

 24 Mar 94

IASSNS-HEP-94/8

INDIRECT DETECTION

OF WIMPS

Marc Kamionk

owski

y

Scho ol of Natur

al Scienc

es, Institute

for Advanc

ed Study,

Princ eton, NJ 08540

ABSTRA CT

Ireview sev eral

prop osed tec hniques

for indirect

detection

of weakly

interacting

massiv eparticles

(WIMPs)

in the

halo.

Ifo cus

on distinctiv

esignatures

from cosmic-ra

yp ositrons,

an tiprotons,

and gamma

rays pro duced

by annihilation

of WIMPs

in the

galactic

halo.

Marc h1994Toapp ear in Particle

Astr ophysics,

Atomic Physics,

and Gr avitation

,pro ceedings

of the

the XIVth

Moriond

Workshop,

Villars

sur Ollon,

Switzerland,

Jan. 22-29,

1994.

y kamion@guinness.ias.edu

1. In tro

duction

There

is almost

univ ersal

agreemen

ton the existence

of dark

matter

in

the Univ

erse

1). Luminous

matter con tributes

only afraction,

\Omega LUM , 0:01,

of

critical densit y. On

the other

hand, numerous

observ ations suggest

that \Omega is

in fact

muc hlarger.

A num

ber of theoretical

argumen ts, suc has

inflation

and

the Dic ke-P

eebles

timing coincidence

suggest that the Univ

erse isactually

flat,

\Omega = 1.Although

there is considerable

debate on exactly

ho w muc

hdark

matter

there is, observ

ations

of flat

galactic

rotation curv es pro

vide

incon tro vertible

evidence for the

existence

of dark

matter

in galactic

halos, including

our own.

In general,

rotation curv es seem

to remain

flat as far

out

from

the galactic

cen ter

as are

observ

ed. Therefore,

although itremains

unclear exactly ho wm

uch mass

is entrained

in galactic

halos, it seems

that the mass

densit ycon tributed

by

halos isat least \Omega halo

?, 0:1.

In other

words,

the dark

matter

in spiral

galaxies

out weighs

the luminous

matter by at least

an order

of magnitude.

Big-bang

nucleosyn thesis suggests

that there

are more

bary ons than

are seen,

but italso

constrains the mass

densit yin bary ons to be

\Omega b!,

0:1 (Ref.

2). Therefore,

it is plausible

that there

ma yb

esome

bary onic

dark matter

in the

form

of

nonluminous massiv ecompact

halo ob jects

(MA CHOs)

suc has

neutron

stars,

bro wn dw arfs,

or blac

kholes,

but itis difficult

to see

ho wbary

ons could

accoun

t

for all the

halo

dark matter.

One of the

leading

candidates

for the

dark

matter

is aw

eakly-in

teracting

massiv eparticle

(WIMP). Supp ose that

in addition

to the

kno wn particles

of the

Standard Mo del

there

exists

anew,

yet undisco

vered, stable weakly-in

teracting

massiv eparticle,

X. It isstraigh

tforw ard to sho

w (see,

e.g. Ref. 3) that

ifsuc h

aparticle exists, it will

ha ve

acurren

tcosmological

mass densit yin units

of

critical densit ygiv en roughly

by \Omega Xh

2'

hoe Av

i= (3 \Theta 10

\Gamma 27 cm

3sec

\Gamma 1 ), where

hoe Av

iis

the thermally

averaged cross section

for annihilation

of X's

into all

ligh ter particles

times relativ ev elo cit yv

,and

his the Hubble

constan tin units

of 100

km/sec/Mp

c.

One can then

ask, what

annihilation

cross section

is required

to giv e

\Omega X

, 1?

The answ er turns

out to be a weak

scale cross section,

i.e.,

1

oeA , ff2 =(100

GeV)

2, where

ff , 0:01.

Virtually

all particle

ph ysicists

will

agree that there

is new

ph ysics

bey ond

the Standard

Mo del,

and man y(if

not

most) of the

best

ideas

for new

ph ysics

intro duce the existence

of aWIMP

.F or

example, ahea vy neutrino

asso ciated

with an extra

generation

could be the

WIMP ,but perhaps

the most

promising

WIMP candidate

is the

neutralino,

a

linear com bination

of the

sup ersymmetric

partners of the

photon,

Z boson,

and

Higgs bosons

4). Although

there can be significan

tv ariet

yin the detailed

properties of the

WIMP

,generically

,the interactions

of the

WIMP

are constrained

(by \Omega X

, 1) to be weak

scale, and in most

mo dels,

the mass

of the

WIMP

varies from ab out

10 GeV

to afew

TeV.

A num

ber of directand indirect-detection

schemes are being

pursued

in

an effort

to disco

ver WIMPs

in the

halo.

The first class

of exp

erimen

ts are

lab oratory

efforts to detect

the recoil

energy

dep osited

in alo

w-bac

kground

detector when ahalo

WIMP

elastically

scatters off an ucleus

in the

detector

5).

The most

promising

aven ue for

indirect

detection

is observ

ation of energetic

neutrinos from WIMP

annihilation

in the

Sun

and Earth.

WIMPs

in the

halo

whic haccum

ulate in the

Sun

and Earth

will annihilate

therein and pro duce

energetic neutrinos that can poten

tially be detected

by the

man yhigh-energy

neutrino telescop es curren

tly in op eration

or construction.

Iha ve review

ed this

aven ue for

detection

elsewhere

6), so in this

lecture,

Iwill instead

focus on sev eral

possible cosmic-ra ysignatures

of WIMPs

in the

galactic

halo.

Although the WIMP

is stable,

tw oWIMPs

can annihilate

into ordinary

matter suc has

quarks,

leptons, gauge bosons,

etc. in the

same

wa ythey

did

in the

early

Univ erse.

If WIMPs

exist in the

galactic

halo, then they will occasionally annihilate, and their

annihilation

pro ducts

will pro duce

cosmic

rays.

The difficult

yin inferring

the existence

of particle

dark matter

from cosmic

rays lies in discrimination

bet ween

WIMP-induced

cosmic rays and those

from

standard "bac kground"

sources. As will

be argued

belo w, it is quite

plausible that

WIMPs

ma ypro

duce distinctiv

ecosmic-ra

ysignatures

distinguishable

from bac kground.

It should

also be made

clear that propagation

of cosmic

rays

in the

Galaxy

isquite po orly

understo

od. Due

to these

astroph

ysical uncertainties, itis difficult

to mak

ereliable

predictions

for agiv

en particle

dark-matter

2

candidate, so negativ

eresults

from cosmic-ra

ysearc hes cannot

generally

be used

to constrain

dark-matter

candidates. On the other

hand, if observ

ed, these

cosmic-ra ysignatures

could pro vide

asmoking-gun

signal for the

existence

of

WIMPs in the

halo.

2. Cosmic-Ra

y An

tiprotons

The best place

to look

for adistinctiv

ecosmic-ra ysignature is where

the

bac kground

issmallest.

The ma jorit

yof cosmic

rays are protons,

and most

of

the rest

are hea vier

nuclei.

Only av ery

small

fraction

are an tiprotons.

Cosmicray an tiprotons

are pro duced

in standard

propagation

mo dels

by spallation

of

primary cosmic rays on hydrogen

atoms in the

interstellar

medium (ISM)

7).

The exact

flux of an tiprotons

pro duced

by this

mec hanism

actually

varies quite

abit in standard

propagation

mo dels,

and the observ

ational

situation

isequally

cloudy .Ho wev er, there

isone

feature

of the

energy

spectrum

of suc

hsecondary

an tiprotons

that isquite

generic to standard

cosmic-ra ymo dels: It isexp

ected

that the flux

of an tiprotons

from primary

spallation

should fall dramatically

at

low energies,

E _p!,

GeV.

This is simply

because

an an tiproton

at rest

must

be

pro duced

with alarge

bac kw ard

momen

tum in the

cen ter-of-momen

tum frame.

This requires

aprimary

cosmic-ra yan tiproton

with alarge

energy ,and the

cosmic-ra ysp ectrum

falls steeply

with energy

.

Annihilation of WIMPs,

on the

other

hand, can pro duce

low-energy

an tiprotons

8). WIMPs

will annihilate

into quarks,

leptons, gauge bosons,

etc.

whic hwill

then hadronize

and pro duce,

among

other end pro ducts,

an tiprotons.

There isno reason

wh ythe

flux of suc

han

tiprotons

should decrease

dramatically

at energies

less than

aGeV.

Therefore,

observ ation of low-energy

cosmic-ra y

an tiprotons

would pro vide

evidence

for WIMPs

in the

halo.

Calculation of the

an tiproton

flux from

WIMP

annihilation

is straigh

tforward. One assumes

that the WIMPs

ha ve

an isothermal

distribution

in the

halo with adensit

ysuitable

for accoun

ting for the

rotation

curv es. The

flux

is prop

ortional

to the

annihilation

rate in the

halo.

The energy

spectrum

of

the the an tiprotons

isdetermined

by the

fragmen

tation functions

for pro ducing

3

0.01 0.1 1 10 100

0.0001 Fig.

1Observ

ed an tiproton/proton

ratio as afunction

of kinetic

energy .(F rom

Ref. 8.) an tiprotons

from the various

annihilation

pro ducts,

whic hare

obtained

from

Mon te Carlos

and from

fits to accelerator

data. Propagation

of the

an tiprotons

through the interstellar

medium and solar

mo dulation

must also be considered.

In Fig.

1are

sho wn the cosmic-ra

yan tiproton

spectra exp ected

from mo dels

where the dark

matter

ismade

up of aB

-inos

of mass

30 GeV

(the upp er solid

curv e) or 60 GeV

(the low er solid

curv e)

8).

For

simplicit

y,w ec hose

the WIMP

to be aB

-ino

and assumed

that the WIMPs

con tribute

closure densit y, \Omega ~O/h

2=

0:25 with h= 0:5 to fix

the

annihilation

cross section.

We also

assumed

that

WIMPs con tribute

the entire

halo densit

y,and

used standard

confinemen

ttimes

and solar-mo

dulation mo dels.

The dotted

curv eis the exp ected

bac kground

due to spallation

in the

standard

leaky-b ox mo del

of cosmic-ra

ypropagation.

Also sho wn

is the

curren

tobserv

ational upp er limit

9). As the

WIMP

mass is

increased, the num ber densit

yin the halo,

and therefore

the cosmic-ra

yflux,

4

decrease. As illustrated,

observ ation of low-energy

cosmic-ra yan tiprotons

could

plausibly pro vide

evidence

for the

existence

of particle

dark matter.

It should

be noted,

ho wev

er, that

ifthe

WIMP

mass is too

large,

the an tiproton

signal

would be unobserv

ably small.

In addition,

even ifthe

WIMP

is fairly

ligh t,

there are considerable

astroph ysical uncertain

ties, so itis

possible

that WIMPs

could be the

dark

matter

and still not pro duce

an observ

able an tiproton

signal.

3. Cosmic-Ra

y Positrons

There isalso ap ossibilit

ythat annihilation

of some

WIMP

candidates

will

pro duce

adistinctiv

ecosmic-ra yp ositron

signature

at high

energies.

Again,

there is a"bac

kground"

of cosmic-ra

yp ositrons

from spallation

of primary

cosmic rays off the

ISM.

Pions

pro duced

when primary

cosmic rays interact

with

ISM protons

deca yto

muons

whic hdeca

yto positrons.

The flux of positrons,

expressed as afraction

of the

flux

of electrons,

decreases slo wly

with

increasing

energies. The sho wering

of WIMP

annihilation

pro ducts

will pro duce

positrons

in

the same

wa ythat

an tiprotons

are pro duced.

The energies

of the

positrons

that come

from sho wering

of annihilation

pro ducts

will ha ve

abroad

energy

distribution. The bac kground

spectrum

of positrons

exp ected

from standard

pro duction

mec hanisms

is quite

uncertain,

and precise

measuremen

ts of the

positron energy spectrum

are quite

difficult,

so it is unlik

ely that

positrons

from WIMP

annihilation

with abroad

energy spectrum

could be distinguished

from bac kground.

Ho wev

er, in addition

to the

positrons

that come

from deca ys of hadrons,

there isalso

the possibilit

ythat WIMPs

ma yannihilate

directly into electronpositron pairs thereb ypro ducing

a"line"

source of positrons.

Although propagation through the Galaxy

would broaden

the line

somewhat,

the observ

ed

positron energy spectrum

would still ha ve

adistinctiv

ep eak

at an

energy

equal

to the

WIMP

mass

10) . There

are no standard

pro duction

mec hanisms

that

would pro duce

ap ositron

peak at energies

of 10-1000

GeV, so suc han

observation would be aclear

signature

of particle

dark matter

in the

halo.

It isalso

5

Fig. 2The

differen

tial positron

flux divided

by the

sum

of the

differen

tial electron and positron

fluxes as afunction

of energy

for aneutralino

of mass

120

GeV. (From

Ref. 11.)

interesting to note

that some

recen tmeasuremen

ts of the

positron

spectrum

indicate an increase

in the

positron

fraction at high

energies

possibly suggestiv e

of WIMP

annihilation,

although these results

are far from

conclusiv

e.

Unfortunately ,most of the

leading

WIMP candidates

(e.g. neutralinos)

are Ma jorana

particles,

and suc hparticles

do not

deca ydirectly

into electronpositron pairs. On the other

hand, ifthe WIMP

ishea vier than

the W

\Sigma b

oson,

it can

in some

cases (for example,

ifthe WIMP

is ahiggsino)

annihilate into

mono chromatic

W

+W

\Gamma pairs,

and the W

+ bosons

can then

deca y directly

into positrons

with adistinctiv

eenergy spectrum peak ed at roughly

half the

WIMP mass

11) .In

addition,

there will be acon

tin uum

of low

er energy

positrons

pro duced

by the

other

deca yc hannels

of the

gauge

bosons.

6

Fig. 2sho

ws the

differen

tial positron

flux as aratio

of the

electron-pluspositron flux as afunction

of energy

for ahiggsino

of mass

120 GeV

for tw o

differen tmo dels of cosmic-ra

ypropagation

(the solid

and dashed

curv es). The

dotted curv eis the exp ected

bac kground.

The peak

at higher

energies

isdue to

direct deca ys of gauge

bosons

pro duced

by WIMP

annihilation

into positrons,

and the broader

peak at low

er energies

comes from the other

deca yc hannels

of the

gauge

bosons.

The dramatic

heigh tof the peak

in Fig.

2is the result

of

some fairly optimistic,

yet reasonable

astroph ysical assumptions.

Again, due to

the astroph

ysical uncertain

ties, nonobserv

ation of suc

ha

signal

cannot

be used

to rule

out WIMP

candidates.

4. Cosmic

Gamma Ra ys

Cosmic gamm ara ys will

be pro duced

by annihilation

of WIMPs

in muc

h

the same

wa ythat

an tiprotons

and positrons

are pro duced.

Sho wering

of the

annihilation pro ducts

will pro duce

gamma

rays with abroad

energy distribution

cen tered

roughly

around 1/10th the WIMP

mass. Suc ha

signal

will in general

be difficult

to distinguish

from bac kground.

Ho wev

er, there

are tw op

ossible

signatures of WIMP

annihilation

in the

halo.

The first signature

will be a distinctiv

edirectional

dep endence

of the

gamma -ra yflux.

In the

simplest

(and most plausible)

mo dels

that accoun

t

for galactic

rotation curv es, WIMPs

populate

the halo

with aspherically

symmetric isothermal

distribution.

Then, the densit

yae of WIMPs

as afunction

of distance

rfrom the galactic

cen ter

is ae(r

)=

ae0( R

2+

a2) =(r

2+

a2),

where

R ' 8kp

cthe

distance

bet ween

the solar

system

and the cen ter

of the

Galaxy

,

and ais the scale

length

of the

halo.

The ratio

R=a varies

bet ween

roughly

1/3

and 2. Giv

en suc ha

distribution,

it is straigh

tforw ard to calculate

the angular dep endence

of the

gamm

a-ra yin tensit

yI ( )from

WIMP annihilation

as a

function of ,

the

angle

bet ween

the line of sigh

tand

the galactic

cen ter.

Fig. 3

sho ws the

result

for the

angular

dep endence

of the

gamma

-ra yflux

for three

values of the

ratio

R=a .Observ

ation of suc

ha

signal

would pro vide

evidence

for WIMPs

in the

halo.

7

Fig. 3The

intensit

yof agammaray signal

from WIMP

annihilation

in the

halo

as afunction

of the

angle

bet ween

the line

of sigh

tand

the galactic

cen ter.

(As

in Ref.

12.) Along

similar

lines, it has

been

suggested

that there

ma yalso

be an enhancemen tin the dark-matter

densit yin the galactic

bulge or in the

disk

and

ifthis dark matter

were made

of WIMPs,

annihilation

could lead to astrong

gamma -ra ysignal

from the galactic

cen ter

or the

disk

13) ;ho

wev er, it is difficult to see

wh yWIMPs

would accum ulate at the

galactic

cen ter

or in the

disk. Recen tly ,Gondolo

has suggested

that the Large

Magellanic

Cloud could

be immersed

in ahalo

of dark

matter

with acen tral densit

y10 times

that of

our own

galaxy

,and that annihilation

of dark

matter

therein could lead to a

gamma -ra yin

tensit

yfrom

the LMC

roughly

ten times

stronger

than that from

our own

halo

14) .

The other,

and very

distinguishable,

signature is agammaray line

from

direct annihilation

of WIMPs

into photons.

WIMPs, essen tially

by definition,

8

ha ve

no direct

coupling

to photons.

Ho wev

er, by virtue

of the

fact

that the

WIMP must ha ve

some

appreciable

coupling to ordinary

matter (or else

annihilation in the

early

Univ erse would

be too

weak

to pro

vide

\Omega Xh

2!,

1), it is

almost guaran teed that an yrealistic

WIMP will couple

to photons

through loop

diagrams. Therefore, there will alw ays

be some

small,

but finite,

cross section

for direct

annihilation

of tw oWIMPs

into gamma

rays. Therefore,

WIMP annihilation in the

halo

can pro duce

agamm

a-ra ysignal

that ismono

chromatic

at

an energy

equal to the

WIMP

mass. There isno easily

imaginable

astroph ysical

source that would

lead to agamm

a-ra yline

at at an

energy

bet ween

roughly

aGeV and aT eV,

so disco

very of suc

ha

line could

almost

certainly

imply the

existence of WIMPs

in the

halo.

The problem

with gamma

-ra ysignatures

from dark-matter

annihilation is

that the signals

are at best

only marginally

observ able with curren

tdetectors

even with the most

optimistic

assumptions.

There is, ho wev

er, hop

ethat

hea vier WIMPs

whic hcouple

to the

W

\Sigma boson,

suc has

higgsinos,

will annihilate

more efficien

tly into

gamma

rays

15) .Also,

there should

be substan

tial impro

vemen ts in observ

ational

high-energy

gammaray astronom

yin the forthcoming

years.5. ConclusionsOf

the man yprop

osed dark-matter

candidates, the WIMP

is perhaps

the

most promising.

The rather

suggestiv

eresult that astable

particle with weakscale interactions

has acosmological

mass densit yof order

unit yhas

spurred

tremendous theoretical and exp erimen

tal activit

yin an attempt

to detect

darkmatter particles.

The most

reliable

detection

metho ds inv olv eterrestrial

lowbac kground

detectors and searc hes for energetic

neutrinos from WIMP

annihilation in the

Sun

and Earth.

Ho wev

er, ifWIMPs

populate the halo,

they will

annihilate and pro duce

cosmic

rays. Although

it will

generally

be difficult

to

distinguish suc hcosmic

rays from

bac kground,

WIMP annihilation

ma yp ossibly lead

to distinctiv

ecosmic-ra

ysignatures.

Suc hsignatures

are by no means

guaran teed even ifWIMPs

are the dark

matter,

but in man

ymo

dels itis quite

9

plausible that observ

ations of low-energy

an tiprotons,

high-energy

positrons, or

gamma rays could

pro vide

indirect

evidence

for the

existence

of particle

dark

matter in our

halo.

6. Ac kno

wledgmen

ts

Igratefully ackno wledge

very pro ductiv

eand enjo yable

collab orations

with

Man uel Drees,

Kim Griest,

Francis Halzen, Gerard Jungman,

Mihok oNo jiri,

Tim Stelzer,

and Mic hael

Turner.

This work was supp orted

by the

U.S.

Departmen tof Energy

under con tract

DEF G02-90-ER

40542.

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