Dark Matter Search in Space: Combined Analysis of Cosmic Ray Antiproton-to-Proton Flux Ratio and Positron Flux Measured by AMS-02

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by  Jie Feng

Dark Matter Search in Space: Combined Analysis of Cosmic Ray
Antiproton-to-Proton Flux Ratio and Positron Flux Measured by AMS-02
Jie Feng and Hong-Hao Zhang∗
School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
Dark matter search in space has been carried out for many years. Measurements of cosmic ray
photons, charged antiparticles and neutrinos are useful tools for dark matter indirect search. The
antiparticle energy spectra of cosmic rays have several exciting features such as the unexpected
positron excess at E ∼ 10 – 500GeV and the remarkably flattening antiproton/proton at E ∼ 60–
450GeVpreciselymeasuredbytheAMS-02experiment,whichcannotbeexplainedsimultaneously
by secondary production in interstellar medium. In this work, we report a combined analysis of
cosmic ray antiproton and positron spectra arising from dark matter on the top of a secondary
production in a spatial-dependent propagation model. We discuss the systematics from antiproton
productioncrosssectionusingthetwolatestMonteCarlogenerators,i.e. EPOSLHCandQGSJET-
7
II-04m, respectively. We compare their results. In the case of EPOS LHC, we find that the dark
1
matter pair annihilating into τ leptons channel with 100% branching ratio is the only possible one
0
channel scenario to explain data. On the other hand, there is not a single possible channel in the
2
caseofQGSJET-II-04m. Wealsoproposepossibletwo-channelscenariosbasedonthesetwoMonte

n Carlo generators.
a
J

2 I. INTRODUCTION straight lines, charged particles are difficult to be traced
1 backtotheirsourcesduetothecomplexmagneticturbu-
After nearly one century of physics investigation, the lence in the Galaxy. To constrain secondary production
]
h searchfordarkmatterisstillongoing. Thissearchiscar- contribution, one also need to study the CR B/C ele-
p ried out in three complementary ways: dark matter pro- mental ratio, which can be measured by PAMELA and
- duction in colliders, direct detection with underground AMS-02 in space, or by or the Advanced Thin Ionization
p
e instrumentsandindirectdetectionincosmicrays(CRs). Calorimeter (ATIC-2) and the Cosmic Ray Energetics
h Dark matter annihilation or decay may produce elemen- and Mass (CREAM) on balloon. Besides, systematics
[ tary particles, including neutral particles (photons (γ) from solar modulation and antiparticle production cross

and neutrinos) and charged ones ( positrons (e+) and section should also be studied [8]. Ref. [8] showed that
2
v antiprotons (p¯) ). An impressive amount of dark mat- the excess of antiprotons was not significant but that of
3 ter information is being achieved by γ-ray data com- positronswassolidgivenbythecurrentunderstandingof
6 ing from spacebased or groundbased telescopes such as systematics. Some studies were carried out to interpret
2 Fermi’s Large Area Telescope (Fermi-LAT) [1] or High the positron excess that were consistent with a smooth
2 EnergyStereoscopicSystem(H.E.S.S)[2]. Besides,valu- B/C spectrum. Unless the sources accelerating C-N-O
0 able pieces of dark matter information from neutrinos is are not the same as those accelerating helium or protons
.
1 being collected by IceCube [3]. At the same time, an [9], it seems unavoidable to introduce extra source com-
0 increase in the accuracy of charged elementary CR par- ponentssuchasdarkmatterparticleannihilation[10–14],
7 ticles spectra is driving us to a deeper understanding of or e± pair production mechanisms inside nearby pulsars
1
thefundamentalphysicsprocessesintheGalaxy. Thanks [13–21]. Observations by Fermi-LAT [22] indicated that
:
v tothenewgenerationdetectionexperiments,suchasthe γ-rays of pulsars were produced by leptons rather than
Xi Payload for Antimatter Matter Exploration and Light- hadrons, which can basically exclude the possibility of
nuclei Astrophysics (PAMELA) or the Alpha Magnetic pulsars to be high energy antiproton sources.
r
a Spectrometer (AMS-02) in space, we are able to read Numerous analyses have been performed to interpre-
thedarkmatterinformationinchargedparticlechannels. tateprecisep¯/pspectrummeasuredbyAMS-02indepen-
TheAMS-02collaborationhasnowpublishedtheprecise dentofe+ withdarkmatterscenarios[23–26]. Thereare
p¯/p ratio measurement between ∼0.5 and ∼450GeV of some also some combined analysis of PAMELA p¯, which
kinetic energy, showing that the ratio above ∼60GeV haslargeruncertainties, andAMS-02e+ [27]. Inthispa-
experiences a remarkably flat behaviour [4]. PAMELA per, we perform a combined analysis of p¯/p and e+ in
hasalsopublishedsimilarresultsbutwithlessstatistical dark matter scenarios. We can reduce some uncertainty
significance [5]. Together with the resent e+ flux data from normalization by analyzing p¯/p instead of p¯ spec-
[6, 7], which shows a surprising excess above ∼10GeV, trum because p are p¯progenitors. For a similar reason,
those results give us a hint of extra sources. we avoid injection uncertainties of e− by analyzing e+
Unlike neutral particles that travel almost along instead of e+/(e++e−). Our basic idea is that the cross
section and the mass of dark matter annihilation esti-
mated from e+ data should be consistent with that from
p¯ data. Besides, we notice that antiproton production
∗ [email protected] cross section introduces major systematic uncertainties
2
inp¯/pspectrum[8,28]. Followingtheimplementationof physical background of antiparticles, we adopt a spatial-
the cross section from MC generators in [8], we present dependent model of CR diffusion [31, 32], which can
our study with EPOS LHC and QGSJET-II-04m, which explain the high-energy departures from the standard
weretunedagainstthelatestLHCexperimentaldataand universal power-law expectations in p and He spectra
reproduce the p¯production well [8, 25]. We quantify the observed by PAMELA [33] and confirmed by AMS-02
agreement between model prediction and data with “p- [34, 35] while the convectional models failed to do so
value”method. Wefindthatχχ→τ+τ−istheonlypos- [36]. In this scenario, the scaling index δ(z) = δ in
0
siblechannelwith100%branchingratiobasedonthean- the region of |z| < ξL (inner halo) and δ(z) = δ +∆
0
tiproton background calculated by EPOS LHC, while no when |z|≥ξL (outer halo) . The normalizations are D
0
channel is possible for QGSJET-II-04m. We also study fortheinnerhaloandχD fortheouter. Thereisacon-
0
the scenarios that dark matter decays into two channels, necting function of the type F(z) = (z/L)n to ensure a
which gives a larger p-value compared to the one chan- smooth transition of the parameters χ and ∆ across the
nel scenarios. Comparisons with the analysis of γ-ray two zones [37]. The injection spectral indices of all the
observation are also shown. nuclei whose z >1 all equal to ν, while that of proton is
Thispaperisorganizedasfollows. InSec.II,wepresent ν +∆ν. Our parameters are set as the best fit param-
our calculations. In Sec.IIA, we review briefly the p¯and eters L = 5.67 kpc, D = 1.92×1028cm2/s, δ = 0.15,
0 0
e+ from astro-physical sources as the background of our ∆ = 0.52, ξ = 0.15, χ = 0.36, δν = 0.096 and ν = 2.27
analysis. InSec.IIB,weintroducep¯ande+fluxproduced in [8], where we take the 1-σ and 2-σ error bands. We
at dark matter annihilation. In Sec.IIC, it is presented use DRAGON package to solve the transport equation [38].
our definition of a good fit. In Sec. III, we show our Antiproton production cross section systematic is one
resultsanddiscussionincludingoneannihilationchannel of the main uncertainties of the astro-physical back-
in Sec. IIIA and two annihilation channels in Sec. IIIB. ground. As has been studied in [8, 39], two of the
Finally, the conclusion is drawn in Sec. IV. mostadvancedMonteCarlo(MC)generatorsEPOSLHC
[40] and QGSJET-II-04m [39] can reproduce the recent
ground experiments well. However, due to the scarcity
II. CALCULATIONS of the anti-neutron production data, we have no way
to test anti-neutron production cross sections. EPOS
A. Astro-physical background LHC predicts the anti-neutron/anti-proton ratio varies
between 1.2 and 2.0, while QGSJET-II-04m shows it is
In convectional CR propagation models, antiparticles close to 1 except near the production threshold. We be-
areonlyproducedincollisionsofhigh-energynucleiwith lieve the truth should be somewhere between these two
interstellar medium (ISM). The fluxs of their progeni- models, so we test the dark matter scenarios with the
tor nuclei and CR propagation process together deter- backgrounds predicted by them individually. Positron
mine the specta of antiparticles. The Galatic disk is production cross section is taken from a recent parame-
surrounded by a halo with half-thickness L. For each terization[41]. AsyoucanfindlatterinSec.III,positron
CR species, its propagation can be described by a two- production cross section is not a dominating component
dimensional transport equation: ofthetotaluncertainties, sincetheexcessofe+ fromthe
background is significant. So we do not discuss other e+
∂ψ ∂ cross section in this paper.
=Q+∇(cid:126) ·(D∇(cid:126)ψ)−ψΓ+ (E˙ψ), (1)
∂t ∂E Pulsars are also important sources which produce sec-
ondary positrons. Previous studies showed that it is
where ψ =ψ(E,r,z) is the number density as a function
better to explain positron spectrum with pulsar models
ofenergyandspacecoordinates,Γ=βcnσisthedestruc-
ratherthanwithdarkmattermodels[14]. Thisisdueto
tionrateinISM,withdensityn,atvelocityβcandcross
the fact that the profile of pulsar model has more degree
section σ. The source term Q includes a primary term,
of freedom than that of dark matter. For example, it
Q , and a secondary production term Q =(cid:80) Γspψ,
pri sec j j j is unavoidable to introduce at least three parameters in
from interaction of heavier j–type nuclei with rate Γsp.
j the pulsar fit, i.e., the cutoff energy, the injection spec-
The term E˙ = −dE describes ionization and Coulomb tral index and the normalization [21]. In dark matter
dt
losses, as well as radiative cooling of CR leptons. The scenarios, however, there are only two free parameters:
diffusioncoefficientistakenasD(p,z)=βD (R/R )δ(z), the mass of the dark matter m and the normalization
0 0 χ
where D shows its normalization, R≡pc/Ze is defined (i.e. thermally averaged annihilation cross section (cid:104)σv(cid:105)
0
asthemagneticrigidityandR isitsnormalizationrigid- in the case of annihilation, where σ is the annihilation
0
ity. δ(z) expresses the scaling index. cross section and v is the velocity, or τ which is the life-
Recent studies were done to get a set of injection and time in the case of decay [23]). The γ-ray spectrum of
propagation parameters which could simultaneously re- a single pulsar is preferred to be explained by a leptonic
produce a large set of nuclear data including proton model rather than hadronic one [22]. The spectral in-
and helium fluxes, the B/C elemental ratio, and the dex of γ-ray produced from pion-decay emission [42] of
10Be/9Be isotopic ratio [8, 13, 29, 30]. To assess astro- hadronicinteractionsshouldbeharderthanthatthrough
3
theInverse-Comptonscatteringbyleptonsapulsar. Ob- sourceterminthetransportequationeq.(1). Thediffer-
servation of RX J1713.7-3946 supports the latter one. ential fluxes of antimatter at production are Q (E) ∝
DM
One might easily explain the CR antiproton spectrum (ρ/m )2 in the case of annihilation and Q (E) ∝
χ DM
by dark matter and the positron by pulsar. In this way, (ρ/m )inthecaseofdecay[43]. Sincethefluxeshavethe
χ
there will be five free parameters so everything can be sameenergydependenceforthetwocasesandtheenergy
explained. However, this is not what we are going to do spectra at the position of the earth would be similar, we
in this paper. Since the parameters of pulsars are not discuss dark matter annihilation here as an example.
easy to be constrained, we do not consider contribution
of them into the astro-physical background.
C. Formalism of the statistical test method
B. The fluxes of anti-matter from dark matter We adopt a frequentist statistical test in this work.
annihilation
Generally speaking, for discovering dark matter, we de-
fine the null hypothesis, H , as the astrophysical back-
0
The CR anti-particle fluxes produced by dark mat- ground, which is to be tested against the alternative H
1
ter have been studied and collected in A Poor Particle that includes both astrophysical background and dark
Physicist Cookbook for Dark Matter Indirect Detection matter signal. For setting dark matter limits, we define
(PPPC) [43]. The authors calculated the results with H astheastrophysicalbackgroundplusdarkmattersig-
0
PYTHIAandHERWIGMonteCarlossotheyhadafeel- naltobetestedagainstthebackground-onlyhypothesis,
ing of the uncertainties. Historically, leptons and vector H . This work is in the former case. To quantify the
1
bosonsweretreatedasunpolarized. Andpartonshowers agreement between data and the predictions of H, we
were assumed not to emite W’s and Z’s. Under these compute the probability, the widely used “p-value” [48],
assumptions, p¯ will not be produced in leptonic chan-
(cid:90) ∞
nels. However, as is pointed out by [44], polarizations
p = f(t |θ)dt , (3)
θ θ θ
and electroweak corrections should be considered, which
tθ,obs
will modify e± spectra at low energies E << m and
χ
produce p¯in leptonic channels due to W/Z radiation. wheretθ istheχ2 normalizedbythenumberofdegreeof
We consider dark matter annihilation into the fol- freedom (n.d.f) for a given signal strength θ. tθ,obs is the
l(oτw+iτn−g)p,rliimghatryquchaarknsne(lqsq:¯),e+beo−tt,ommuoqnusar(kµs+µ(b−¯b)),atnaduoWns oofbster.ved one. f(tθ|θ) = √21πtθe−tθ/2 is the distribution
θ
bosons (WW¯) in order to compare this study with the
γ-ray observations [1]. As you can see latter in this pa-
per, qq¯, b¯b and WW¯ predict too many p¯but not enough III. RESULTS AND DISCUSSION
e+. In order to improve the model, we also study the
VV → 4e, VV → 4µ and VV → 4τ, where the an- A. dark matter annihilation into one channel
nihilation first goes into a new light boson V that will
later decay into a pair of leptons proposed by [45, 46]. We investigate the possibility to explain p¯and e+ by
These so-called “4-body” channels will not produce p¯. A one annihilation channel with 100% branching ratio. We
recent study proposed a “3-body” channel where dark study p¯/p spectrum instead of p¯ flux, since the uncer-
matter decays into a stable neutral particle and a pair of tainties of p¯and those of p are cancelled. To avoid the
super symmetry fermions [27], which is also interesting uncertainties of the e− injection spectra, we study e+
but more complex. Another recent work proposed a new flux. Toavoidsolarmodultionuncertainties,weusedata
“4-body” channel that dark matter annihilate into light above 30 GeV. We found that only χχ→τ+τ− channel
mediators that later decays into 2qq¯[26]. We do not dis- gives us a p-value greater than 10−5, with a normalized
cuss this case since it produces mostly p¯in its final state chisquare χ2/n.d.f. = 98.53/49 and p =3.52×10−5.
while we prefer more e+ in this study. We get the best fit values: m = 77m8χ+58 GeV and
We adopt the Navarro, Frenk and White (NFW) [47] χ −54
(cid:104)σv(cid:105)=269.14+24.99×10−26cm3/s. Otherchannelsareim-
profiletodescribethegalacticdistributionofdarkmatter −22.87
possible. To give a feeling of the goodness of the fit, we
in the Milky Way, which reads:
plot the calculated p¯/p and e+ spectra together with the
r (cid:18) r (cid:19)−2 AMS-02 data in Fig. 1. On the other hand, however,
ρNFW(r)=ρs rs 1+ r , (2) there is no channel that gives us a large p-value with
s
QGSJET-II-04m.
where ρ =0.184 GeV/cm3 and r =24.42 kpc are typ- In Fig. 2, it is shown that this scenario has been ex-
s s
ical scale density and radius [43]. These values are ob- cluded by γ-ray observations from Milky Way Dwarf
tained by setting the density to be ρ = 0.3 GeV/cm3 Spheroidal Galaxies under the s-wave-dominated dark
(cid:12)
at the Sun position r =8.33 kpc. matter assumption. However, there is still a possibility
(cid:12)
After getting the fluxes of antiparticles produced by toacceptthisscenarioifp-waveannihilationisnotnegli-
dark matter with NFW distribution, we take it as the gible,accordingtoarecentstudy[49]. Intheirwork,itis
4
· 10-3
0.4
10-1 cc -> t+t- & cc -> VV -> 2t+t-
0.35
EPOS LHC 10-2 cc -> qq & cc -> VV -> 2m +m -
0.3
cc -> qq & cc -> VV -> 2t+t-
0.25 e10-3
u
al cc -> bb & cc -> VV -> 2m +m -
/pp 0.2 p-v10-4
cc -> bb & cc -> VV -> 2t+t-
0.15 10-5
cc -> WW & cc -> VV -> 2m +m -
0.1 10-6
cc -> WW & cc -> VV -> 2t+t-
0.05 10-7
102 103 104 105
0 mx (GeV)
102 103 104
40 Ek(GeV) FIG. 3: P-values as a function of dark matter mass m
χ
35 for different combinations of two channels with EPOS
AMS
LHC.
30 CR Background
-1-1)ssr 25 CR Background 1-s
-2m
2V 20 CR Background 2-s bythreeordersofmagnitude. Inageneralcase, thecon-
Ge straint is between these two. If we take this into account
( 15 DM + CR Background
forthesystematicsofγ-rayobservation,darkmattersce-
3FE
10 nario driven from AMS-02 antiparticle data has not yet
been rejected by Fermi-LAT.
5
From this exercise, it is shown that most of the single
0 102 103 104 channel scenarios can not simultaneously explain p¯ and
E(GeV) e+. With respect to the astro-physical background, the
excess of e+ is a solid evidence of extra e+ source, while
FIG. 1: Combined fit of p¯/p (TOP) and e+ thatof p¯ismarginal. Thisrequiresalarge(cid:104)σv(cid:105)toexplain
(BOTTOM) for the 1-channel scenario with EPOS e+ data,whileasmall(cid:104)σv(cid:105)toproducep¯. Forquark(e.g.
LHC: χχ→τ+τ−. qq¯and b¯b) or boson channels (e.g. WW¯), it predicts not
enough e+ and too much p¯. For leptonic channels (i.e.
e+e−,µ+µ−andτ+τ−),itpredictsenoughe+butthee+
10-21 profile of dark matter signal does not match data quite
well. Thus, we introduce one more channel to get more
c c fi t + t -
10-22 e+ in Sec. IIIB to improve the fit.
s)10-23 AMS-02 (2-s )
3/m
> (c10-24 Fermi-LAT (2-s ) B. dark matter annihilation into two channels
v

s <10-25 Now we come to the possibility that dark matter an-
nihilates into two channels. In Sec. IIIA, it is shown
10-26 that more e+ in the annihilation will improve the fit. In
addition to the 6 channels in Sec. IIIA, those “4-body”
10-27 10 102 103 104 lepton channels have been studied as the second chan-
mc (GeV) nels, which are pure lepton channels and do not produce
any p¯. In this kind of scenarios, we will have more e+
FIG. 2: AMS-02 etimation of dark matter mass m for
χ while keeping almost the same amount of p¯.
τ+τ− channel with EPOS LHC, comparing with
Theresultswithap-valuegreaterthan10−7 areshown
Fermi-LAT 6-year observation[1].
inTable.IandinTable.IIforEPOSLHCandQGSJET-
II-04m as the antiproton production model respectively.
The number of degree of freedom is 48. CH stands for
i
shownthat(cid:104)σv(cid:105)canbeexpandedinaformlike(cid:104)σv(cid:105)=a the ith channel. BR is short for the branching ratio
i
+bv2 insteadofaconstantfors-wavedominatedannihi- of the ith channel. The p-values v.s. m s are shown
χ
lation. Ifb=0,theyobtainaconstraintthesameasthat in Fig. 3 and Fig. 4. Compared with the one channel
inFermi-LATpublication. Ifa=0,theconstraintwillbe scenarios, these two channel scenarios can improve the
weaker than that measured by Fermi-LAT collaboration quality of the fit a lot. For EPOS LHC antiproton pro-
5
CH CH m (cid:104)σv(cid:105)×BR (cid:104)σv(cid:105)×BR χ2 p-value
1 2 χ 1 2
(GeV) (10−26cm3/s) (10−26cm3/s)
τ+τ− VV→2τ+τ− 1331+161 251.24+6.08 264.9+4.0 76.6 5.44e-03
−143 −5.94 −4.0
qq¯ VV→2µ+µ− 613+71 0.72+0.11 86.0+8.0 104.2 4.97e-06
−64 −0.10 −7.3
qq¯ VV→2τ+τ− 1866+134 3.75+0.60 593.3+69.1 61.6 9.03e-02
−125 −0.52 −61.9
b¯b VV→2µ+µ− 585+33 0.98+0.16 87.1+10.0 110.0 9.15e-07
−31 −0.13 −9.0
b¯b VV→2τ+τ− 1680+154 4.08+0.38 592.3+68.5 65.6 4.65e-02
−141 −0.35 −61.4
WW¯ VV→2µ+µ− 615+55 1.13+0.15 87.1+9.9 110.2 8.39e-07
−51 −0.13 −8.9
WW¯ VV→2τ+τ− 1694+157 5.33+0.76 606.7+71.7 60.9 9.94e-02
−144 −0.67 −64.1
TABLE I: m s, (cid:104)σv(cid:105)s, χ2s and p-values given by the “Good” fits in two-channel scenarios with EPOS LHC. The
χ
number of degree of freedom is 48.
CH CH m (cid:104)σv(cid:105)×BR (cid:104)σv(cid:105)×BR χ2 p-value
1 2 χ 1 2
(GeV) (10−26cm3/s) (10−26cm3/s)
qq¯ VV→2µ+µ− 568+35 3.44+0.24 75.9+6.2 100.0 1.59e-05
−33 −0.23 −5.7
qq¯ VV→2τ+τ− 1426+124 12.12+1.41 465.1+49.9 113.7 2.96e-07
−114 −1.27 −45.1
b¯b VV→2µ+µ− 615+52 0.58+0.07 84.2+8.9 100.9 1.26e-05
−48 −0.06 −8.0
b¯b VV→2τ+τ− 1474+122 15.36+1.39 490.5+50.8 81.0 2.04e-03
−113 −1.28 −46.0
WW¯ VV→2µ+µ− 581+47 0.52+0.05 78.8+8.0 87.6 4.18e-04
−44 −0.04 −7.3
WW¯ VV→2τ+τ− 1259+97 14.09+1.36 401.3+39.6 107.1 2.12e-06
−90 −1.24 −36.0
TABLE II: m s, (cid:104)σv(cid:105)s, χ2s and p-values given by the “Good” fits in two-channel scenarios with QGSJET-II-04m.
χ
The number of degree of freedom is 48.
while those with χχ → VV → 2τ+τ− channel require
that m ∼1500 GeV.
χ
10-1 cc -> qq & cc -> VV -> 2m +m -
We draw the p¯/p and e+ plots of dark matter annihi-
10-2 cc -> qq & cc -> VV -> 2t+t- lation into WW¯ and VV→2τ+τ− channel as the “best”
fit example for EPOS LHC in Fig. 5. This scenario
e10-3 cc -> bb & cc -> VV -> 2m +m - shows the mass of dark matter is 1694+157 GeV and its
u −144
p-val10-4 cc -> bb & cc -> VV -> 2t+t- (cid:104)oσfv0(cid:105).8=71+610.21.204+−%7614f..o71r×χ1χ0−→26WcmW¯3/sanwditthhaatbofra9n9c.h13in+g11r.7a1t%io
−0.109 −10.5
10-5 cc -> WW & cc -> VV -> 2m +m - for χχ → VV → 2τ+τ−. In Fig. 6, it is shown the
p¯/p and e+ plots of dark matter annihilation into b¯b and
10-6
cc -> WW & cc -> VV -> 2t+t- VV→2τ+τ− channel for QGSJET-II-04m. We obtained
10-7102 103 m (GeV) 104 105 t(cid:104)σhavt(cid:105) t=he50m5a.9s+s5o0f.8d×ar1k0−m26actmte3r/issw14it7h4+−a1121b23raGncehVinagnrdatitios
x −46.0
of3.036+0.275%forχχ→b¯bandthatof96.96+10.04%for
FIG. 4: P-values as a function of dark matter mass mχ χχ→V−V0.2→532τ+τ−. −9.09
for different combinations of two channels with
These two plots show that the two antiproton pro-
QGSJET-II-04m.
duction models do not give consistent results for all the
scenarios. As is discussed in Sec. IIA, the difference of
anti-neutron production in these two MC generators is
duction model, the “best” fit p-value is increased by a the source of the systematics of the antiproton astro-
factor of ∼3000. In Fig. 3 and Table.I, it is shown that physical background. Some recent works parameterized
χχ → VV → 2τ+τ− is the dominating channel in three the antiproton production cross sections with the latest
scenarioswiththelargestp-values. ForQGSJET-II-04m, ground experimental data [28, 50], which is also a good
the p-value is improved by a factor of more than 105. way to obtain this cross section. For antineutron pro-
ThepeakpositionsinFig.3andFig.4tellusacommon duction, however, they assumed an energy independent
figure for these two MC generators: scenarios combin- scale factor κ≡antineutron/antiproton to be a constant
ing quark or boson channel and χχ → VV → 2µ+µ− according to isospin symmetry, based on a preliminary
channel require that the dark matter mass is ∼600 GeV, experimentalresultpublishedinaconferenceproceeding
6
· 10-3 · 10-3
0.4 0.4
0.35 0.35
EPOS LHC QGSJET-II-04m
0.3 0.3
0.25 0.25
/pp 0.2 /pp 0.2
0.15 0.15
0.1 0.1
0.05 0.05
0 0
102 103 104 102 103 104
40 Ek(GeV) 40 Ek(GeV)
35 35
AMS AMS
-1-1)ssr 2350 CCRR BBaacckkggrroouunndd 1-s -1-1)ssr 2350 CCRR BBaacckkggrroouunndd 1-s
-2m -2m
2V 20 CR Background 2-s 2V 20 CR Background 2-s
e e
G G
( 15 DM + CR Background ( 15 DM + CR Background
3FE 3FE
10 10
5 5
0 0
102 103 104 102 103 104
E(GeV) E(GeV)
FIG. 5: Combined fit of p¯/p (TOP) and e+ FIG. 6: Combined fit of p¯/p (TOP) and e+
(BOTTOM) for the 2-channel scenario with EPOS (BOTTOM) for the 2-channel scenario with
LHC: χχ→WW¯ and χχ→VV →2τ+τ−. QGSJET-II-04m: χχ→b¯b and χχ→VV →2τ+τ−.
IV. CONCLUSIONS
[51]. One should notice that this energy independent as-
sumption of κ is not precise enough to describe antineu- An increase in the accuracy of the CR antiparticle
tron production. When the antiproton energy is close to spectra measurements is driving us closer to the answer
the production threshold, κ should be maximum in any of dark matter. Together with CR γ-ray [1, 2] and neu-
model. κ goes down when the antiproton energy moves trino [3] spectra, p¯ and e+ spectra help us study astro-
away from the threshold [8]. An energy dependent κ, physical properties of the potential dark matter with
however, changes the shape of the p¯ flux. More cross m ∼100−105 GeV.
χ
section measurement data from accelerators will help to
We summarize everything here. We present our study
reduce this kind of systematic errors. on dark matter search from CR p¯and e+ data above 30
GeV. For the first time, we simultaneously interpretate
Sincebothofthesetwogeneratorspredictap¯/pastro-
p¯and e+ spectra in the framework of AMS-02 with dark
physical background going down with energy above 60
matterscenarios. Wefindthatχχ→τ+τ− channelwith
GeV where AMS-02 data shows no energy dependence,
100% branching ratio is the best one channel scenario
a hint of an extra p¯ source like dark matter is seen in
to reproduce CR p¯/p and e+ flux measurement, with
the top plots of Fig. 5 and Fig. 6. The dark matter
m =778+58 GeVand(cid:104)σv(cid:105)=269.14+24.99×10−26cm3/s,
signal makes the p¯/p spectrum harder and closer to ob- χ −54 −22.87
in the case of EPOS LHC. For the antiproton back-
served data. However, compared to the uncertainties of
ground using the same MC generator, we also propose
the astro-physical background, the signal of dark mat-
ter is not very significant. On the other hand, e+ flux a two channel scenario: mχ = 1694+−115474 GeV and (cid:104)σv(cid:105)
measured by AMS-02 is significantly higher than asto- = 612.0+71.7 ×10−26cm3/s. The dominating channel
−64.1
physical background. The dark matter profile can pro- is χχ → VV → 2τ+τ− with a branching ratio of
duce a “cut-off” like spectrum as is measured by AMS- 99.13+0.09%,whilethesecondchannelisχχ→WW¯ with
−0.10
02. The “best” fit results can match measurement up to abranchingratioof0.87+0.12%. InthecaseofQGSJET-
−0.11
a few hundred GeV. II-04m,noonechannelscenariogivesagoodfit. Forthis
7
MC generator, however, we find a best fit two channel advanced MC generators, EPOS LHC and QGSJET-II-
scenario as the following one: m = 1474+122 GeV and 04m, do not give consistent results. This systematics is
χ −113
(cid:104)σv(cid:105) = 505.9+50.8 ×10−26cm3/s. The dominating chan- due to the lack of knowledge of anti-neutron production,
−46.0
nel is χχ → VV → 2τ+τ− with a branching ratio of which could be supplemented with new data of future
96.96+0.28%, while the second channel is χχ → b¯b with underground experiments.
−0.30
a branching ratio of 3.04+0.28%. These scenarios predict To perform a dark matter search below 30 GeV, we
−0.11 have to reduce the uncertainties from solar modulation,
p¯/p spectra harder than those in the background only
scenario. They also predict a e+ spectrum with a cut as is pointed out by a recent study [8]. Recent time
dependent e+/e− measurements by PAMELA [52] con-
off between 100 and 2000 GeV, which is also observed
firmed charge-sign-dependent solar modulation models
by AMS-02, even though the shape does not completely
[53, 54]. The convectional force field approximation [55]
match data.
isnotpreciseenoughforus. AMS-02willpublishitstime
Comparing to the pulsar scenarios [21], we find that dependente+,e−,p¯andpfluxesinthenearfuture,which
the χ2/n.d.f.s in dark matter fits are higher. This is will make it possible for us to reconstruct the fluxes out
due to the fact that pulsar models have more degrees of oftheheliosphere. Welookforwardtosearchingfordark
freedom. For example, the injection spectral index of a matter below 30 GeV at that time.
pulsar is a free parameter, which will adjust the pulsar
profiletomatche+ data. Oncontrast,thespectralindex
ofe+ fluxproducedbydarkmatterisfixedbytheoretical ACKNOWLEDGMENTS
models. Itisnecessarytohavesomemodelstoconstrain
the spectral index of a pulsar or to link it with the cor- We thank Qiang Yuan and Zhao-Huan Yu for helpful
respondingγ-rayspectrum. Moreover,ifonetrystoper- discussions. ThisworkissupportedbytheNationalNat-
form a combined fit on p¯/p and e+ spectra with quark ural Science Foundation of China (NSFC) under Grant
channel dark matter and pulsar model, he has 2+3=5 Nos. 11375277, 11410301005, 11647606, and 11005163,
free parameters and will obtain a good fit. Here we have the Fundamental Research Funds for the Central Uni-
only 3 free parameters for two channel dark matter sce- versities, the Natural Science Foundation of Guangdong
nario. We also investigate the impact of the antiproton ProvinceunderGrantNo. 2016A030313313,andtheSun
background caused by cross sections. Two of the most Yat-Sen University Science Foundation.
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