Skip to main content

Dark matter spectra from the electroweak to the Planck scale

A preprint version of the article is available at arXiv.

Abstract

We compute the decay spectrum for dark matter (DM) with masses above the scale of electroweak symmetry breaking, all the way to the Planck scale. For an arbitrary hard process involving a decay to the unbroken standard model, we determine the prompt distribution of stable states including photons, neutrinos, positrons, and antiprotons. These spectra are a crucial ingredient in the search for DM via indirect detection at the highest energies as being probed in current and upcoming experiments including IceCube, HAWC, CTA, and LHAASO. Our approach improves considerably on existing methods, for instance, we include all relevant electroweak interactions.

References

  1. T. Sjöstrand, S. Mrenna and P.Z. Skands, PYTHIA 6.4 Physics and Manual, JHEP 05 (2006) 026 [hep-ph/0603175] [INSPIRE].

  2. T. Sjöstrand, S. Mrenna and P.Z. Skands, A Brief Introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852 [arXiv:0710.3820] [INSPIRE].

  3. T. Sjöstrand et al., An introduction to PYTHIA 8.2, Comput. Phys. Commun. 191 (2015) 159 [arXiv:1410.3012] [INSPIRE].

  4. https://github.com/nickrodd/HDMSpectra.

  5. IceCube collaboration, Search for neutrinos from decaying dark matter with IceCube, Eur. Phys. J. C 78 (2018) 831 [arXiv:1804.03848] [INSPIRE].

  6. D.J.H. Chung, E.W. Kolb and A. Riotto, Superheavy dark matter, Phys. Rev. D 59 (1998) 023501 [hep-ph/9802238] [INSPIRE].

  7. K. Benakli, J.R. Ellis and D.V. Nanopoulos, Natural candidates for superheavy dark matter in string and M-theory, Phys. Rev. D 59 (1999) 047301 [hep-ph/9803333] [INSPIRE].

  8. E.W. Kolb, D.J.H. Chung and A. Riotto, WIMPzillas!, AIP Conf. Proc. 484 (1999) 91 [hep-ph/9810361] [INSPIRE].

  9. P. Blasi, R. Dick and E.W. Kolb, Ultra-High Energy Cosmic Rays from Annihilation of Superheavy Dark Matter, Astropart. Phys. 18 (2002) 57 [astro-ph/0105232] [INSPIRE].

  10. E.W. Kolb and A.J. Long, Superheavy dark matter through Higgs portal operators, Phys. Rev. D 96 (2017) 103540 [arXiv:1708.04293] [INSPIRE].

    Article  ADS  Google Scholar 

  11. E. Alcantara, L.A. Anchordoqui and J.F. Soriano, Hunting for superheavy dark matter with the highest-energy cosmic rays, Phys. Rev. D 99 (2019) 103016 [arXiv:1903.05429] [INSPIRE].

    Article  ADS  Google Scholar 

  12. A.E. Faraggi and M. Pospelov, Selfinteracting dark matter from the hidden heterotic string sector, Astropart. Phys. 16 (2002) 451 [hep-ph/0008223] [INSPIRE].

  13. 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].

    Article  ADS  Google Scholar 

  14. L. Forestell, D.E. Morrissey and K. Sigurdson, Non-Abelian Dark Forces and the Relic Densities of Dark Glueballs, Phys. Rev. D 95 (2017) 015032 [arXiv:1605.08048] [INSPIRE].

    Article  ADS  Google Scholar 

  15. J. Halverson, B.D. Nelson and F. Ruehle, String Theory and the Dark Glueball Problem, Phys. Rev. D 95 (2017) 043527 [arXiv:1609.02151] [INSPIRE].

    Article  ADS  Google Scholar 

  16. T. Cohen, K. Murase, N.L. Rodd, B.R. Safdi and Y. Soreq, γ-ray Constraints on Decaying Dark Matter and Implications for IceCube, Phys. Rev. Lett. 119 (2017) 021102 [arXiv:1612.05638] [INSPIRE].

  17. L. Forestell, D.E. Morrissey and K. Sigurdson, Cosmological Bounds on Non-Abelian Dark Forces, Phys. Rev. D 97 (2018) 075029 [arXiv:1710.06447] [INSPIRE].

    Article  ADS  Google Scholar 

  18. H. Pagels and J.R. Primack, Supersymmetry, Cosmology and New TeV Physics, Phys. Rev. Lett. 48 (1982) 223 [INSPIRE].

    Article  ADS  Google Scholar 

  19. F.D. Steffen, Gravitino dark matter and cosmological constraints, JCAP 09 (2006) 001 [hep-ph/0605306] [INSPIRE].

  20. K. Ishiwata, S. Matsumoto and T. Moroi, High Energy Cosmic Rays from the Decay of Gravitino Dark Matter, Phys. Rev. D 78 (2008) 063505 [arXiv:0805.1133] [INSPIRE].

    Article  ADS  Google Scholar 

  21. S. Chang, C. Corianò and A.E. Faraggi, Stable superstring relics, Nucl. Phys. B 477 (1996) 65 [hep-ph/9605325] [INSPIRE].

  22. A.E. Faraggi, K.A. Olive and M. Pospelov, Probing the desert with ultraenergetic neutrinos from the sun, Astropart. Phys. 13 (2000) 31 [hep-ph/9906345] [INSPIRE].

  23. C. Corianò, A.E. Faraggi and M. Plümacher, Stable superstring relics and ultrahigh-energy cosmic rays, Nucl. Phys. B 614 (2001) 233 [hep-ph/0107053] [INSPIRE].

  24. L. Delle Rose, A.E. Faraggi, C. Marzo and J. Rizos, Wilsonian dark matter in string derived Zmodel, Phys. Rev. D 96 (2017) 055025 [arXiv:1704.02579] [INSPIRE].

    Article  ADS  Google Scholar 

  25. R. Contino, A. Mitridate, A. Podo and M. Redi, Gluequark Dark Matter, JHEP 02 (2019) 187 [arXiv:1811.06975] [INSPIRE].

    Article  ADS  Google Scholar 

  26. E. Babichev, D. Gorbunov and S. Ramazanov, New mechanism of producing superheavy Dark Matter, Phys. Lett. B 794 (2019) 69 [arXiv:1812.03516] [INSPIRE].

    Article  ADS  Google Scholar 

  27. H. Kim and E. Kuflik, Superheavy Thermal Dark Matter, Phys. Rev. Lett. 123 (2019) 191801 [arXiv:1906.00981] [INSPIRE].

    Article  ADS  Google Scholar 

  28. E. Dudas, L. Heurtier, Y. Mambrini, K.A. Olive and M. Pierre, Model of metastable EeV dark matter, Phys. Rev. D 101 (2020) 115029 [arXiv:2003.02846] [INSPIRE].

    Article  ADS  Google Scholar 

  29. E.D. Kramer, E. Kuflik, N. Levi, N.J. Outmezguine and J.T. Ruderman, Heavy Thermal Dark Matter from a New Collision Mechanism, Phys. Rev. Lett. 126 (2021) 081802 [arXiv:2003.04900] [INSPIRE].

    Article  ADS  Google Scholar 

  30. T. Hambye, M. Lucca and L. Vanderheyden, Dark matter as a heavy thermal hot relic, Phys. Lett. B 807 (2020) 135553 [arXiv:2003.04936] [INSPIRE].

    Article  Google Scholar 

  31. M.A.G. Garcia, Y. Mambrini, K.A. Olive and S. Verner, Case for decaying spin-3/2 dark matter, Phys. Rev. D 102 (2020) 083533 [arXiv:2006.03325] [INSPIRE].

    MathSciNet  Article  ADS  Google Scholar 

  32. HAWC collaboration, A Search for Dark Matter in the Galactic Halo with HAWC, JCAP 02 (2018) 049 [arXiv:1710.10288] [INSPIRE].

  33. IceCube collaboration, Search for dark matter from the Galactic halo with the IceCube Neutrino Telescope, Phys. Rev. D 84 (2011) 022004 [arXiv:1101.3349] [INSPIRE].

  34. A. Esmaili and P.D. Serpico, Are IceCube neutrinos unveiling PeV-scale decaying dark matter?, JCAP 11 (2013) 054 [arXiv:1308.1105] [INSPIRE].

    Article  ADS  Google Scholar 

  35. C. Rott, K. Kohri and S.C. Park, Superheavy dark matter and IceCube neutrino signals: Bounds on decaying dark matter, Phys. Rev. D 92 (2015) 023529 [arXiv:1408.4575] [INSPIRE].

    Article  ADS  Google Scholar 

  36. A. Bhattacharya, A. Esmaili, S. Palomares-Ruiz and I. Sarcevic, Update on decaying and annihilating heavy dark matter with the 6-year IceCube HESE data, JCAP 05 (2019) 051 [arXiv:1903.12623] [INSPIRE].

    Article  ADS  Google Scholar 

  37. M. Chianese, D.F.G. Fiorillo, G. Miele, S. Morisi and O. Pisanti, Decaying dark matter at IceCube and its signature on High Energy gamma experiments, JCAP 11 (2019) 046 [arXiv:1907.11222] [INSPIRE].

    Article  ADS  Google Scholar 

  38. Q. Liu, J. Lazar, C.A. Argüelles and A. Kheirandish, χaroν: a tool for neutrino flux generation from WIMPs, JCAP 10 (2020) 043 [arXiv:2007.15010] [INSPIRE].

  39. ANTARES collaboration, Search for dark matter towards the Galactic Centre with 11 years of ANTARES data, Phys. Lett. B 805 (2020) 135439 [arXiv:1912.05296] [INSPIRE].

  40. ANTARES and IceCube collaborations, Combined search for neutrinos from dark matter self-annihilation in the Galactic Center with ANTARES and IceCube, Phys. Rev. D 102 (2020) 082002 [arXiv:2003.06614] [INSPIRE].

  41. Pierre Auger collaboration, The Pierre Auger Cosmic Ray Observatory, Nucl. Instrum. Meth. A 798 (2015) 172 [arXiv:1502.01323] [INSPIRE].

  42. A. Esmaili, A. Ibarra and O.L.G. Peres, Probing the stability of superheavy dark matter particles with high-energy neutrinos, JCAP 11 (2012) 034 [arXiv:1205.5281] [INSPIRE].

    Article  ADS  Google Scholar 

  43. M.Y. Kuznetsov, Hadronically decaying heavy dark matter and high-energy neutrino limits, JETP Lett. 105 (2017) 561 [arXiv:1611.08684] [INSPIRE].

    Article  ADS  Google Scholar 

  44. Pierre Auger collaboration, Probing the origin of ultra-high-energy cosmic rays with neutrinos in the EeV energy range using the Pierre Auger Observatory, JCAP 10 (2019) 022 [arXiv:1906.07422] [INSPIRE].

  45. V. Verzi, D. Ivanov and Y. Tsunesada, Measurement of Energy Spectrum of Ultra-High Energy Cosmic Rays, Prog. Theor. Exp. Phys. 2017 (2017) 12A103 [arXiv:1705.09111] [INSPIRE].

  46. Telescope Array collaboration, Constraints on the diffuse photon flux with energies above 1018 eV using the surface detector of the Telescope Array experiment, Astropart. Phys. 110 (2019) 8 [arXiv:1811.03920] [INSPIRE].

  47. CTA Consortium, Science with the Cherenkov Telescope Array, World Scientific (2019) [10.1142/10986] [arXiv:1709.07997] [INSPIRE].

  48. H. Silverwood, C. Weniger, P. Scott and G. Bertone, A realistic assessment of the CTA sensitivity to dark matter annihilation, JCAP 03 (2015) 055 [arXiv:1408.4131] [INSPIRE].

    Article  ADS  Google Scholar 

  49. X. Bai et al., The Large High Altitude Air Shower Observatory (LHAASO) Science White Paper, arXiv:1905.02773 [INSPIRE].

  50. D.-Z. He, X.-J. Bi, S.-J. Lin, P.-F. Yin and X. Zhang, Expected LHAASO sensitivity to decaying dark matter signatures from dwarf galaxies gamma-ray emission, Chin. Phys. C 44 (2020) 085001 [arXiv:1910.05017] [INSPIRE].

    Article  ADS  Google Scholar 

  51. IceCube collaboration, IceCube-Gen2: A Vision for the Future of Neutrino Astronomy in Antarctica, arXiv:1412.5106 [INSPIRE].

  52. KM3Net collaboration, Letter of intent for KM3NeT 2.0, J. Phys. G 43 (2016) 084001 [arXiv:1601.07459] [INSPIRE].

  53. K.C.Y. Ng et al., Sensitivities of KM3NeT on decaying dark matter, arXiv:2007.03692 [INSPIRE].

  54. K. Griest and M. Kamionkowski, Unitarity Limits on the Mass and Radius of Dark Matter Particles, Phys. Rev. Lett. 64 (1990) 615 [INSPIRE].

    Article  ADS  Google Scholar 

  55. A. Berlin, D. Hooper and G. Krnjaic, PeV-Scale Dark Matter as a Thermal Relic of a Decoupled Sector, Phys. Lett. B 760 (2016) 106 [arXiv:1602.08490] [INSPIRE].

    Article  ADS  Google Scholar 

  56. K. Harigaya, M. Ibe, K. Kaneta, W. Nakano and M. Suzuki, Thermal Relic Dark Matter Beyond the Unitarity Limit, JHEP 08 (2016) 151 [arXiv:1606.00159] [INSPIRE].

    Article  ADS  Google Scholar 

  57. A. Berlin, D. Hooper and G. Krnjaic, Thermal Dark Matter From A Highly Decoupled Sector, Phys. Rev. D 94 (2016) 095019 [arXiv:1609.02555] [INSPIRE].

    Article  ADS  Google Scholar 

  58. M. Cirelli, Y. Gouttenoire, K. Petraki and F. Sala, Homeopathic Dark Matter, or how diluted heavy substances produce high energy cosmic rays, JCAP 02 (2019) 014 [arXiv:1811.03608] [INSPIRE].

    Article  ADS  Google Scholar 

  59. V.N. Gribov and L.N. Lipatov, Deep inelastic ep scattering in perturbation theory, Sov. J. Nucl. Phys. 15 (1972) 438 [Yad. Fiz. 15 (1972) 781] [INSPIRE].

  60. Y.L. Dokshitzer, Calculation of the Structure Functions for Deep Inelastic Scattering and e+e Annihilation by Perturbation Theory in Quantum Chromodynamics, Sov. Phys. JETP 46 (1977) 641 [Zh. Eksp. Teor. Fiz. 73 (1977) 1216] [INSPIRE].

  61. G. Altarelli and G. Parisi, Asymptotic Freedom in Parton Language, Nucl. Phys. B 126 (1977) 298 [INSPIRE].

    Article  ADS  Google Scholar 

  62. A. Chudakov, On an ionization effect related to the observation of electron-positron pairs at very high energies (in Russian), Bull. Acad. Sci. USSR Phys. Ser. 19 (1955) 589.

    Google Scholar 

  63. B.I. Ermolaev and V.S. Fadin, Log - Log Asymptotic Form of Exclusive Cross-Sections in Quantum Chromodynamics, JETP Lett. 33 (1981) 269 [Pisma Zh. Eksp. Teor. Fiz. 33 (1981) 285] [INSPIRE].

  64. A.H. Mueller, On the Multiplicity of Hadrons in QCD Jets, Phys. Lett. B 104 (1981) 161 [INSPIRE].

    Article  ADS  Google Scholar 

  65. A. Bassetto, M. Ciafaloni, G. Marchesini and A.H. Mueller, Jet Multiplicity and Soft Gluon Factorization, Nucl. Phys. B 207 (1982) 189 [INSPIRE].

    Article  ADS  Google Scholar 

  66. A. Bassetto, M. Ciafaloni and G. Marchesini, Jet Structure and Infrared Sensitive Quantities in Perturbative QCD, Phys. Rept. 100 (1983) 201 [INSPIRE].

    Article  ADS  Google Scholar 

  67. M. Ciafaloni, P. Ciafaloni and D. Comelli, Bloch-Nordsieck violating electroweak corrections to inclusive TeV scale hard processes, Phys. Rev. Lett. 84 (2000) 4810 [hep-ph/0001142] [INSPIRE].

  68. A.V. Manohar and W.J. Waalewijn, Electroweak Logarithms in Inclusive Cross Sections, JHEP 08 (2018) 137 [arXiv:1802.08687] [INSPIRE].

    Article  ADS  Google Scholar 

  69. C.W. Bauer, D. Provasoli and B.R. Webber, Standard Model Fragmentation Functions at Very High Energies, JHEP 11 (2018) 030 [arXiv:1806.10157] [INSPIRE].

    MATH  Article  ADS  Google Scholar 

  70. C.W. Bauer and B.R. Webber, Polarization Effects in Standard Model Parton Distributions at Very High Energies, JHEP 03 (2019) 013 [arXiv:1808.08831] [INSPIRE].

    MathSciNet  Article  ADS  Google Scholar 

  71. G. Marchesini and B.R. Webber, Simulation of QCD Jets Including Soft Gluon Interference, Nucl. Phys. B 238 (1984) 1 [INSPIRE].

    Article  ADS  Google Scholar 

  72. G. Marchesini and B.R. Webber, Monte Carlo Simulation of General Hard Processes with Coherent QCD Radiation, Nucl. Phys. B 310 (1988) 461 [INSPIRE].

    Article  ADS  Google Scholar 

  73. M. Cirelli et al., PPPC 4 DM ID: A Poor Particle Physicist Cookbook for Dark Matter Indirect Detection, JCAP 03 (2011) 051 [Erratum JCAP 10 (2012) E01] [arXiv:1012.4515] [INSPIRE].

  74. P. Ciafaloni, D. Comelli, A. Riotto, F. Sala, A. Strumia and A. Urbano, Weak Corrections are Relevant for Dark Matter Indirect Detection, JCAP 03 (2011) 019 [arXiv:1009.0224] [INSPIRE].

    Article  ADS  Google Scholar 

  75. C.W. Bauer, N. Ferland and B.R. Webber, Combining initial-state resummation with fixed-order calculations of electroweak corrections, JHEP 04 (2018) 125 [arXiv:1712.07147] [INSPIRE].

    Article  ADS  Google Scholar 

  76. K. Murase and J.F. Beacom, Constraining Very Heavy Dark Matter Using Diffuse Backgrounds of Neutrinos and Cascaded Gamma Rays, JCAP 10 (2012) 043 [arXiv:1206.2595] [INSPIRE].

    Article  ADS  Google Scholar 

  77. A. Esmaili and P.D. Serpico, Gamma-ray bounds from EAS detectors and heavy decaying dark matter constraints, JCAP 10 (2015) 014 [arXiv:1505.06486] [INSPIRE].

    Article  ADS  Google Scholar 

  78. R. Alves Batista et al., CRPropa 3 — a Public Astrophysical Simulation Framework for Propagating Extraterrestrial Ultra-High Energy Particles, JCAP 05 (2016) 038 [arXiv:1603.07142] [INSPIRE].

    Article  ADS  Google Scholar 

  79. C. Blanco, γ-cascade: a simple program to compute cosmological gamma-ray propagation, JCAP 01 (2019) 013 [arXiv:1804.00005] [INSPIRE].

  80. J.A.R. Cembranos, A. de la Cruz-Dombriz, V. Gammaldi, R.A. Lineros and A.L. Maroto, Reliability of Monte Carlo event generators for gamma ray dark matter searches, JHEP 09 (2013) 077 [arXiv:1305.2124] [INSPIRE].

    Article  ADS  Google Scholar 

  81. S. Amoroso, S. Caron, A. Jueid, R. Ruiz de Austri and P. Skands, Estimating QCD uncertainties in Monte Carlo event generators for gamma-ray dark matter searches, JCAP 05 (2019) 007 [arXiv:1812.07424] [INSPIRE].

    Article  ADS  Google Scholar 

  82. C. Niblaeus, J.M. Cornell and J. Edsjö, Effect of polarisation and choice of event generator on spectra from dark matter annihilations, JCAP 10 (2019) 079 [arXiv:1907.02488] [INSPIRE].

    Article  ADS  Google Scholar 

  83. V. Berezinsky and M. Kachelriess, Monte Carlo simulation for jet fragmentation in SUSY QCD, Phys. Rev. D 63 (2001) 034007 [hep-ph/0009053] [INSPIRE].

  84. V. Berezinsky, M. Kachelriess and S. Ostapchenko, Electroweak jet cascading in the decay of superheavy particles, Phys. Rev. Lett. 89 (2002) 171802 [hep-ph/0205218] [INSPIRE].

  85. R. Aloisio, V. Berezinsky and M. Kachelriess, Fragmentation functions in SUSY QCD and UHECR spectra produced in top-down models, Phys. Rev. D 69 (2004) 094023 [hep-ph/0307279] [INSPIRE].

  86. C. Barbot and M. Drees, Production of ultraenergetic cosmic rays through the decay of superheavy X particles, Phys. Lett. B 533 (2002) 107 [hep-ph/0202072] [INSPIRE].

  87. C. Barbot and M. Drees, Detailed analysis of the decay spectrum of a super heavy X particle, Astropart. Phys. 20 (2003) 5 [hep-ph/0211406] [INSPIRE].

  88. M. Lisanti, S. Mishra-Sharma, N.L. Rodd, B.R. Safdi and R.H. Wechsler, Mapping Extragalactic Dark Matter Annihilation with Galaxy Surveys: A Systematic Study of Stacked Group Searches, Phys. Rev. D 97 (2018) 063005 [arXiv:1709.00416] [INSPIRE].

    Article  ADS  Google Scholar 

  89. K.K. Boddy, J. Kumar and L.E. Strigari, Effective J-factor of the Galactic Center for velocity-dependent dark matter annihilation, Phys. Rev. D 98 (2018) 063012 [arXiv:1805.08379] [INSPIRE].

    Article  ADS  Google Scholar 

  90. P. Asadi, M. Baumgart, P.J. Fitzpatrick, E. Krupczak and T.R. Slatyer, Capture and Decay of Electroweak WIMPonium, JCAP 02 (2017) 005 [arXiv:1610.07617] [INSPIRE].

    Article  ADS  Google Scholar 

  91. J. Smirnov and J.F. Beacom, TeV-Scale Thermal WIMPs: Unitarity and its Consequences, Phys. Rev. D 100 (2019) 043029 [arXiv:1904.11503] [INSPIRE].

    Article  ADS  Google Scholar 

  92. R. Mahbubani, M. Redi and A. Tesi, Indirect detection of composite asymmetric dark matter, Phys. Rev. D 101 (2020) 103037 [arXiv:1908.00538] [INSPIRE].

    Article  ADS  Google Scholar 

  93. O.E. Kalashev and M.Y. Kuznetsov, Heavy decaying dark matter and large-scale anisotropy of high-energy cosmic rays, JETP Lett. 106 (2017) 73 [Pisma Zh. Eksp. Teor. Fiz. 106 (2017) 65] [arXiv:1704.05300] [INSPIRE].

  94. J.R. Christiansen and T. Sjöstrand, Weak Gauge Boson Radiation in Parton Showers, JHEP 04 (2014) 115 [arXiv:1401.5238] [INSPIRE].

    Article  ADS  Google Scholar 

  95. S. Sarkar and R. Toldra, The High-energy cosmic ray spectrum from relic particle decay, Nucl. Phys. B 621 (2002) 495 [hep-ph/0108098] [INSPIRE].

  96. O.E. Kalashev, G.I. Rubtsov and S.V. Troitsky, Sensitivity of cosmic-ray experiments to ultra-high-energy photons: reconstruction of the spectrum and limits on the superheavy dark matter, Phys. Rev. D 80 (2009) 103006 [arXiv:0812.1020] [INSPIRE].

    Article  ADS  Google Scholar 

  97. O.E. Kalashev and M.Y. Kuznetsov, Constraining heavy decaying dark matter with the high energy gamma-ray limits, Phys. Rev. D 94 (2016) 063535 [arXiv:1606.07354] [INSPIRE].

    Article  ADS  Google Scholar 

  98. M. Kachelriess, O.E. Kalashev and M.Y. Kuznetsov, Heavy decaying dark matter and IceCube high energy neutrinos, Phys. Rev. D 98 (2018) 083016 [arXiv:1805.04500] [INSPIRE].

    Article  ADS  Google Scholar 

  99. O.E. Kalashev, M.Y. Kuznetsov and Y.V. Zhezher, Dark matter component decaying after recombination: constraints from diffuse gamma-ray and neutrino flux measurements, JCAP 10 (2019) 039 [arXiv:1905.05170] [INSPIRE].

    Article  ADS  Google Scholar 

  100. O.E. Kalashev, M.Y. Kuznetsov and Y.V. Zhezher, Constraining superheavy decaying dark matter with directional ultra-high energy gamma-ray limits, arXiv:2005.04085 [INSPIRE].

  101. K. Ishiwata, O. Macias, S. Ando and M. Arimoto, Probing heavy dark matter decays with multi-messenger astrophysical data, JCAP 01 (2020) 003 [arXiv:1907.11671] [INSPIRE].

    Article  ADS  Google Scholar 

  102. B.L. Ioffe, Associated production of gluonic jets and heavy mesons in e+e annihilation, Phys. Lett. B 78 (1978) 277 [INSPIRE].

    Article  ADS  Google Scholar 

  103. A. Coogan, L. Morrison and S. Profumo, Hazma: A Python Toolkit for Studying Indirect Detection of Sub-GeV Dark Matter, JCAP 01 (2020) 056 [arXiv:1907.11846] [INSPIRE].

    Article  ADS  Google Scholar 

  104. M. Baumgart et al., Precision Photon Spectra for Wino Annihilation, JHEP 01 (2019) 036 [arXiv:1808.08956] [INSPIRE].

    Article  ADS  Google Scholar 

  105. A. Buckley et al., LHAPDF6: parton density access in the LHC precision era, Eur. Phys. J. C 75 (2015) 132 [arXiv:1412.7420] [INSPIRE].

    Article  ADS  Google Scholar 

  106. D. Amati and G. Veneziano, Preconfinement as a Property of Perturbative QCD, Phys. Lett. B 83 (1979) 87 [INSPIRE].

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nicholas L. Rodd.

Additional information

Publisher’s Note

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

ArXiv ePrint: 2007.15001

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

Bauer, C.W., Rodd, N.L. & Webber, B.R. Dark matter spectra from the electroweak to the Planck scale. J. High Energ. Phys. 2021, 121 (2021). https://doi.org/10.1007/JHEP06(2021)121

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP06(2021)121

Keywords

  • Perturbative QCD
  • Resummation