SciPost Phys. Proc. 12, 035 (2023)

Constraints on heavy dark matter annihilation and decay
from electron and positron cosmic ray spectra
Holger Motz⋆
Global Center for Science and Engineering, Faculty of Science and Engineering,
Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan⋆ motz@aoni.waseda.jp

14th International Conference on Identification of Dark Matter
Vienna, Austria, 18-22 July 2022
doi:10.21468/SciPostPhysProc.12

Abstract
Annihilation or decay of dark matter (DM) could contribute to the electron and positroncosmic-ray flux, allowing for constraints on DM parameters from its measurement.
CALET is directly measuring the energy spectrum of electron+positron cosmic rays up
into the TeV region most important for studying heavy DM, while AMS-02 provides a
positron-only spectrum below the TeV range. Limits on DM annihilation and decay wellinto the TeV mass range have been derived from a combined analysis of both data-setswith an astrophysical background model including pulsars as the origin of the positron
excess and individual nearby supernova remnant sources.
Copyright H. Motz.
This work is licensed under the Creative Commons
Attribution 4.0 International License.
Published by the SciPost Foundation.

1

Received 02-10-2022
Accepted 24-04-2023
Check forupdatesPublished 04-07-2023
doi:10.21468/SciPostPhysProc.12.035

Introduction

Limits on DM annihilation and decay are derived from the all-electron (electron+positron)
spectrum measured by CALET [1], and the positron spectrum from AMS-02 [2]. The astrophysical background for the positron spectrum is limited to pulsars and secondary particles, but
it reaches only up to 1 TeV, while the background for the all-electron spectrum which extends
up to 4.8 TeV includes also SNRs. Based on previously established methods [3–5], this study
focuses on TeV-mass-range DM, with an improved background model treating the nearby SNRs
Vela, Monogem and Cygnus Loop, which dominate the TeV-region [6], as individual sources.

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SciPost Phys. Proc. 12, 035 (2023)

Table 1: Propagation model parameters, see text for explanation.
parametervalue
rn
[kpc]
2D0
D0(@sol)[1028 cm2 /s] [1028 cm2 /s]
1.295
5.064
rs
[kpc]
4.62

zn
[kpc]0.15

R0[GV]
4L
[kpc]
6

va
[km/s]
9.9

R bi
[GV]
7.81

γl
2.0s bi

γi0.224 2.2642

R cut
[TV]
27zs
R blR bhδlslδshδh
[kpc]
[GV]
[GV]
2.68 0.3126 12.3284 0.0535 0.574 914.5 0.3262 0.053

2Method

2.1

Propagation model and calculation of dark matter signal

The calculation of DM signals and background flux requires an underlying model of cosmic
ray propagation. The model used in this work is founded on the hypothesis that all primary
nuclei species have a common source spectrum, a power law with index γl below, and γi above
the break at R bi with softness s bi , and with an exponential cut-off at R cut . Spectral differences
between the nuclei species are attributed to propagation with a rigidity and position dependent(increasing with galactic radius r and distance from the disk z) diffusion coefficient as given
by equation 1 and diffusive re-acceleration with Alven speed va .
 δl

RD(r, z, R) = D0 max e(r−rn )/rs , 1 max e(z−zn )/zs , 1R0R1+R bl δls−δ
l!s l

R1+R bhh δ−δsh!−sh. (1)The parameters of the model were determined by comparing nuclei spectra calculated withDRAGON [7] to experimental proton [8–10], helium [11–13] (including low-energy Voyager
data [14]), carbon, oxygen spectra [15], and B/C [16, 17], 3 He/4 He [18] ratios. By a random
walk scan of the parameter space, the parameters listed in table 1, which fit the combined
nuclei spectra data with χ 2 /ndof < 1, were found. Using these parameters, the propagation of
the DM annihilation/decay spectra obtained with PYTHIA was calculated in DRAGON, takinga NFW halo profile and a local DM density of 0.3 GeV/cm3 .

2.2

Astrophysical base model and limit calculation

Limit calculation is based on the reduction of the fit quality when adding the DM signal toa purely astrophysical base model. In the base model, the primary electron spectrum fromdistant SNR is represented by a power-law function with a low-energy spectral break and exponential cut-off. The nearby SNRs and pulsars are treated as individual point sources withfree source-spectrum parameters, with the propagated spectrum calculated following ref. [19].
Position and age of the point sources are taken from the Green (SNR) [20] and ATNF (pulsar) [21] catalogs. The secondary particle fluxes are taken from DRAGON nuclei spectra calculations with a free re-scale parameter. To the fit of this model to the CALET and AMS-02
data as shown in fig. 1, the flux from DM annihilation/decay is added with a scale-factor increased in iteratively smaller steps under readjustment of all free parameters. The relative
limit is set where χ 2 increases by 3.841 from the base model, disfavoring the addition of DM
at 95% CL, while an absolute limit can be set where χ 2 exceeds the 95% CL threshold forthe fit’s number of degrees of freedom, excluding the model including the DM flux. Examples are shown in fig. 2. The base model is over-fitted (χ 2 /ndof « 1), thus only the absolute
limit should be considered conservative. However, the reliability of the relative limit may beincreased by studying a variation of background model cases giving a good fit (χ 2 /ndof ≈ 1)
and taking the worst limit. To this end, the fixed cut-off energy parameters in the base model
were varied, for the parameterized distant SNR spectrum between [0.5, 1, 2] TeV and for the035.2

SciPost Phys. Proc. 12, 035 (2023)

Figure 1: Base model fit with contributions of individual astrophysical sources shown.

Figure 2: Left: Relative limit fit for 10 TeV DM annihilation to e+ +e− , for explanationof lines representing the background, see legend of fig. 1. Right: Absolute limit fit.
near SNR source spectrum between [10,20,50,100] TeV. Furthermore, two values of 3.75 µG
and 7.50 µG were used for the turbulent magnetic field strength. It was found that indeed
the relative limit varies with the background model parameter choices, but the absolute limit
is nearly constant.

3Limits on dark matter annihilation and decay parameters

The obtained limits on the annihilation cross-section are presented in fig. 3, top panel, with acomparison to limits from γ-ray observation of dwarf galaxies with VERITAS [22] and FermiLAT [23]. The limits on DM lifetime (fig .3, middle panel) are comparable to the most conservative EGRB limits from [24] which assume no astrophysical background, however based on
specific astrophysical background models much stricter limits of O(1028 s) have been published(e.g. ref [25]). In addition, limits on the lifetime of topological defect DM (Skyrmions [26])decaying through a π+lepton channel [27] are shown in the bottom panel of fig. 3.

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SciPost Phys. Proc. 12, 035 (2023)

Figure 3: Top: 95% CL limits on 〈σv〉 as a function of DM mass. Middle: 95% CLlimits on DM lifetime as a function of DM mass for generic decay channels. Bottom:
95% CL limits on DM lifetime as a function of DM mass for π+lepton decay channels.

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SciPost Phys. Proc. 12, 035 (2023)

4Conclusions

From CALET all-electron and AMS-02 positron-only data, limits on DM lifetime (annihilationcross-section) have been calculated up to a DM mass of 100 TeV (50 TeV), which are comparable and complementing those from other messengers such as γ-rays and neutrinos.

Acknowledgments
The author gratefully acknowledges the support of the CALET collaboration team in making
the preliminary results published at ICRC2021 available for use in this work.
Funding information

Supported by JSPS KAKENHI No. JP21H05463 and No. JP21K03604.

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