [arXiv:1607.07400] [INSPIRE].
  13. [13]
    XENON collaboration, E. Aprile et al., First Dark Matter Search Results from the XENON1T Experiment, Phys. Rev. Lett. 119 (2017) 181301 [arXiv:1705.06655] [INSPIRE].
  14. [14]
    J.D. Vergados and H. Ejiri, The role of ionization electrons in direct neutralino detection, Phys. Lett. B 606 (2005) 313 [hep-ph/0401151] [INSPIRE].
  15. [15]
    C.C. Moustakidis, J.D. Vergados and H. Ejiri, Direct dark matter detection by observing electrons produced in neutralino-nucleus collisions, Nucl. Phys. B 727 (2005) 406 [hep-ph/0507123] [INSPIRE].
  16. [16]
    H. Ejiri, C.C. Moustakidis and J.D. Vergados, Dark matter search by exclusive studies of X-rays following WIMPs nuclear interactions, Phys. Lett. B 639 (2006) 218 [hep-ph/0510042] [INSPIRE].
  17. [17]
    J.D. Vergados, H. Ejiri and K.G. Savvidy, Theoretical direct WIMP detection rates for inelastic scattering to excited states, Nucl. Phys. B 877 (2013) 36 [arXiv:1307.4713] [INSPIRE].
  18. [18]
    R. Bernabei et al., On electromagnetic contributions in WIMP quests, Int. J. Mod. Phys. A 22 (2007) 3155 [arXiv:0706.1421] [INSPIRE].
  19. [19]
    B.M. Roberts, V.V. Flambaum and G.F. Gribakin, Ionization of atoms by slow heavy particles, including dark matter, Phys. Rev. Lett. 116 (2016) 023201 [arXiv:1509.09044] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    B.M. Roberts, V.A. Dzuba, V.V. Flambaum, M. Pospelov and Y.V. Stadnik, Dark matter scattering on electrons: Accurate calculations of atomic excitations and implications for the DAMA signal, Phys. Rev. D 93 (2016) 115037 [arXiv:1604.04559] [INSPIRE].
  21. [21]
    A.B. Migdal, Ionization of atoms accompanying α- and β-decay, J. Phys. USSR 4 (1941) 449.Google Scholar
  22. [22]
    G. Baur, F. Rosel and D. Trautmann, Ionisation induced by neutrons, J. Phys. B 16 (1983) L419.Google Scholar
  23. [23]
    L.D. Landau and E.M. Lifshits, Quantum Mechanics, in Course of Theoretical Physics, Vol. 3, Butterworth-Heinemann, Oxford (1991).Google Scholar
  24. [24]
    J.R. Ellis, R.A. Flores and J.D. Lewin, Rates for Inelastic Nuclear Excitation by Dark Matter Particles, Phys. Lett. B 212 (1988) 375 [INSPIRE].
  25. [25]
    R. Bernabei et al., Improved limits on WIMP- 129 Xe inelastic scattering, New J. Phys. 2 (2000) 15.Google Scholar
  26. [26]
    C. McCabe, The Astrophysical Uncertainties Of Dark Matter Direct Detection Experiments, Phys. Rev. D 82 (2010) 023530 [arXiv:1005.0579] [INSPIRE].
  27. [27]
    A.M. Green, Astrophysical uncertainties on direct detection experiments, Mod. Phys. Lett. A 27 (2012) 1230004 [arXiv:1112.0524] [INSPIRE].
  28. [28]
    W.R. Johnson, Atomic Structure Theory: Lectures on Atomic Physics, Springer (2007).Google Scholar
  29. [29]
    W. Bambynek et al., X-Ray Fluorescence Yields, Auger and Coster-Kronig Transition Probabilities, Rev. Mod. Phys. 44 (1972) 716 [Erratum ibid. 46 (1974) 853] [INSPIRE].
  30. [30]
    J. Campbell and T. PAPP, Widths of the atomic K-N7 levels, Atom. Data Nucl. Data tables 77 (2001) 1.Google Scholar
  31. [31]
    S.-K. Son and R. Santra, Monte Carlo calculation of ion, electron, and photon spectra of xenon atoms in x-ray free-electron laser pulses, Phys. Rev. A 85 (2012) 063415 [arXiv:1206.1875].
  32. [32]
    M. Gu, The flexible atomic code, Canad. J. Phys. 86 (2008) 675.ADSCrossRefGoogle Scholar
  33. [33]
    A. Thompson et al., X-ray Data Booklet, Lawrence Berkeley Laboratory, (2001).Google Scholar
  34. [34]
    R.S. Mulliken, Potential Curves of Diatomic Rare-Gas Molecules and Their Ions, with Particular Reference to Xe 2, J. Chem. Phys. 52 (1970) 5170.Google Scholar
  35. [35]
    A. Hitachi, T. Doke and A. Mozumder, Luminescence quenching in liquid argon under charged-particle impact: Relative scintillation yield at different linear energy transfers, Phys. Rev. B 46 (1992) 11463 [INSPIRE].
  36. [36]
    E. Aprile and T. Doke, Liquid Xenon Detectors for Particle Physics and Astrophysics, Rev. Mod. Phys. 82 (2010) 2053 [arXiv:0910.4956] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    C.E. Dahl, The physics of background discrimination in liquid Xenon, and first results from Xenon10 in the hunt for WIMP dark matter, Ph.D. Thesis, Princeton University (2009) [INSPIRE].
  38. [38]
    J. Lindhard, V Nielsen, M. Scharff and P.V. Thomsen, Integral equations governing radiation effects, Mat. Fys. Medd. Dan. Vid. Selsk. 33 (1963).Google Scholar
  39. [39]
    A. Hitachi, Properties of liquid xenon scintillation for dark matter searches, Astropart. Phys. 24 (2005) 247 [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    P. Sorensen and C.E. Dahl, Nuclear recoil energy scale in liquid xenon with application to the direct detection of dark matter, Phys. Rev. D 83 (2011) 063501 [arXiv:1101.6080] [INSPIRE].
  41. [41]
    P. Sorensen, Atomic limits in the search for galactic dark matter, Phys. Rev. D 91 (2015) 083509 [arXiv:1412.3028] [INSPIRE].
  42. [42]
    P. Sorensen et al., Lowering the low-energy threshold of xenon detectors, PoS(IDM2010)017 [arXiv:1011.6439] [INSPIRE].
  43. [43]
    M. Horn et al., Nuclear recoil scintillation and ionisation yields in liquid xenon from ZEPLIN-III data, Phys. Lett. B 705 (2011) 471 [arXiv:1106.0694] [INSPIRE].
  44. [44]
    XENON100 collaboration, E. Aprile et al., Response of the XENON100 Dark Matter Detector to Nuclear Recoils, Phys. Rev. D 88 (2013) 012006 [arXiv:1304.1427] [INSPIRE].
  45. [45]
    LUX collaboration, D.S. Akerib et al., Low-energy (0.7-74 keV ) nuclear recoil calibration of the LUX dark matter experiment using D-D neutron scattering kinematics, arXiv:1608.05381 [INSPIRE].
  46. [46]
    E. Aprile et al., Scintillation response of liquid xenon to low energy nuclear recoils, Phys. Rev. D 72 (2005) 072006 [astro-ph/0503621] [INSPIRE].
  47. [47]
    A. Manzur, A. Curioni, L. Kastens, D.N. McKinsey, K. Ni and T. Wongjirad, Scintillation efficiency and ionization yield of liquid xenon for mono-energetic nuclear recoils down to 4 keV, Phys. Rev. C 81 (2010) 025808 [arXiv:0909.1063] [INSPIRE].
  48. [48]
    K. Abe et al., XMASS detector, Nucl. Instrum. Meth. A 716 (2013) 78 [arXiv:1301.2815] [INSPIRE].
  49. [49]
    D. Tucker-Smith and N. Weiner, Inelastic dark matter, Phys. Rev. D 64 (2001) 043502 [hep-ph/0101138] [INSPIRE].
  50. [50]
    R. Essig, A. Manalaysay, J. Mardon, P. Sorensen and T. Volansky, First Direct Detection Limits on sub-GeV Dark Matter from XENON10, Phys. Rev. Lett. 109 (2012) 021301 [arXiv:1206.2644] [INSPIRE].
  51. [51]
    R. Essig, T. Volansky and T.-T. Yu, New Constraints and Prospects for sub-GeV Dark Matter Scattering off Electrons in Xenon, Phys. Rev. D 96 (2017) 043017 [arXiv:1703.00910] [INSPIRE].
  52. [52]
    T. Takahashi et al., Average energy expended per ion pair in liquid xenon, Phys. Rev. A 12 (1975) 1771 [INSPIRE].
  53. [53]
    C. Kouvaris and J. Pradler, Probing sub-GeV Dark Matter with conventional detectors, Phys. Rev. Lett. 118 (2017) 031803 [arXiv:1607.01789] [INSPIRE].
  54. [54]
    C. McCabe, New constraints and discovery potential of sub-GeV dark matter with xenon detectors, Phys. Rev. D 96 (2017) 043010 [arXiv:1702.04730] [INSPIRE].
  55. [55]
    D.Z. Freedman, Coherent neutrino nucleus scattering as a probe of the weak neutral current, Phys. Rev. D 9 (1974) 1389 [INSPIRE].
  56. [56]
    D.Z. Freedman, D.N. Schramm and D.L. Tubbs, The Weak Neutral Current and its Effects in Stellar Collapse, Ann. Rev. Nucl. Part. Sci. 27 (1977) 167.ADSCrossRefGoogle Scholar
  57. [57]
    A. Drukier and L. Stodolsky, Principles and Applications of a Neutral Current Detector for Neutrino Physics and Astronomy, Phys. Rev. D 30 (1984) 2295 [INSPIRE].
  58. [58]
    A. Serenelli, Alive and well: a short review about standard solar models, Eur. Phys. J. A 52 (2016) 78 [arXiv:1601.07179] [INSPIRE].
  59. [59]
    R. Essig, J. Mardon and T. Volansky, Direct Detection of Sub-GeV Dark Matter, Phys. Rev. D 85 (2012) 076007 [arXiv:1108.5383] [INSPIRE].
  60. [60]
    P.W. Graham, D.E. Kaplan, S. Rajendran and M.T. Walters, Semiconductor Probes of Light Dark Matter, Phys. Dark Univ. 1 (2012) 32 [arXiv:1203.2531] [INSPIRE].CrossRefGoogle Scholar
  61. [61]
    Y. Hochberg, Y. Zhao and K.M. Zurek, Superconducting Detectors for Superlight Dark Matter, Phys. Rev. Lett. 116 (2016) 011301 [arXiv:1504.07237] [INSPIRE].
  62. [62]
    S.K. Lee, M. Lisanti, S. Mishra-Sharma and B.R. Safdi, Modulation Effects in Dark Matter-Electron Scattering Experiments, Phys. Rev. D 92 (2015) 083517 [arXiv:1508.07361] [INSPIRE].
  63. [63]
    R. Essig, M. Fernandez-Serra, J. Mardon, A. Soto, T. Volansky and T.-T. Yu, Direct Detection of sub-GeV Dark Matter with Semiconductor Targets, JHEP 05 (2016) 046 [arXiv:1509.01598] [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    Y. Hochberg, M. Pyle, Y. Zhao and K.M. Zurek, Detecting Superlight Dark Matter with Fermi-Degenerate Materials, JHEP 08 (2016) 057 [arXiv:1512.04533] [INSPIRE].ADSCrossRefGoogle Scholar
  65. [65]
    Y. Hochberg, Y. Kahn, M. Lisanti, C.G. Tully and K.M. Zurek, Directional detection of dark matter with two-dimensional targets, Phys. Lett. B 772 (2017) 239 [arXiv:1606.08849] [INSPIRE].
  66. [66]
    F. Kadribasic, N. Mirabolfathi, K. Nordlund, E. Holmström and F. Djurabekova, Directional Sensitivity In Light-Mass Dark Matter Searches With Single-Electron Resolution Ionization Detectors, arXiv:1703.05371 [INSPIRE].
  67. [67]
    G. Cavoto, F. Luchetta and A.D. Polosa, Sub-GeV Dark Matter Detection with Electron Recoils in Carbon Nanotubes, Phys. Lett. B 776 (2018) 338 [arXiv:1706.02487] [INSPIRE].
  68. [68]
    W. Kohn and L.J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, Phys. Rev. 140 (1965) A1133 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  69. [69]
    D.H. Sampson, H.L. Zhang, A.K. Mohanty and R.E.H. Clark, A Dirac-Fock-Slater approach to atomic structure for highly charged ions, Phys. Rev. A 40 (1989) 604.Google Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Masahiro Ibe
    • 1
    • 2
  • Wakutaka Nakano
    • 1
  • Yutaro Shoji
    • 1
  • Kazumine Suzuki
    • 1
  1. 1.ICRR, The University of TokyoKashiwaJapan
  2. 2.Kavli IPMU (WPI), UTIAS, The University of TokyoKashiwaJapan

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