Revisiting GeV-scale annihilating dark matter with the AMS-02 positron fraction Iason Krommydas1 2and Ilias Cholis3y 1Physics Division National Technical University of Athens Zografou Athens 15780 Greece

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Revisiting GeV-scale annihilating dark matter with the AMS-02 positron fraction

Iason Krommydas1, 2, ∗and Ilias Cholis3, †

1Physics Division, National Technical University of Athens, Zografou, Athens, 15780, Greece

2Department of Physics and Astronomy, Rice University, Houston, Texas, 77005, USA

3Department of Physics, Oakland University, Rochester, Michigan, 48309, USA

(Dated: October 12, 2022)

Antimatter cosmic-rays are used to probe new phenomena in physics, including dark matter an-

nihilation. We use the cosmic-ray positron fraction spectrum by the Alpha Magnetic Spectrometer,

to search for such an annihilation signal in the Galaxy. We focus on dark matter with mass between

5 and 120 GeV, producing high-energy electrons and positrons. In these cosmic-ray energies the

interplay of multiple astrophysical sources and phenomena, makes this search highly sensitive to

the underlying astrophysical background assumptions. We use a vast public library of astrophysical

models for the cosmic-ray positron fraction background, to derive robust upper limits on the dark

matter’s annihilation cross section for a number of annihilation channels. This library accounts for

diﬀerent types of cosmic-ray sources and uncertainties on their distribution in space and time. Also,

it accounts for uncertainties on those sources’ output, their injected into the interstellar medium

cosmic-ray spectra and for uncertainties on cosmic-ray propagation. For any given dark matter

particle mass and annihilation channel, upper limits on the annihilation cross section are given by

bands that stretch a full order of magnitude in its value. Our work provides weaker limits compared

to earlier results, that are however robust to all the relevant astrophysical uncertainties. Between

5 and 15 GeV, we ﬁnd indications for a possible excess ﬂux of cosmic-ray electrons and positrons.

That excess is found for most, but not all of our astrophysical background parameter space, and

its signiﬁcance can vary appreciably. Further scrutiny is necessary to improve the understanding

of these lower energy cosmic rays. Finally, we note that even if an excess signal is found in these

energies, the current background uncertainties do not allow us to accurately deduce its underlying

particle properties.

I. INTRODUCTION

Dark matter has been observed in a variety of as-

trophysical systems through its gravitational impact, in

scales from as small as dwarf galaxies to as large as

colliding galaxy clusters [1–13]. In addition, through

detailed measurements of the cosmic microwave back-

ground (CMB), we know that dark matter accounts for

about 27% of the critical density in the universe, corre-

sponding to about 85% of its matter [14–18]. Further-

more, accurate measurements probing Big Bang nucle-

osynthesis, the evolution of structures in the universe,

observations on the mass distribution of diﬀerent grav-

itationally collapsed structures and observations of the

Layman-alpha forest, set a strong preference for what is

referred to as “cold dark matter” [11, 14, 16, 19–29]. How-

ever, the nature of dark matter remains a puzzle, with

its mass ranging from 10−22 eV to as large as O(10)M

[30–54].

One class of dark matter candidates includes weakly

interacting massive particles (WIMPs), that were ther-

mally produced in the early universe through approx-

imately electroweak scale interactions with Standard

Model particles and a mass very approximately of O(10)

GeV - O(10) TeV [45, 47, 55–57]. In this paper, we fo-

cus on the lower end of that mass range, probing dark

∗ik23@rice.edu, ORCID: orcid.org/0000-0001-7849-8863

†cholis@oakland.edu, ORCID: orcid.org/0000-0002-3805-6478

matter with mass from 5 GeV and up to 120 GeV. For

such dark matter particles we constrain the annihilation

cross section they may have to leptons and to bottom

quarks. Bottom quarks would be the prominent anni-

hilation product for dark matter in that mass range,

if dark matter couples to the Higgs boson [58]. These

dark matter masses are interesting to search for, also be-

cause excesses in gamma-rays [59–70] and in cosmic-ray

antiprotons [71–74] have been claimed to be compatible

with WIMPs in that mass range. We use the most re-

cent measurements of the cosmic-ray positron fraction,

i.e. the ratio of the positron ﬂux over the electron plus

positron ﬂux, versus those particle’s energy; made by the

Alpha Magnetic Spectrometer (AMS-02 ) onboard the In-

ternational Space Station [75, 76].

Over the last decades antimatter cosmic-ray measure-

ments have been used to probe possible dark matter sig-

nals [77–81]. Such cosmic rays are produced from rare

inelastic collisions between cosmic-ray nuclei with the in-

terstellar medium (ISM) gas and are commonly referred

to as secondary cosmic rays. Primary cosmic rays are

instead accelerated in supernova remnant (SNR) envi-

ronments. A hypothetical dark matter particle in the

GeV-TeV mass scale annihilating (or decaying) and pro-

ducing among other byproducts antimatter cosmic rays,

may give a detectable additional ﬂux in measurements of

such particles. This is the focus of this work. Dark mat-

ter particles producing cosmic-ray positrons could cause

a feature in the positron ﬂux and positron fraction. The

qualities of such a feature, depend on the dark matter

particle’s mass, annihilation cross section and channel,

arXiv:2210.04903v1 [astro-ph.HE] 10 Oct 2022

i.e. the ﬁst generation of Standard Model particles pro-

duced from the annihilation event. Dark matter origi-

nated features may be as small as a localized in energy,

to give a few %bump on the positron fraction, or as

wide in energy and large in amplitude as the entire rising

above 5 GeV positron fraction spectrum.

Inversely, using the AMS-02 positron fraction’s rela-

tively smooth spectrum, one can set upper limits on the

annihilation cross section of dark matter particles. That

is done for a range of masses and a variety of annihilation

channels [82–84]. This is the main aim of this paper.

The origin of the rising above 5 GeV positron frac-

tion spectrum that was ﬁrst measured by the Payload

for Antimatter Matter Exploration and Light-nuclei As-

trophysics (PAMELA) satellite [85, 86], then conﬁrmed

by the Fermi-LAT [87] and further measured with an un-

precedented accuracy by AMS-02 [75, 88, 89], has been

a subject of great interest. One explanation for the ad-

ditional positron ﬂux, is relatively close-by “young” and

“middle-aged” Milky Way pulsars that during their pul-

sar wind nebula (PWN) phase converted an apprecia-

ble fraction (O(0.01) −O(0.1)) of their rotational energy

into high-energy cosmic-ray electrons (e−) and positrons

(e+) [90–108]. Another explanation is Milky Way SNRs,

that in their ﬁrst O(10) kyr produced and accelerated

secondary cosmic rays including positrons [109–117] (see

however [118–121]). Furthermore, detailed modiﬁcations

on the distribution of cosmic-ray sources and the prop-

agation of cosmic rays through the ISM [122–124] and

annihilating or decaying dark matter models have been

explored to explain the positron fraction measurement

[101, 125–144]. We assume in this work that the over-

all rise of the positron fraction, shown with its AMS-02

measurement in Fig. 1, is not caused by dark matter, but

instead from a more conventional source; a population of

Milky Way pulsars.

Pulsars are localized sources of cosmic-ray electrons

and positrons. Due to their rapid spin-down, pulsars

convert their initial rotational energy into cosmic-ray e±

and subsequently release those e±into the ISM in a com-

paratively short amount of time1. That makes pulsars

cosmic-ray e±sources approximately localized both in

space and time. High-energy e±lose rapidly their en-

ergy through synchrotron radiation and inverse Comp-

ton scattering as they interact with the ISM and before

reaching us. That results in an upper energy cut-oﬀ, on

the e±spectra from individual pulsars [95, 96, 98]. In

turn, a population of pulsars that could collectively ex-

plain the rising positron fraction spectrum, could also

give spectral features at the higher energies where the

number of contributing pulsars is reduced to the point

1The time required for most cosmic-ray e±produced around the

PWN environments to be released into the ISM, is at least an or-

der of magnitude smaller than the propagation time required for

these cosmic rays to reach our detectors [96]. The only exception

would be a very close (O(10) pc) pulsar (see however [145]).

of individual sources dominating narrow parts of that

spectrum [96, 98, 104, 108]. Such features can then be

searched for as in [146]. Similar arguments can be made

for PWNe. However, their expected higher energy cut-

oﬀs are less sharp by comparison [117]. We use modeled

populations of Milky Way pulsars produced in our ear-

lier work of [108]. In Ref. [108], a library of publicly

available pulsar population models was created that is in

agreement with the cosmic-ray e±ﬂux spectral measure-

ments from AMS-02 [75, 76], the CALorimetric Electron

Telescope (CALET ) [147] and the DArk Matter Parti-

cle Explorer (DAMPE ) telescope [148], as well as the

AMS-02 positron fraction spectrum [89]. As the pulsar’s

contribution to the positron fraction spectrum is not per-

fectly smooth and with uncertainties, we use a library of

models instead of just one generic parameterization. As

we will show, we derive more conservative and more real-

istic limits on the dark matter annihilation cross section.

In Section II, we discuss the general methodology of

our approach, including the observations that we use, the

astrophysical background modeling of the positron frac-

tion and the statistical treatment followed in ﬁtting the

data. We also create mock positron fraction data to an-

swer the question on the robustness of the positron frac-

tion measurement as a means to study the particle prop-

erties of dark matter. Then in Section III, we present the

results of searching for a possible dark matter signal in

the positron fraction. We ﬁnd that the limits on the anni-

hilation cross section are not well deﬁned. That is due to

the underlying astrophysical background uncertainties.

The annihilation cross section limits have a width that is

at least one order of magnitude in the mas range of 5 to

120 GeV that we study. In addition, we ﬁnd indications

for a possible excess of 5-15 GeV in cosmic-ray energy e±.

That excess while compatible with a WIMP-scale dark

matter signal, has a signiﬁcance that varies with the as-

trophysical background modeling and is not claimed to

be a robust one. Further scrutiny will be required as

cosmic-ray physics in that energy range improve with fu-

ture observations. Moreover, in Section III, we perform

our mock positron fraction analysis. We ﬁnd that if dark

matter contributes to the positron fraction spectrum at

the few percent level within an range spanning several

AMS-02 energy bins, such an excess signal can not be

absorbed by the astrophysical background uncertainties.

However, identifying the exact particle properties of the

dark matter particle responsible for that excess is a a

more model-dependent inquiry. Finally, in Section IV,

we give our conclusions and discuss connections to other

types of dark matter searches as well as future prospects.

II. METHODOLOGY

In this section, we describe the energy range of the

AMS-02 positron fraction (e+/(e++e−)) measurement

used in this analysis. We also explain how we construct

our background astrophysical models, which are ﬁtted

to the AMS-02 positron fraction. We then describe the

statistical analysis performed to set upper limits on dark

matter particles annihilating, giving a contribution to the

positron fraction. Finally, we construct positron frac-

tion mock data based on the AMS-02 sensitivity to test

whether a dark matter signal would be detectable; and

how accurately we would be able to determine the dark

matter mass, annihilation channel and cross section by

our analysis.

We use astrophysical realizations created within

Ref. [108], as a base to construct our background models

for the positron fraction. We take the e−and e+ﬂuxes

calculated from these realizations and add a dark matter

contribution. Using these ﬂuxes we perform ﬁts, where

we search for a potential dark matter component to the

positron fraction and compute the 95% conﬁdence level

upper limits on the dark matter annihilation cross sec-

tion as a function of mass. These ﬁts are performed using

a library of astrophysical/background realizations.

A. Cosmic-ray data

We use the recently published AMS-02 positron frac-

tion measurement from [75, 76] taken between May 2011

and November 2017. In Ref. [108], we found that the

positron fraction spectrum sets stronger constraints on

sources of cosmic-ray positrons, compared to the cosmic-

ray positron ﬂux spectrum. This is due to its smaller

errors. Some systematic errors cancel when calculating

cosmic-ray fractions versus cosmic-ray ﬂuxes. We ignore

the positron fraction measurement below 5 GeV, as that

energy range is strongly aﬀected by solar modulation and

any dark matter annihilation signal from an approxi-

mately thermal relic would be hidden within the solar

modulation modeling uncertainties. Given that there is

no publicly released covariance matrix by the AMS-02

collaboration on that measurement, we treat the diﬀer-

ent energy bins as uncorrelated and add the systematic

and statistical errors in quadrature.

B. Modeling the background to the dark matter

contribution on the positron fraction

In this work, as signal we refer to a potential anni-

hilating dark matter contribution on the positron frac-

tion spectrum. As background we refer to all other as-

trophysical sources contributing to the positron fraction.

Our modeling of the astrophysical background is based

on Ref. [108]. These astrophysical realizations contain

e−ﬂuxes from primary sources i.e. supernova remnants,

secondary e±produced from inelastic collisions of pri-

mary cosmic ray nuclei with the ISM gas and e±from

Milky Way pulsars. The main goal of Ref. [108], was to

study the properties of Milky Way pulsars. Thus, a large

number of astrophysical realizations was created. Those

realizations accounted for a sequence of astrophysical un-

certainties, as the stochastic nature of the neutron stars’

birth in time and location, the stochasticity in the initial

spin-down power of pulsars and their subsequent time

evolution. Also Ref. [108], studied the fraction of pul-

sar spin-down power into cosmic-ray e±and how these

injected cosmic rays propagate in the ISM and the He-

liosphere.

In this work we start with the astrophysi-

cal/background realizations from Ref. [108] that

were shown to be in good agreement with the AMS-02

positron fraction [75, 76], the e+ﬂux [75, 76], the

total e++e−ﬂux [75, 89], and also the total e++e−

ﬂuxes from DAMPE [149] and CALET [147]. The

quality of the ﬁt is heavily impacted by the lowest

energies of the positron fraction where the errors are the

smallest. Adding a dark matter e±ﬂux component that

contributes at these low energies can drastically aﬀect

the quality of the ﬁt. Thus, we include in our analysis

astrophysical/background realizations from Ref. [108]

that have a χ2/ndof <2.2in the positron fraction. This

results in a total of 1020 astrophysical/background sim-

ulations, to account for all the background uncertainties.

Some of those realizations in combination with a dark

matter component may end up giving a much better

quality of ﬁt to the AMS-02 data and can explain the e±

observations at energies where there is no contribution

from dark matter.

For the dark matter contribution, we assume a local

dark matter density of 0.4 GeV/cm3[6, 8, 9, 150], set at

8.5 kiloparsec (kpc) from the galactic center. We take

the dark matter halo in the Galaxy to follow an Navarro-

Frenk-White (NFW) proﬁle [151], with a characteristic

radius of 20 kpc. We consider four simpliﬁed dark matter

annihilation channels. These are: χχ →e+e−,χχ →

µ+µ−,χχ →τ+τ−and χχ →b¯

b. The annihilation cross

section is set to be free in our analysis. We focus on low

dark matter masses mχbetween 5 and 50 GeV for the

e+e−and the µ+µ−channels, between 5 and 80 GeV for

the τ+τ−channel and between 10 and 120 GeV for the

b¯

bone.

We calculate the injected e±production spectra from

these dark matter annihilations using PPPC4DMID[152]

and calculate the ﬁnal e−and e+spectra at the loca-

tion of the Sun using GALPROP v54 [153, 154]. The dark

matter e±spectra are propagated through the ISM us-

ing the same 12 alternative propagation models as those

deﬁned in Table II of Ref. [108]. Every time that we

test for a potential dark matter signal in the AMS-02

data, we make sure that the hypothetical dark matter

e±ﬂux, is evaluated under the same propagation condi-

tions as its relevant astrophysical background. The 12

ISM models account for diﬀerent choices on the thick-

ness of the zone within which cosmic rays diﬀuse before

escaping the Milky Way, how that diﬀusion depends on

the cosmic-ray energy and ﬁnally for the energy losses of

the cosmic-ray e±within the local volume of the Milky

Way. This combination of ISM models encompasses the

relevant astrophysical uncertainties within O(kpc)from

the Sun [70, 81, 155]. For more details we refer the reader

to Section II.E of Ref. [108]. In each astrophysical back-

ground, we add a dark matter contribution by choosing a

speciﬁc annihilation channel and a speciﬁc mass and con-

struct our ﬁnal astrophysical+dark matter model. Given

the diﬀerent choices for the particle dark matter proper-

ties, we simulate 64 diﬀerent combinations of annihila-

tion channel and mass for each of the 1020 astrophysical

backgrounds (65280 ﬁts in total). The annihilation cross-

section is left as a free parameter to be set by the ﬁt to

the data. These ﬁnal ISM e−and e+spectra include

the contribution of primary cosmic rays, secondary cos-

mic rays, cosmic rays from pulsars and from dark matter

annihilations. We also propagate each of the ISM cosmic-

ray spectra to the location of the Earth and account for

solar modulation. That is done following the prescrip-

tion of [156], where the modeling of the time, charge

and energy-dependence of solar modulation is accounted

for by two ﬁtting parameters, set within a range sug-

gested by [157, 158]. That same procedure was followed

in Ref. [108]. The associated Bartels’ Rotation numbers

-relevant for the modeling of solar modulation eﬀects- for

the data-taking era are 2426-2514.

C. Statistical analysis

When we ﬁt the astrophysical/background models to

the AMS-02 positron fraction we have seven parameters.

These account for the cosmic-ray primary e−ﬂux, the

secondary e±ﬂux and the pulsar e±ﬂux normalizations.

We include two parameters to allow for a spectral soften-

ing/hardening of the cosmic-ray primary and secondary

spectra; and two more for the solar modulation model-

ing. Once adding the dark matter component we have

an additional (eighth) parameter, that is directly pro-

portional to the ﬁtted annihilation cross section. For a

given astrophysical background, once adding a potential

dark matter component in the ﬁtting procedure, we al-

lowed the other seven parameters to be free within 50%

of their best-ﬁt value achieved in the background only ﬁt.

In Appendix A we give the full parameter space tested

in our astrophysical &dark matter models and its sub-

sequent minimization procedure.

We perform a χ2minimization; and use a combina-

tion of SciPy’s [159] least_squares routine from the

optimize module and iminuit [160, 161]. We found

that the fastest minimization is achieved by performing a

few minimization steps with the least_squares routine

with high tolerance and ﬁnishing the minimization with

iminuit.

In Fig. 1, we show the ﬁt to the positron fraction

for one of our background models with a dark mat-

ter component included. For the dark matter we have

taken, mχ= 25 GeV and the annihilation channel to be

χχ →b¯

b. One can see all the relevant contributions from

primary e−, secondary e+, pulsar e+, and e+originating

from dark matter. The background only hypothesis gave

10 100 1000

0.01

0.10

0.50

e+/(e++e−)

101

102

103

104

E3dN/dE [GeV2m−2s−1sr−1]

10 100 1000

E[GeV]

−4

−2

Pull

AMS-02 6.5 yrs positron fraction

Astrophysical model + 25 GeV dark matter, χχ →b¯

b(χ2/ndof =1.15)

Primary e−(×0.5)

Secondary e+(×10)

Pulsar e+(×10)

Dark matter e+(×500)

FIG. 1. The ﬁt of a pulsar model from Ref. [108], to the AMS-

02 positron fraction after including the contribution from 25

GeV dark matter that annihilates to b¯

b. On the right y-axis in

units of E3dN/dE where dN/dE is the diﬀerential cosmic-ray

ﬂux, we show the solar modulated contribution from primary

e−, secondary e+, pulsar e+, and e+ﬂuxes originating from

dark matter annihilation scaled by some appropriate arbitrary

factors from their best ﬁt normalization to make them well-

visible. The secondary, pulsar and dark matter e−ﬂuxes are

not shown since they are only slightly diﬀerent due to solar

modulation. We also show the pull ((data −model)/σdata)

distribution of the ﬁt at the bottom.

for this model a χ2

DM=0/ndof = 2.11; while after includ-

ing dark matter we got a χ2

DM/ndof = 1.15.ndof is the

number of degrees of freedom. The pull of the ﬁt, which

is (data −model)/σdata is also shown at the bottom of

the ﬁgure.

The dark matter mass range that we study in this

work, contributes at the lower energies and has no ef-

fect on the higher energies where the spectrum is dom-

inated by the local pulsar population. Also, other than

the χχ →e+e−annihilation channel, the dark matter

component cannot produce sharp peaks in the positron

fraction that could explain features like the one we iden-

tiﬁed in Ref. [108] and studied in Ref. [162] at ∼12 GeV.

We ﬁnd that statement to be true for every astrophysi-

cal/background model.

In order to derive upper limits on the dark matter an-

nihilation cross section, presented as hσvi, we use a like-

lihood ratio test. The null hypothesis is that there is

no dark matter contribution and we just have the astro-

physical background, i.e. seven ﬁtting parameters with

hσvi= 0. The alternative hypothesis is that there is some

contribution from dark matter annihilation with annihi-

lation cross section (times velocity, thermally averaged)

hσvi, i.e. eight ﬁtting parameters. We rely on Wilks’

theorem [163], and use the statistic LR =−2 log Λ(=χ2

diﬀerence), with Λthe likelihood ratio of the null (back-

ground only) hypothesis over the alternative dark matter

+ background hypothesis. This is distributed according

to a χ2

ν-distribution with νdegrees of freedom, where νis

the diﬀerence of ﬁtting parameters between the two hy-

potheses models. In our case, we have ν= 1. However,

that would give a naive estimate of the p-value since the

null hypothesis corresponds to the case hσvi= 0, i.e. it

lies on a boundary of our parameter space. This problem

can be overcome by using Chernoﬀ’s theorem [164]. The

LR follows a 1

2δ(x)+ 1

2χ2distribution (half chi-square dis-

tribution) with one degree of freedom [165]. This means

that the p-value is reduced by half compared to the naive

estimate.

Following the standard convention in the literature, we

can deduce 95% upper limits on hσvifor each astrophys-

ical background at a ﬁxed annihilation channel and dark

matter mass. This is done by scanning over hσvi, com-

puting the χ2proﬁle and ﬁnding at which value of hσvi

we have χ2

DM =χ2

DM=0 + 2.71. This corresponds to the

95% upper limit of a half chi-square distribution with one

degree of freedom. Because we have multiple masses, we

essentially have a 2D grid of masses and cross sections

where we compute the χ2proﬁle and draw the contour

where the χ2

DM increased by 2.71 from χ2

DM=0. At each

point of the grid the rest of the background nuisance

parameters are optimized such that the χ2is minimum.

This contour is the 95% upper limit on the dark matter

annihilation cross section as a function of the mass. This

can be done for each annihilation channel and for each

pulsar background, resulting in each background giving

a diﬀerent upper limit. We report the combination of

those upper limits.

D. Mock data

In this paper, we produce mock data of the AMS-02

positron fraction. We do that to test whether a dark

matter contribution in the positron fraction would be

detectable and with its properties (mass, annihilation

cross section and channel) correctly identiﬁed. We pro-

duce these mock data by taking existing backgrounds and

adding a ﬂux component from dark matter of speciﬁc

mass, annihilation channel and cross section. We then

calculate the positron fraction spectra that the AMS-02

would observe. These mock spectra include only statis-

tical errors. We treat these mock spectra as we treated

the AMS-02 measurement and scan them with our back-

ground+dark matter models to see if we can recover the

original mass, annihilation channel and cross section. By

keeping only the statistical errors we are optimistic on

the ability of the positron fraction measurement to help

us probe the properties of a dark matter signal.

For the mock positron fraction spectra we use two an-

nihilation channels: χχ →µ+µ−and χχ →τ+τ−; and

test four dark matter mass and annihilation cross section

combinations. For the χχ →µ+µ−channel we have,

(a) mχ= 15 GeV and hσvi= 2 ×10−26 cm3s−1,

(b) mχ= 15 GeV and hσvi= 5 ×10−27 cm3s−1,

10 100 1000

0.01

0.10

0.50

e+/(e++e−)

101

102

103

104

E3dN/dE [GeV2m−2s−1sr−1]

10 100 1000

E[GeV]

−4

−2

Pull

Mock positron fraction with mχ=30 GeV , hσvi=5×10−27 cm3s−1and χχ →τ+τ−

AMS-02 6.5 yrs positron fraction

Astrophysical model + dark matter ﬁt (χ2/ndof =0.87)

Total e−

Total e+(×4)

Dark matter e+(×2000)

FIG. 2. A mock positron fraction created by the combination

of an astrophysical background with a dark matter signal.

We chose an astrophysical background that without the dark

matter contribution gave a good ﬁt to the positron fraction

(χ2/ndof = 1.14). We add the contribution from a 30 GeV

dark matter particle that annihilates to τ+τ−with a cross

section of hσvi= 5 ×10−27 cm3s−1. We show an astrophysi-

cal background+dark matter model ﬁt to the mock positron

fraction and also the total e−,e+and e+originating from

dark matter ﬂuxes within that model in the green dashed,

blue dotted and orange dash-dotted lines with the units pro-

vided by the right y-axis. At the bottom, we show the pull

distribution of the ﬁt. We also show with faint grey the real

AMS-02 positron fraction measurements.

(d) mχ= 30 GeV and hσvi= 5 ×10−28 cm3s−1.

For the χχ →τ+τ−channel we have,

(a) mχ= 15 GeV and hσvi= 1 ×10−25 cm3s−1,

(b) mχ= 15 GeV and hσvi= 2 ×10−26 cm3s−1,

(d) mχ= 30 GeV and hσvi= 5 ×10−27 cm3s−1.

We use two astrophysical backgrounds to create these

mock data, one for each channel. These two backgrounds

are in agreement with the AMS-02 e+ﬂux, positron frac-

tion and total e++e−ﬂux measurements, and also with

the DAMPE and CALET total e++e−ﬂux measure-

ments.

In Fig. 2, we show an example of such a mock positron

fraction where there is a contribution from 30 GeV dark

matter particles annihilating to τ+τ−with an cross sec-

tion of hσvi= 5 ×10−27 cm3s−1. We also show a ﬁt to

that mock positron fraction by one of our models and the

original AMS-02 data with a fainter color for compari-

son to the mock ones. The errors of the mock positron

fraction are much smaller as we only consider statistical

uncertainties.

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RevisitingGeV-scaleannihilatingdarkmatterwiththeAMS-02positronfractionIasonKrommydas1,2,andIliasCholis3,y1PhysicsDivision,NationalTechnicalUniversityofAthens,Zografou,Athens,15780,Greece2DepartmentofPhysicsandAstronomy,RiceUniversity,Houston,Texas,77005,USA3DepartmentofPhysics,OaklandUniversity,Roc...

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Revisiting GeV-scale annihilating dark matter with the AMS-02 positron fraction Iason Krommydas1 2and Ilias Cholis3y 1Physics Division National Technical University of Athens Zografou Athens 15780 Greece.pdf

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Revisiting GeV-scale annihilating dark matter with the AMS-02 positron fraction Iason Krommydas1 2and Ilias Cholis3y 1Physics Division National Technical University of Athens Zografou Athens 15780 Greece

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