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Relic density of dark matter in the inert doublet model beyond leading order for the low mass region. III. Annihilation to three-body final states

Shankha Banerjee, Fawzi Boudjema, Nabarun Chakrabarty, and Hao Sun
Phys. Rev. D 104, 075004 – Published 5 October 2021
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  • INTRODUCTION
  • TREE-LEVEL CONSIDERATIONS
  • XX→Wff¯ AND XX→Zff¯ AT ONE LOOP: GENERAL…
  • XX→ZZ⋆ AT ONE LOOP: XX→Zνν¯
  • XX→Zff¯ AND XX→Wff¯′: ONE-LOOP RESULTS
  • INTERMEDIATE SUMMARY
  • EFFECT ON THE RELIC DENSITY
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    We perform the first one-loop electroweak corrections for 2→3 processes for dark matter annihilation. These are the dominant processes that enter the computation of the relic density for the low mass region of the inert doublet model (IDM) when annihilations to two on shell vector bosons are closed. The impact of the one-loop corrections are important as they involve, through rescattering effects, not only a dependence on the parameter controlling the dark sector, not present if a calculation at tree level is conducted, but also on the renormalization scale. These combined effects should be taken into account in analyses based on tree-level cross sections of the relic density calculations, as a theoretical uncertainty, which we find to be much larger than the cursory ±10% uncertainty that is routinely assumed, independently of the model parameters.

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    • Received 20 February 2021
    • Accepted 13 August 2021

    DOI:https://doi.org/10.1103/PhysRevD.104.075004

    Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

    Published by the American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Electroweak radiative correctionsExtensions of Higgs sectorParticle dark matterWeakly interacting massive particles
    Particles & Fields

    Authors & Affiliations

    Shankha Banerjee1,*, Fawzi Boudjema2,†, Nabarun Chakrabarty3,4,‡, and Hao Sun5,§

    • 1CERN, Theoretical Physics Department, CH-1211 Geneva 23, Switzerland
    • 2LAPTh, Université Savoie Mont Blanc, CNRS, BP 110, F-74941 Annecy-le-Vieux, France
    • 3Centre for High Energy Physics, Indian Institute of Science, C.V. Raman Avenue, Bangalore 560012, India
    • 4Department of Physics, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh 208016, India
    • 5Institute of Theoretical Physics, School of Physics, Dalian University of Technology, Dalian 116024, People’s Republic of China

    • *shankha.banerjee@cern.ch
    • †boudjema@lapth.cnrs.fr
    • ‡chakrabartynabarun@gmail.com
    • §haosun@dlut.edu.cn

    See Also

    Relic density of dark matter in the inert doublet model beyond leading order for the low mass region. I. Renormalization and constraints

    Shankha Banerjee, Fawzi Boudjema, Nabarun Chakrabarty, and Hao Sun
    Phys. Rev. D 104, 075002 (2021)

    Relic density of dark matter in the inert doublet model beyond leading order for the low mass region. II. Coannihilation

    Shankha Banerjee, Fawzi Boudjema, Nabarun Chakrabarty, and Hao Sun
    Phys. Rev. D 104, 075003 (2021)

    Relic density of dark matter in the inert doublet model beyond leading order for the low mass region. IV. The Higgs resonance region

    Shankha Banerjee, Fawzi Boudjema, Nabarun Chakrabarty, and Hao Sun
    Phys. Rev. D 104, 075005 (2021)

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    Vol. 104, Iss. 7 — 1 October 2021

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    Images

    • Figure 1
      Figure 1

      A selection of tree-level Feynman diagrams for XX→Zff¯ in the Feynman gauge. The displayed diagrams can be built up from XX→ZZ⋆→Zff¯ but note also the Z-“bremsstrahlung” contribution triggered from XX→ff⋆→ff¯Z (last diagram in the first row).

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    • Figure 2
      Figure 2

      Benchmark point G. The tree-level cross section times the relative velocity for XX→Zνν¯ (upper-left panel), RZff¯XX−1 for f=τ, b (upper-right panel). The lower panel displays RZττ¯XX≃1 and the ratio of the tree-level cross sections RW/ZXX=σ(XX→Wτν¯τ)/σ(XX→Zντν¯τ) as a function of the relative velocity, v.

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    • Figure 3
      Figure 3

      A small selection of Feynman diagrams for XX→Zff¯ at one loop. We only show a very small subset of pentagons, boxes, and triangles but not self-energy corrections and counterterms. f′ stands for the SU(2) partner of f (νl for f=l). F stands for the sum of all SM fermions. Although some diagrams may not look like boxes, they fall under the box category because of the four-particle vertices they involve. The same applies to triangles. We see rescattering effects within the dark sector, XX→AA, H+H−, XX that explicitly involve the λ2 parameter that does not show up at tree level. Also note that because of the off shell Z, charged fermion ff pairs from γ⋆ must also be taken into account.

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    • Figure 4
      Figure 4

      Point G. Comparing the relative correction in % as a function of the relative velocity for Zντν¯τ for λ2=0.01, 1, 2, and for 3 scales μ=MX/,MX,2MX. We also display the improved tree level based on the use of α(MZ2). The panel on the right is a zoom on the choice μ=2MX for better readability.

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    • Figure 5
      Figure 5

      As in 4 but for point F (upper panels) and point A (lower panels).

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    • Figure 6
      Figure 6

      The relative corrections for σv(XX→Zντν¯τ) with μ=MA for the benchmark point A (left panel) and point F (right panel).

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    • Figure 7
      Figure 7

      Point G. The relative correction, dσ(Vff¯′)/σ0(Vff¯′), V=W, Z, in % as a function of the relative velocity for XX→Zτ+τ−, Zντν¯τ, Wτν¯τ for μ=2MX and λ2=0.01, 1, 2. The right panel shows the difference dσ(Vff¯′)/σ(Vff¯′)−dσ(Zνν¯)/σ(Zνν¯).

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    • Figure 8
      Figure 8

      Point G. Percentage corrections for μ=MA for the Zντν¯τ and Zbb¯ final states. The latter are about 6% lower than the neutrino case for all values of v and λ2.

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