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Multi-channel direct detection of light dark matter: theoretical framework

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We present a unified theoretical framework for computing spin-independent direct detection rates via various channels relevant for sub-GeV dark matter — nuclear re- coils, electron transitions and single phonon excitations. Despite the very different physics involved, in each case the rate factorizes into the particle-level matrix element squared, and an integral over a target material- and channel-specific dynamic structure factor. We show how the dynamic structure factor can be derived in all three cases following the same procedure, and extend previous results in the literature in several aspects. For electron transitions, we incorporate directional dependence and point out anisotropic target materials with strong daily modulation in the scattering rate. For single phonon excitations, we present a new derivation of the rate formula from first principles for generic spin-independent couplings, and include the first calculation of phonon excitation through electron couplings. We also discuss the interplay between single phonon excitations and nuclear recoils, and clarify the role of Umklapp processes, which can dominate the single phonon production rate for dark matter heavier than an MeV. Our results highlight the complementarity between various search channels in probing different kinematic regimes of dark matter scattering, and provide a common reference to connect dark matter theories with ongoing and future direct detection experiments.


  1. J. Amaré et al., First Results on Dark Matter Annual Modulation from the ANAIS-112 Experiment, Phys. Rev. Lett.123 (2019) 031301 [arXiv:1903.03973] [INSPIRE].

  2. C. Cozzini et al., Results of CRESST phase I, in Low temperature detectors. Proceedings of 9th International Workshop, LTD-9, Madison U.S.A. (2001) [AIP Conf. Proc.605 (2002) 481] [INSPIRE].

  3. CRESST collaboration, First results on low-mass dark matter from the CRESST-III experiment, in 15th International Conference on Topics in Astroparticle and Underground Physics (TAUP 2017), Sudbury (Canada) (2017) [J. Phys. Conf. Ser.1342 (2020) 012076] [arXiv:1711.07692] [INSPIRE].

  4. CRESST collaboration, Results on light dark matter particles with a low-threshold CRESST-II detector, Eur. Phys. J.C 76 (2016) 25 [arXiv:1509.01515] [INSPIRE].

  5. S. Baum, K. Freese and C. Kelso, Dark Matter implications of DAMA/LIBRA-phase2 results, Phys. Lett.B 789 (2019) 262 [arXiv:1804.01231] [INSPIRE].

    ADS  Article  Google Scholar 

  6. DAMIC collaboration, The DAMIC dark matter experiment, PoS(ICRC2015)1221 [arXiv:1510.02126] [INSPIRE].

  7. DAMIC collaboration, Constraints on Light Dark Matter Particles Interacting with Electrons from DAMIC at SNOLAB, Phys. Rev. Lett.123 (2019) 181802 [arXiv:1907.12628] [INSPIRE].

  8. DarkSide collaboration, Low-Mass Dark Matter Search with the DarkSide-50 Experiment, Phys. Rev. Lett.121 (2018) 081307 [arXiv:1802.06994] [INSPIRE].

  9. DM-Ice collaboration, Results from the DM-Ice17 Dark Matter Experiment at the South Pole, PoS(ICHEP2016)1223 [arXiv:1612.07426] [INSPIRE].

  10. KIMS collaboration, Status of the KIMS-NaI experiment, in Proceedings of Meeting of the APS Division of Particles and Fields (DPF 2015) Ann Arbor U.S.A. (2015) [arXiv:1511.00023] [INSPIRE].

  11. LUX collaboration, Liquid xenon scintillation measurements and pulse shape discrimination in the LUX dark matter detector, Phys. Rev.D 97 (2018) 112002 [arXiv:1802.06162] [INSPIRE].

  12. LUX collaboration, Extending light WIMP searches to single scintillation photons in LUX, Phys. Rev.D 101 (2020) 042001 [arXiv:1907.06272] [INSPIRE].

  13. LUX collaboration, Results of a Search for Sub-GeV Dark Matter Using 2013 LUX Data, Phys. Rev. Lett.122 (2019) 131301 [arXiv:1811.11241] [INSPIRE].

  14. E. Shields, J. Xu and F. Calaprice, SABRE: A New NaI(T1) Dark Matter Direct Detection Experiment, in Proceedings of 13th International Conference on Topics in Astroparticle and Underground Physics (TAUP 2013), Asilomar U.S.A. (2013) [Phys. Procedia61 (2015) 169] [INSPIRE].

  15. SuperCDMS collaboration, Search for Low-Mass Weakly Interacting Massive Particles with SuperCDMS, Phys. Rev. Lett.112 (2014) 241302 [arXiv:1402.7137] [INSPIRE].

  16. SuperCDMS collaboration, Projected Sensitivity of the SuperCDMS SNOLAB experiment, Phys. Rev.D 95 (2017) 082002 [arXiv:1610.00006] [INSPIRE].

  17. SuperCDMS collaboration, New Results from the Search for Low-Mass Weakly Interacting Massive Particles with the CDMS Low Ionization Threshold Experiment, Phys. Rev. Lett.116 (2016) 071301 [arXiv:1509.02448] [INSPIRE].

  18. SuperCDMS collaboration, Low-mass dark matter search with CDMSlite, Phys. Rev.D 97 (2018) 022002 [arXiv:1707.01632] [INSPIRE].

  19. SuperCDMS collaboration, Search for Low-Mass Dark Matter with CDMSlite Using a Profile Likelihood Fit, Phys. Rev.D 99 (2019) 062001 [arXiv:1808.09098] [INSPIRE].

  20. SuperCDMS collaboration, First Dark Matter Constraints from a SuperCDMS Single-Charge Sensitive Detector, Phys. Rev. Lett.121 (2018) 051301 [arXiv:1804.10697] [INSPIRE].

  21. XENON collaboration, Dark Matter Search Results from a One Ton-Year Exposure of XENON1T, Phys. Rev. Lett.121 (2018) 111302 [arXiv:1805.12562] [INSPIRE].

  22. XENON collaboration, Light Dark Matter Search with Ionization Signals in XENON1T, Phys. Rev. Lett.123 (2019) 251801 [arXiv:1907.11485] [INSPIRE].

  23. R. Essig, J. Mardon and T. Volansky, Direct Detection of Sub-GeV Dark Matter, Phys. Rev.D 85 (2012) 076007 [arXiv:1108.5383] [INSPIRE].

  24. 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].

  25. 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].

  26. 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].

  27. 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, JHEP05 (2016) 046 [arXiv:1509.01598] [INSPIRE].

  28. S. Derenzo, R. Essig, A. Massari, A. Soto and T.-T. Yu, Direct Detection of sub-GeV Dark Matter with Scintillating Targets, Phys. Rev.D 96 (2017) 016026 [arXiv:1607.01009] [INSPIRE].

  29. Y. Hochberg, T. Lin and K.M. Zurek, Absorption of light dark matter in semiconductors, Phys. Rev.D 95 (2017) 023013 [arXiv:1608.01994] [INSPIRE].

  30. I.M. Bloch, R. Essig, K. Tobioka, T. Volansky and T.-T. Yu, Searching for Dark Absorption with Direct Detection Experiments, JHEP06 (2017) 087 [arXiv:1608.02123] [INSPIRE].

  31. 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].

  32. N.A. Kurinsky, T.C. Yu, Y. Hochberg and B. Cabrera, Diamond Detectors for Direct Detection of Sub-GeV Dark Matter, Phys. Rev.D 99 (2019) 123005 [arXiv:1901.07569] [INSPIRE].

  33. Y. Hochberg, Y. Zhao and K.M. Zurek, Superconducting Detectors for Superlight Dark Matter, Phys. Rev. Lett.116 (2016) 011301 [arXiv:1504.07237] [INSPIRE].

  34. Y. Hochberg, M. Pyle, Y. Zhao and K.M. Zurek, Detecting Superlight Dark Matter with Fermi-Degenerate Materials, JHEP08 (2016) 057 [arXiv:1512.04533] [INSPIRE].

  35. Y. Hochberg, T. Lin and K.M. Zurek, Detecting Ultralight Bosonic Dark Matter via Absorption in Superconductors, Phys. Rev.D 94 (2016) 015019 [arXiv:1604.06800] [INSPIRE].

  36. Y. Hochberg et al., Detection of sub-MeV Dark Matter with Three-Dimensional Dirac Materials, Phys. Rev.D 97 (2018) 015004 [arXiv:1708.08929] [INSPIRE].

  37. A. Coskuner, A. Mitridate, A. Olivares and K.M. Zurek, Directional Dark Matter Detection in Anisotropic Dirac Materials, arXiv:1909.09170 [INSPIRE].

  38. R.M. Geilhufe, F. Kahlhoefer and M.W. Winkler, Dirac Materials for Sub-MeV Dark Matter Detection: New Targets and Improved Formalism, arXiv:1910.02091 [INSPIRE].

  39. K. Schutz and K.M. Zurek, Detectability of Light Dark Matter with Superfluid Helium, Phys. Rev. Lett.117 (2016) 121302 [arXiv:1604.08206] [INSPIRE].

  40. S. Knapen, T. Lin and K.M. Zurek, Light Dark Matter in Superfluid Helium: Detection with Multi-excitation Production, Phys. Rev.D 95 (2017) 056019 [arXiv:1611.06228] [INSPIRE].

  41. F. Acanfora, A. Esposito and A.D. Polosa, Sub-GeV Dark Matter in Superfluid He-4: an Effective Theory Approach, Eur. Phys. J.C 79 (2019) 549 [arXiv:1902.02361] [INSPIRE].

  42. A. Caputo, A. Esposito and A.D. Polosa, Sub-MeV Dark Matter and the Goldstone Modes of Superfluid Helium, Phys. Rev.D 100 (2019) 116007 [arXiv:1907.10635] [INSPIRE].

  43. S. Knapen, T. Lin, M. Pyle and K.M. Zurek, Detection of Light Dark Matter With Optical Phonons in Polar Materials, Phys. Lett.B 785 (2018) 386 [arXiv:1712.06598] [INSPIRE].

    ADS  Article  Google Scholar 

  44. S. Griffin, S. Knapen, T. Lin and K.M. Zurek, Directional Detection of Light Dark Matter with Polar Materials, Phys. Rev.D 98 (2018) 115034 [arXiv:1807.10291] [INSPIRE].

  45. A. Coskuner, D.M. Grabowska, S. Knapen and K.M. Zurek, Direct Detection of Bound States of Asymmetric Dark Matter, Phys. Rev.D 100 (2019) 035025 [arXiv:1812.07573] [INSPIRE].

  46. 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].

    ADS  Article  Google Scholar 

  47. 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].

    ADS  Article  Google Scholar 

  48. F. Kadribasic, N. Mirabolfathi, K. Nordlund, A.E. Sand, E. Holmström and F. Djurabekova, Directional Sensitivity In Light-Mass Dark Matter Searches With Single-Electron Resolution Ionization Detectors, Phys. Rev. Lett.120 (2018) 111301 [arXiv:1703.05371] [INSPIRE].

  49. R. Budnik, O. Chesnovsky, O. Slone and T. Volansky, Direct Detection of Light Dark Matter and Solar Neutrinos via Color Center Production in Crystals, Phys. Lett.B 782 (2018) 242 [arXiv:1705.03016] [INSPIRE].

    ADS  Article  Google Scholar 

  50. S. Rajendran, N. Zobrist, A.O. Sushkov, R. Walsworth and M. Lukin, A method for directional detection of dark matter using spectroscopy of crystal defects, Phys. Rev.D 96 (2017) 035009 [arXiv:1705.09760] [INSPIRE].

  51. S.M. Griffin, K. Inzani, T. Trickle, Z. Zhang and K.M. Zurek, Multi-Channel Direct Detection of Light Dark Matter: Target Comparison, arXiv:1910.10716 [INSPIRE].

  52. R. Essig, J. Mardon, O. Slone and T. Volansky, Detection of sub-GeV Dark Matter and Solar Neutrinos via Chemical-Bond Breaking, Phys. Rev.D 95 (2017) 056011 [arXiv:1608.02940] [INSPIRE].

  53. A. Arvanitaki, S. Dimopoulos and K. Van Tilburg, Resonant absorption of bosonic dark matter in molecules, Phys. Rev.X 8 (2018) 041001 [arXiv:1709.05354] [INSPIRE].

  54. R. Essig, J. Pérez-Ríos, H. Ramani and O. Slone, Direct Detection of Spin-(In)dependent Nuclear Scattering of Sub-GeV Dark Matter Using Molecular Excitations, arXiv:1907.07682 [INSPIRE].

  55. S. Chang, A. Pierce and N. Weiner, Momentum Dependent Dark Matter Scattering, JCAP01 (2010) 006 [arXiv:0908.3192] [INSPIRE].

  56. A.L. Fitzpatrick and K.M. Zurek, Dark Moments and the DAMA-CoGeNT Puzzle, Phys. Rev.D 82 (2010) 075004 [arXiv:1007.5325] [INSPIRE].

  57. A.L. Fitzpatrick, W. Haxton, E. Katz, N. Lubbers and Y. Xu, The Effective Field Theory of Dark Matter Direct Detection, JCAP02 (2013) 004 [arXiv:1203.3542] [INSPIRE].

  58. M.I. Gresham and K.M. Zurek, Effect of nuclear response functions in dark matter direct detection, Phys. Rev.D 89 (2014) 123521 [arXiv:1401.3739] [INSPIRE].

  59. T. Trickle, Z. Zhang and K.M. Zurek, Direct Detection of Light Dark Matter with Magnons, arXiv:1905.13744 [INSPIRE].

  60. T. Lin, Dark matter models and direct detection, in Proceedings of Theoretical Advanced Study Institute in Elementary Particle Physics: Theory in an Era of Data (TASI 2018), Boulder U.S.A. (2018) [PoS(333)009] [arXiv:1904.07915] [INSPIRE].

  61. S. Knapen and T. Lin, private communications.

  62. S. Knapen, T. Lin and K.M. Zurek, Light Dark Matter: Models and Constraints, Phys. Rev.D 96 (2017) 115021 [arXiv:1709.07882] [INSPIRE].

  63. H. An, M. Pospelov and J. Pradler, New stellar constraints on dark photons, Phys. Lett.B 725 (2013) 190 [arXiv:1302.3884] [INSPIRE].

  64. E. Hardy and R. Lasenby, Stellar cooling bounds on new light particles: plasma mixing effects, JHEP02 (2017) 033 [arXiv:1611.05852] [INSPIRE].

  65. G. Cappellini, R. Del Sole, L. Reining and F. Bechstedt, Model dielectric function for semiconductors, Phys. Rev.B 47 (1993) 9892.

    ADS  Article  Google Scholar 

  66. R.H. Helm, Inelastic and Elastic Scattering of 187-Mev Electrons from Selected Even-Even Nuclei, Phys. Rev.104 (1956) 1466 [INSPIRE].

  67. M. Battaglieri et al., US Cosmic Visions: New Ideas in Dark Matter 2017: Community Report, in U.S. Cosmic Visions: New Ideas in Dark Matter, College Park U.S.A. (2017) [arXiv:1707.04591] [INSPIRE].

  68. P. Cox, T. Melia and S. Rajendran, Dark matter phonon coupling, Phys. Rev.D 100 (2019) 055011 [arXiv:1905.05575] [INSPIRE].

  69. X. Wang and D. Vanderbilt, First-principles perturbative computation of dielectric and Born charge tensors in finite electric fields, Phys. Rev.B 75 (2007) 115116.

  70. H. Vogel and J. Redondo, Dark Radiation constraints on minicharged particles in models with a hidden photon, JCAP02 (2014) 029 [arXiv:1311.2600] [INSPIRE].

  71. G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev.B 47 (1993) 558.

  72. G. Kresse and J. Hafner, Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium, Phys. Rev.B 49 (1994) 14251.

  73. G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mat. Sci.6 (1996) 15.

  74. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev.B 54 (1996) 11169.

  75. P.E. Blöchl, Projector augmented-wave method, Phys. Rev.B 50 (1994) 17953 [INSPIRE].

  76. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev.B 59 (1999) 1758.

  77. J.P. Perdew, K. Burke and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett.77 (1996) 3865.

    ADS  Article  Google Scholar 

  78. S. Grimme, J. Antony, S. Ehrlich and H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys.132 (2010) .

  79. S. Grimme, S. Ehrlich and L. Goerigk, Effect of the damping function in dispersion corrected density functional theory, J. Comput. Chem.32 (2011) 1456.

    Article  Google Scholar 

  80. K. Bystrom, D. Broberg, S. Dwaraknath, K.A. Persson and M. Asta, Pawpyseed: Perturbation-extrapolation band shifting corrections for point defect calculations, arXiv:1904.11572.

  81. R.W. Lynch and H.G. Drickamer, Effect of High Pressure on the Lattice Parameters of Diamond, Graphite, and Hexagonal Boron Nitride, J. Chem. Phys.44 (1966) 181.

  82. K. Watanabe, T. Taniguchi and H. Kanda, Direct-bandgap properties and evidence for ultraviolet lasing of hexagonal boron nitride single crystal, Nature Mat.3 (2004) 404.

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Trickle, T., Zhang, Z., Zurek, K.M. et al. Multi-channel direct detection of light dark matter: theoretical framework. J. High Energ. Phys. 2020, 36 (2020).

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