Enhanced Emission and Accumulation of Antiprotons and Positrons from Supersymmetric Dark Matter

0.15 MB·English

by  Chen Jacoby

Enhanced Emission and Accumulation of Antiprotons and Positrons from
Supersymmetric Dark Matter
Chen Jacoby∗ and Shmuel Nussinov†
School of Physics and Astronomy, Tel Aviv University Ramat-Aviv, Tel Aviv 69978, Israel
We estimate the amount of antiprotons and positrons in cosmic rays due to neutralino annihila-
tionsinthegalactichaloassumingthatdarkmattertendstoclusterandthattheseclustersarenot
disturbedbytidalforces. Wefindthat,assumingneutralinosannihilatemostlytogaugebosons,the
amount of antiprotons should exceed the number seen at BESS, whereas the increase in positron
fluxis below thepresent detection threshold.
PACSnumbers: 11.30.Pb,95.35.+d
Keywords: supersymmetry,darkmatter
7
0
I. INTRODUCTION VI.
0
2

n Thenatureofdarkmatterremainsoneofnature’spuz-
II. CLUSTERING OF COLD DARK MATTER
a zles. Supersymmetry with conserved R-parity, besides
J having many desirable properties for particle physicists,
2 provides a natural candidate for cold dark matter, since Unlike hot dark matter with light constituents, which
2 if R-parity is conserved, then the lightest supersymmet- arerelativisticthroughoutmostoftherelevanthistory,or
baryons,whichviaelectromagneticinteractionswith the
ric partner is stable. In most models, the lightest su-
2 cosmicmicrowavebackgroundradiationtendtomaintain
persymmetric partner is the lightest neutralino, a linear
v
theirtemperatureuntillatetimes,colddarkmatterclus-
5 combinationoftheneutralsupersymmetricpartners: the
6 Bino B˜, the Wino W˜3 and the two neutral Higgsinos h˜1 ters in the early universe, once the perturbations δ(ρ)/ρ
0 and h˜2. onthescaleconsideredenterthehorizon. Structuresthen
2 Detection of supersymmetric dark matter can be forminadown-uphierarchialfashion: smallerstructures
1 form first and merge into bigger ones.
achievedindirectlythroughitseffectoncosmicrays,and
6 This culminates in forming galaxies with local dark
morespecificallyonantiprotonsandpositronsinthecos-
0 matter density in our neighborhood of
/ mic rays [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. (See also ref.
h
[11,12, 13,14]fordiscussiononthe effects ofWIMPs on GeV
p ρlocal ∼0.4 , (1)
- cosmic rays). χ cm3
p RecentN-bodynumericalsimulationssuggestthatthe
clusters thereof and even larger structures.
e firststructuresthatwereformedintheuniverseatz =26
h were dark matter mini-halos of mass 10−6M and half At some red-shift z, certain autonomous structures
: ⊙ formintheinitiallyalmostsmoothcolddarkmatter[16].
v mass radius of 0.01pc [15]. If these mini-halos sur-
Those become gravitationally bound and decouple (ex-
i vive disruptive gravitationalforces in the galaxy,the en-
X cept for the center of mass motion) from the Hubble ex-
hanceddarkmatterdensityinsidethemini-halosenhance
r pansion. Thelocaldarkmatterdensitywithinthesefirst
a the neutralino annihilation rate.
mini-halos,isenhancedrelativetotheaverageco-moving
Our goal in this paper is to determine the possible
numberdensity,i.e,thepresentcosmologicaldarkmatter
effects such an enhanced abundance has on the emission
density, and becomes
ofantiprotonsandpositronsandonthedetectionofthese
antiparticles in cosmic rays. nmini−halo ∼(6z)3·ncosmological. (2)
χ χ
In section II we give a short review on recent results
The factor z3 reflects the hubble stretching and n
regarding the clustering of cold dark matter. Section III χ
dilutionwhichoperatescosmologicallybutnotinsidethe
introduces the supersymmetric framework in which we
mini-halos and the 63 factor is due to the extra factor 6
work. The production of antiprotons due to neutralino
shrinkage of the virilized mini-halo.
annihilation is discussed in section IV and the antipro-
Thus, if the first structures form at z = 100−20 we
tons’propagationthroughthegalaxyispresentedinsec-
have enhancement factors of
tion V.
Finally we discuss the implications of the enhanced e ∼(6z)3 ∼2·108−2·106 (3)
f
neutralinodensityonthedetectionofpositronsinsection
over the co-moving average density of neutralinos.
RecentdetailedNbodysimulationswithinitialfluctu-
ationsextrapolateddownfromWMAPtogalaxiestothe
∗Electronicaddress: [email protected] 10−15lessmassivedarkmattermini-halossuggestindeed
†Electronicaddress: [email protected] that [15]:
2
1. These first structures formed early on at z=100-20 namely, approximately 5% of the local dark matter den-
so that the neutralino concentration therein is en- sity, which implies equal enrichment in the galaxy of the
hancedbye ∼2·108−2·106overthecosmological: unclustered neutralinos and the initial mini-halos. This
f
seemsaconservativeestimateofthedensityoftheinitial
ncosmologicalm =Ω ρ ∼1.3 keV/cm3. (4) mini-halosaslargerstructuresarelikelytoformnearthe
χ χ χ C
previous, slightly smaller structures.
Hence,theneutralinomassdensityinsidethemini-
haloisapproximately3−300GeV/cm3,i.e,5−750
times larger than the average dark matter density III. THE SUPERSYMMETRIC MODEL
in our local neighborhood.
We work here in the framework of N = 1 minimal
2. More specifically the masses of the smallest mini-
supergravity [22, 23, 24].
halos were found to be
For our purposes, it is sufficient to describe the model
m ∼10−6m , (5) using only four parameters and a sign. These parame-
mini−halo ⊙
tersarem0,thecommonscalarmass,m1/2,thecommon
and sizes gaugino mass and A0, the common trilinear interaction
term, all of which are evaluated at the GUT scale. The
r ∼0.01pc∼3·1016cm. (6) fourth parameter is tanβ, the ratio between the vacuum
mini−halo
expectation values of the two Higgs doublets, and the
The average density inside these structures is ap- final parameter is the sign of µ, the parameter that ap-
proximately40GeV/cm3,i.e,100timesthatofthe pears in the Higgs superfields interaction.
averagelocaldarkmatterdensity. Thedensitypro- We assume that the mass of the lightest neutralino is
fileofthesemini-haloscanbedescribedbyapower larger than the mass of the W and the Z bosons, but
law either smaller or not much larger than the mass of the
lightest Higgs particle. If this is the case, and assuming
ρ(r)∝r−γ, (7) that the neutralino is mostly Wino-like or Higgsino-like,
annihilation of neutralinos will be dominated by annihi-
with γ in the range from 1.5 to 2.
lation to two gauge bosons (fig. 1).
3. Let fmini−halo be the fraction of all the cosmolog- χ0 W−/Z0 χ0 W−
ical dark matter clustered inside these first mini-
halos. It is important for our present purpose
that subsequent incorporationof mini-halos along-
side some of the background initially unclustered h0i Z0
darkmatter,intolater,biggermini-halos,keepsthe χ0 W+/Z0 χ0 W+
smaller,morecompact,firstmini-halosintact. The
authorsofref. [15]findthatthisisindeedthecase. χ0 W−/Z0
More specifically, tidal disruption by stars and by
the collective gravitational field does not destroy χ+i /χ0i
the above first mini-halos even inside the galactic
disc at distances larger than 3kpc from the cen-
terofourgalaxyand,inparticular,atourlocation χ0 W+/Z0
7kpc from the center. The question of the stabil- FIG. 1: Neutralino annihilation into two gauge bosons
ityofthesestructureshasbeenfurtherdiscussedin
[17, 18, 19, 20, 21] The authors of ref. [25] estimate that the mass of the
lightest neutral higgs boson most likely lies within the
The actual value of f is estimated to be ap-
mini−halo range
proximately0.05. Inthegalaxyandinthehalothemini-
halos track the conventional ordinary unclustered dark 114 GeV <m <127 GeV, (10)
h1
matter distributions ρ(r)∝1/r2. The authors of[15] es-
timate an averageseparationbetween the early compact andthusthemassofthelightestneutralinowillbetaken
mini-halos in our neighborhood of as
m =η·100 GeV, (11)
d∼0.1pc, (8) χ
with η &1.
or more precisely, 500 mini-halos within a (pc)3.
The next to lightest supersymmetric particle is as-
This is equivalent to a local average density of
sumed to be much heavier (several hundreds of GeV),
1 and thus effects of co-annihilations involving almost de-
500·10−6m⊙pc−3 ∼ ·0.4GeV/cm3, (9) generate supersymmetric particles can be neglected.
20
3
IV. PRODUCTION OF ANTIPROTONS FROM
-1
NEUTRALINO ANNIHILATION 10
BESS98f =610MV
BESS97f =500MV
BESS95f =540MV
Our discussion of the enhanced flux of antiparticles is BESS93f =660MV
based on the standard mini-halos of mass m=10−6m⊙, ICMAAPXRICE
MASS
and size r ∼0.01 pc [15].
neiWghebaosrshuomodeoaf l5o0c0alpcm−i3n.i-Thahleoadveenrasigteynienutoruarlingoalmacatsics -1eV)
G
density in such a mini-halo is -1c
e
GeV -1rs10-2
ρχ ∼1057 pc3 , (12) -2ms
x (
u
and a number density of –p fl Secondary P– at BESS ’98
Mitsui f =610MV
at BESS ’97
n ∼η−1·1055pc−3, (13) Mitsui f =500MV
χ
Bergström f =500MV
Bieber 10(cid:176) +
where η is defined in eq. (11)
-3
The lifetime for χχ annihilations within these mini- 10 -1
10 1 10
halos is Kinetic Energy (GeV)
τ =(hσ vin )−1 ∼3·1026η sec, (14)
ann ann χ
FIG. 2: Antiproton spectrum from Bess.
where
hσ vi=10−9GeV−2. (15)
ann
If,asweargueinsectionV,theresidencetimeisindeed
The differential production rate per unit of volume of 107 years, then the expected range of antiproton fluxes
antiprotons can be written as from neutralino annihilations in mini-halos exceeds the
experimental values seen at BESS [27](fig. 2).
The angular differential flux integrated from 0.1 GeV
2
ρ to 10 GeV using the data from BESS is
χ
qp¯=hσannvig(Tp¯) , (16)
(cid:18)m (cid:19)
χ ∼10−5cm−2sec−1sr−1 (21)
where g(Tp¯) denotes the antiproton differential energy
spectrum. It has been known for some time that cosmic ray an-
Assuming that neutralinos annihilate mostly to gauge tiprotons are a sensitive indicator for supersymmetric
bosons, one antiproton is produced on averageper anni- dark matter. This is even more so with the enhanced
hilatingneutralinothroughdecayofW orZ bosons[26], annihilation rates inside the mini-haloes in our galaxy.
leading to about 10−27 antiprotons per cm3 per second The local unclustered dark matter of 0.4 GeV/cm3 in
which are injected in the galactic disc and in the halo in our neighborhood is 0.25·106 times that of the cosmo-
our neighborhood. logical 1.5 keV/cm3 as opposed to about a 100 times
Let the effective residence time of the antiprotons be- larger enhancements inside the mini-halos.
fore slowing down and annihilating be Since the fraction of neutralinos in our galactic neigh-
borhoodresidinginmini-halosis∼0.05,theneteffectof
t =τ ·107years∼τ ·3·1014sec. (17) thelocalmini-halosistoenhancetheantiprotonflux(rel-
res r r
ative to the expectation for a uniformneutralino density
The antiprotons’ density builds up to of0.4GeV/cm3)bymorethan100. Thus,independently
of any detailed estimate of the actual antiproton flux in
np¯∼η−1·τr ·3·10−13cm−3 (18) the two scenarios, the neutralino clustering within mini-
halos can help the signal of antiprotons from neutralino
The antiprotons of interest with energy above 1 GeV
annihilations cross the detectibility threshold.
move with velocities v ≈c making a flux:
Φp¯∼c·n∼η−1τr ·10−2cm−2sec−1, (19) V. PROPAGATION OF ANTIPROTONS
yielding an angular differential flux of
Let us briefly review the estimate of the lifetime of
η−1τ 8·10−4 cm−2sec−1sr−1. (20) the antiprotons. The antiprotons,like other components
r
4
of the cosmic rays, can disappear from the reservoir of 1. The estimated antiproton flux is reduced by a
cosmic rays in two ways: factor of about 0.7, the fraction of hadronic Z0
(and/or W+) decays. With the smaller τ ∼1/2
r
1. by literally ”leaking” out into the intergalactic this reduces the expected flux by factor 3, yielding
space along magnetic field lines which do not close a differential antiproton flux of
inside the galaxy or the halo.
2.7·10−4 cm−2sec−1sr−1. (27)
2. Whiletraversingthediscandtosomeextentalsoin
the halo, the antiprotons lose energy via collisions 2. Byandlarge,theobservedantiprotonsignalagrees
with electrons and protons in the ambient plasma. with that computed from interaction of cosmic ray
Such antiprotons with too low an energy cannot protons with momenta & 8 Gev with interplane-
penetrate the stelar wind and attendant magnetic tary protons suggesting more stringent limits on
fieldsandthusdonotarriveat(ant)arcticballoons the supersymmetric dark matter scenario from an-
with minimal geomagnetic cutoff. tiprotons. The background antiprotons are rela-
tively energetic. It was therefore suggested that
In the special case of antiprotons, losses via annihilation the excess at energies lower than a GeV indicates
are most important. Indeed using: supersymmetric dark matter annihilations.
3. Asnotedabove,themultiplicityofantiprotonspro-
σannv ∼10−25cm2, (22)
p¯−p duced (particularly those at the more interesting
lower energies) grows rapidly with the mass of the
we find the the lifetime for annihilation is
neutralino if the mix of Wino, Bino and Higgsino
τann =(n ·σannv)−1 ∼107years, (23) in χ0 optimizes the annihilation via a virtual Z0
p¯ p p¯−p (and to Z0 →q¯q, in particular). This will enhance
the desired signal of antiprotons from neutralino
and thus, the total traversed grammage is
annihilations. On the other hand, if annihilation
∼1025protons/cm2 ∼10gr/cm2. (24) to W+W− dominates, the multiplicity is fixed but
theenergyspectrumshiftsupwardwithm ,dimin-
χ
ishing the signal of low energy antiprotons.
The magnetic fields in the disc which are of the order
of3·10−6gaussarestrongerbyafactorofabout10than
4. If the mass of the neutralino is large enough, an-
those in the halo, and the latter are a 100 times larger
nihilations into either a higgs boson and a gauge
thanthe intergalacticmagnetic fields. Thusonly a small
boson or into two higgs bosons are possible. The
fraction of the magnetic field lines in the disc connect to
higgs bosons will then decay to b quarks, and the
the halo anda smaller fractionyetofthe magnetic fields
production of antiprotons is suppressed.
in the halo connect to the outside thereby slowing down
the leakage. Indeed the overall residence time (in the 5. The cross section for annihilation of antiprotons
disc andthe halotogether)ofprotonswith energyofthe with energies of the order of 1GeV is larger than
order of 1GeV is estimated using isotopic composition thecorrespondingelasticcrosssection. Further,al-
data to be 30 millions years, allowing 1000 traversals of ready at these energies the momentum transferred
the disc or 100 traversals of the halo. in these scattering, t, and the attendant recoil ki-
We also need to restrict the total grammage traversed neticenergyloss,t/2mp,arerelativelysmall. Thus
bythecosmicrayparticlestobelessthan5gr/cm2. This the detected antiprotons manifest the energy spec-
yields: trum from neutralino annihilations.
t ∼5·106years, (25)
disc
VI. NEUTRALINO DETECTION THROUGH
namely, POSITRONS
τ ∼1/2, (26) We next consider positrons. Could their observation
r
be a better indicator for supersymmetric dark matter?
roughly consistent with 107 years (or τr ∼ 1) used in The answer is clearly negative in so far as the lower
estimating the antiproton signal from neutralino annihi- energypartofthe spectrumwithenergylessthan1GeV
lation. is concerned. Thebackgroundfrompp→pnπ+ with the
Note that in the present scenario antiprotons are pro- chargedpion decayingto muonandthen to a positronis
duced not only in the disc as most cosmic rays but even huge compared to the antiproton background: first the
more within the mini-halos. This enhances the signal as thresholdin this case is lower andit is possible to utilize
antiprotons originating in the halo can go into the disc thelowerandmuchstrongerpartofthecosmicradiation
and arrive to us as well. spectrum. Also the inclusive pion production cross sec-
The following comments are in order: tionisabout1000timeslargerthanthatforantiprotons.
5
Themultiplicityofpositronsfromneutralinoannihilation flux of
is larger by a factor of 15 than that of the antiprotons
but this cannot compensate the above larger factors. 0.4cm−2sec−1sr−1. (30)
The situation is clearly better if we focus on the more
energetic positrons, for instance, those with Ee+ ∼ 8 This is an order of magnitude smaller than the observed
GeVorhigheroriginatingfromchargedpionsofEπ >20 amount.
GeV.Themultiplicityofthoseinneutralinoannihilations The authors of ref. [6] assert that the positron excess
is still O(1) whereas their production in proton-proton observedonbothflightsoftheHEATballoonexperiment
collisions requires now protons of energies greater than [29, 30] can be explained by a single nearby mini-halo.
30GeV.This is stronglysuppressed by the power fall-off This scenario is very unlikely, as shown in [7].
of the cosmic rays spectrum. (The authors of ref. [28]
tried to relate the apparent enhancement in this part to
a particular SUSY model. Here we focus more on the
VII. CONCLUSIONS
overallmagnitude of the signal).
An extra advantage is that the main factor shorten-
ing the accumulation time of antiprotons in the galaxy, Inthispaperwehaveshownthatifneutralinosannihi-
namely, their large annihilation cross section, has no late mostly to gauge bosons there should be an excess of
counterpart here: at these high energies e+e− annihi- antiprotonsovertheobservedamountinBESSduetothe
lations are negligible. enhanced neutralino density in the mini-halos over the
The various losses on some existing electromagnetic cosmologicaldensity. This factmay imply that the mass
background, proportional to γ2, are 2.5·108 faster for of the neutralinos is larger than the mass of the lightest
the energetic positrons than for the 1GeV antiprotons. higgsboson,inwhichcaseannihilationsintohiggsbosons
The actual energy loss rate is suppress the number of antiprotons produced, or that it
is smaller than the mass of the gauge bosons.
dW/dt=γ2·σ ·U ·c∼5·10−6U, (28) We have also shown, that although antiprotons are
Thompson
strong indicators for dark matter, this is not the case
whereU istheenergydensitydue tothe magneticfields, for positrons. The low energy positrons coming from
and neutralinoannihilationcannotbe distinguishedfromthe
large background signal and the contribution of neu-
U =B2/(8π)∼0.22eV ·(cm)−3. (29) tralino annihilation to the positron signal with high en-
ergies is too small to make any predictions.
Thus 8Gev positrons lose 1/2 of their energy via syn-
chrotron radiation in 3.5· 1015sec. This is more than
ten times longer than the lifetimes of the antiprotons.
Acknowledgments
Roughlythesamelossoccursontheequalenergydensity
cosmicmicrowaveradiationviainverseComptonscatter-
ing. Finally the standardCoulombic losses arevery sim- WewouldliketothankRennanBarkanafordiscussions
ilar for the minimally ionizing relativistic positrons and that helped initiate this project, to Yoel Rephaeli for
antiprotonsandinanycasearelessthanthoseofnuclear discussions of other possible manifestations of the mini-
interactions and annihilations at these energies. Using a halos and also to Joseph Silk for further discussions of
similaranalysisasinsectionIVwegetapositronangular the positron signature.
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