Positron Fraction from Dark Matter Annihilation in the CMSSMekpdeboer/html/Talks/talk_adam.pdf ·...

Positr on Fraction from Dark MatterAnnihilation in the CMSSM

Wim de Boer, Markus Horn, Christian Sander

IEKP, Univer sity Karlsruhe

Wim.de .Boer@cern.c h http://home .cern.c h/˜deboerw

ICHEP, Amster dam, July, 2002

OutlineCMSSM Constraints

Positr on fraction in the CMSSM Parameter Space

Comparison with HEAT and AMS data

Summar y

Wim de Boer ICHEP, Amster dam, July, 2002 1

Typical Fits to AMS+HEAT Data vs

10-3

10-2

10-1

1

1 10 102

positron energy [GeV]

e+ /(e+ +

e- ) fr

acti

on

b b–

τ+ τ-

W+ W-

bg+22200• signal χ2=24.2

bg (ep-scaling=0.91)

bg only fit χ2=48.0

HEAT 94/95/2000

AMS 01

tanβ= 1.6; m0= 200; m1/2= 300

10-3

10-2

10-1

1

1 10 102

positron energy [GeV]e+ /(

e+ + e- )

frac

tion

t t–

b b–

τ+ τ-

bg+650•signal χ2=26.2

bg (ep-scaling=0.92)

bg only fit χ2=48.0

HEAT 94/95/2000

AMS 01

tanβ= 35; m0= 250; m1/2= 550

Wim de Boer ICHEP, Amster dam, July, 2002 2

CMSSM Fitpr ocedure

Choose the 10 GUT super gravityinspired parameter s: ! "$# %& ' # %&( )+*, - ./ 0 132 . / 0 154 . / 0 176 . / 0

Minimiz e the Higgs potential in or-der to determine

'98

Calculate masses and couplings atlow energies by integrating about30 coupled RGE’s and decouplingspar tic les at thresholds

calculate

:<; .= >? @ 0 , A BC BDE

Determine the best parameter s byminimizing F G .

H I JKML J KNPO QSR L J KN B BN Q Q TU TJ V WPXY L X

Z []\^ _ ` ab c de d^Z []\f _ gh i c de dfZ []\kj _ ` h a a a ` c de dj

V lnmV lpoV lrq

Z KN O R stvu tw Q TU TO V EH

Z Kxy Kz V| QSR u G ~ t _ Q TU TkZ KM R t ~ t _ Q TU TZ K N R NP J Q TU T$ y N NP J

Z T KM z y ¡ ¢ ¢£ ¤ ¥ y ¦ N B BN Q

and t G str ongl y correlated. Repeat fits for all pair s of t G

Wim de Boer ICHEP, Amster dam, July, 2002 3

10log Q

1/α i

1/α1

1/α2

1/α3

MSSM

10log Q1/

α i

Unification of the Coupling Constants in the SM and the minimal MSSM

0

10

20

30

40

50

60

0 5 10 150

10

20

30

40

50

60

0 5 10 15

U. Amaldi, W. de Boer, H. Furstenau, PL B260(1991)" "! "¨§ coupling constants of electr omagnetic –, weak–, and str ong interactions© ª "$« ¬ ­¯® ° ± !due to radiative corrections (LO)

Wim de Boer ICHEP, Amster dam, July, 2002 4

CMSSM Spar tic le Spectrum

From RGE equations:

0

100

200

300

400

500

600

700

2 4 6 8 10 12 14 16

m1/2

m0

√(µ02+m0

2)

Wino

Bino

GluinoqL~

tL~

tR~

lL~

lR~

m1

m2

tan β = 1.65Yb = Yτ

log10 Q

mas

s [G

eV]

Characteristic MSSM Features:Squarks and gluinos heavy thr oughstr ong rad. corr .Gaugino from U(1) (=Bino) LightestNeutral SUSY Partic le (LSP)(if t G not too large w.r.t. )Mass G in Higgs potential driven negati-ve by

² ¥ >EWSB (determines ( G )

Higgs mixing parameter ( usuall y largecompared with ³t G

Consequentl y:Pseudoscalar Higgs and hig gsinos heavy>light Higgs SM-hig gs-likeLSP bino-like , since no mixing with heavyhig gsinos

>

very good dark mattercandidate

Wim de Boer ICHEP, Amster dam, July, 2002 5

Allo wed Parameter Regions for

´ µ¶

500

1000 500

1000

012345678

500

1000

500 1000

excl

. LS

P

excl. Higgs

excl. bsγm0 · [GeV]

m1/2 [GeV]

χ2 tota

l

m1/

2 [G

eV]

m0 [GeV]

Constraints: Gauge Unification and EWSB¸ free! Fit pref ers¸ ¹

from

= >? @ and ( ¹

from A E >

str ong constraint from

º¼» ¹ ½

(much less for

¸ ¾

!!)

Wim de Boer ICHEP, Amster dam, July, 2002 6

Main Diagrams for Neutralino Annihilation

Gauge Bosons Fermions

¿ À9Á¿ À9Á Â Ã ÄÃÅ

¿ À9Á¿ À9Á ÆÈÇ É Ã ÄÃ Å¿ ÀÊÁ ÃÅ¿ ÄÁ¿ ÀËÁ Ã Ä

¿ ÀÊÁ Ã Å¿ ÄÍÌ¿ ÀËÁ Ã Å

Only heavy final states relevantneutralinos are Majorana par tic les and fermions

>Pauli-Principle at zero momentum>

p-wave

> ¬ fermion mass !)All x-sections str ong function of

Interf erences (Z-,t-channel) NEGATIVEInterf erences (Higgs-,t-c hannel) POSITIVE

Wim de Boer ICHEP, Amster dam, July, 2002 7

p-wave suppression at low momentum for light final states

Î ¬ G at low neutralino momenta

Ï Ð Ï ÐÑ Ò Ó ÒkÔÊÕ Ö Ó ÖÔ

×Ø ÙØ ÚØÛÝÜÞ ß

à Ø Ô áà Ø Ô ×

Øãâ Ø àØâ à

àà Ø

ä åæçè

éêÕ ëÖ

ì í ì í¯î ï ðï

ñò óò ôòõ÷öø ù

ú òû üú òû ñòþý ò úò ý úú

ú òÿ

t G = ( ½ ¸ ¥ ¸z

Wim de Boer ICHEP, Amster dam, July, 2002 8

s,t-c hannel Interf erences

Higgs large, Z small for

= =

final state Higgs small, Z large for

final state

! " #! " %$ !$ !!!

& '() * +-, ++/. 0 1324 45 67 . 0 1324 45 6 8 1:9 ; <

7 . 0 1324 45 6 8= <

> ? > ?@ A BACD E D F DGHI J

K DL MK DL CD%N D KDN KKK D

O PQR S A/T U V3WX XY ZA-[ A]\T U V3WX XY Z ^_ `\T U V3WX XY Z ^ V:a b `

(t-ch, Higgs) Interf . POS , (t-ch, Z) Interf . NEG

>

(

= =

) final states suppressed (enhanced) due to interf erences!

= =

final state dominates at large

t G = ( ½ ¸ ¥ ¸z

Wim de Boer ICHEP, Amster dam, July, 2002 9

Pseudoscalar Higgs exchang e vs

F F > ¸ > = = F F > ¸ >

c dfe c d g h g i j i

kl ml npoq r

s l ts l uv wx

y z |] | ~ ~

p

Fp Fp > ¸ > = =dominates at large

.

Wim de Boer ICHEP, Amster dam, July, 2002 10

Comparison of X-sections in CalcHEP and darkSUSY

¡ ¢

cm

£

s

¤

¦¥ §¨ª© «­¬ ¥ ® ¯

GeV© °²± ¥ ³ ³ ®¯ © °µ´ ¥ ³¶ ³¯GeV

«p ¥ ¨ ¯ ¯

GeV© «¸· ¹º ¥ ¨ ¯ ¯

GeV

CalcHEP darkSUSY» ¼ » ®ª½ ³¿¾ ³¯ À ºÁ ®ª½ ¾ ³¯ À º Áà ¼Ã ¯ ½ ®¾ ³¯ À ºÁ ³ ½ ¶ ¾ ³¯ À º ÁÄ Å Ä À §ª½ ®¾ ³¯ À ºÆ ǽ ®¾ ³¯ À º ÆÈ Å È À  ½ ³¿¾ ³¯ À É Â ½ ³¾ ³¯ À É

Feynar ts agrees with CalcHEP concerning

à Ã

!

Wim de Boer ICHEP, Amster dam, July, 2002 11

Neutralino Annihilation X-sections

¥ ³ ½ ¶ ¦¥ § ¨

200400

600800

1000

200400

600800

1000

10-30

10-29

10-28

sigma vTOT

m1/2

Ê [GeV]m 0

Ë [GeV]

<σv>

[cm

3 s-1

GeV

-1]

200400

600800

1000

200400

600800

1000

10-28

10-27

10-26

10-25

sigma vTOT

m1/2

Ê [GeV]m 0

Ë [GeV]

<σv>

[cm

3 s-1

GeV

-1]

Wim de Boer ICHEP, Amster dam, July, 2002 12

Boost factor for AMS and HEAT Data

¥ ³ ½ ¶ ¦¥ § ¨

200400

600800

1000

200400

600800

1000

10 2

10 3

boost-factor (best fit)

m1/2

Ì [GeV]m 0

Í [GeV]

boos

t fa

ctor

200400

600800

1000

200400

600800

1000

10 2

10 3

boost-factor (best fit)

m1/2

Ì [GeV]m 0

Í [GeV]

boos

t fa

ctor

Wim de Boer ICHEP, Amster dam, July, 2002 13

Dark Matter

Î Â Ï ÐÑ Ò Ð Ñ Ó

(from DarkSusy)

¥ ³ ½ ¶ ¦¥ § ¨

200

400

600

800

1000

200 400 600 800 1000

Ωh2-region

excl. Ωh 2 > 0.5

excl

. LSP

m0 [GeV]

m1/

2 [G

eV]

200

400

600

800

1000

200 400 600 800 1000

Ωh2-region

excl. Ωh 2 > 0.5excl. Ωh 2

< 0.1

excl

. LSP

m0 [GeV]

m1/

2 [G

eV]

Green regions pref erred by Boomerang and SN Ia

Wim de Boer ICHEP, Amster dam, July, 2002 14

Typical Fits to AMS+HEAT Data vs

ÔÖÕ ×

10-3

10-2

10-1

1

1 10 102

positron energy [GeV]

e+ /(e+ +

e- ) fr

acti

on

b b–

τ+ τ-

W+ W-

bg+22200• signal χ2=24.2

bg (ep-scaling=0.91)

bg only fit χ2=48.0

HEAT 94/95/2000

AMS 01

tanβ= 1.6; m0= 200; m1/2= 300

10-3

10-2

10-1

1

1 10 102

positron energy [GeV]e+ /(

e+ + e- )

frac

tion

t t–

b b–

τ+ τ-

bg+650•signal χ2=26.2

bg (ep-scaling=0.92)

bg only fit χØ2=48.0

HEAT 94/95/2000

AMS 01

tanβ= 35; m0= 250; m1/2= 550

¥ ³ ½ ¶ «Ù ¥ ³ ¯ ÚÜÛ Ý ¦¥ §¨ «Ù ¥  §¯ Ú Û Ý

Wim de Boer ICHEP, Amster dam, July, 2002 15

Þ Â

contr . for AMS+HEAT Data vs

ÔÖÕ ×

ßàá ¦¥ ³ ½ ¶ ßà á ¦¥ §¨

200400

600800

1000

200400

600800

10000

20

40

χ2 - term

m1/2

Ì [GeV]m 0

Í [GeV]

χ2 - t

erm

200400

600800

1000

200400

600800

10000

20

40

χ2 - term

m1/2

Ì [GeV]m 0

Í [GeV]

χ2 - t

erm

Wim de Boer ICHEP, Amster dam, July, 2002 16

Possib le AMS-02 Data in 2006

one year AMS

10-2

10-1

10-1

1 10 102

positron energy [GeV]

e+ /(e+ +

e- ) fr

acti

on exp. data by DarkSUSY

bgMosk-Strong (e+-scale=0.92)

generated dummy data

tanβ= 35; m0= 300; m1/2= 400

one year AMS

10-2

10-1

10-1

1 10 102

positron energy [GeV]

e+ /(e+ +

e- ) fr

acti

on exp. data by DarkSUSY

bgMosk-Strong (e+-scale=0.92)

generated dummy data

tanβ= 35; m0= 300; m1/2= 800

ßàá ⥠§ ¨ « ãÙ ¥ ³¶ ¯ Ú Û Ý « ãÙ ¥ § ¯ Ú Û Ý

Wim de Boer ICHEP, Amster dam, July, 2002 17

Possib le Þ Â

after one year AMS-02

200400

600800

1000

20040060080010000

20

40

60

80

100

χ2 - term

m1/2 [GeV]

m0

ä [GeV]

χ2 - t

erm

200400

600800

1000

20040060080010000

20

40

60

80

100

χ2 - term

m1/2 [GeV]

m0

ä [GeV]

χ2 - t

erm

Wim de Boer ICHEP, Amster dam, July, 2002 18

Summar y

Low values of (

åçæ è éçê ëì í

) excluded by LEP Higgs Limit of 114 GeV

At larger values of

åçæ è éî î

DOMINANT FINAL STATE

î î

FINAL STATE has orders of magnitude larger x-section thanï ð

final states and also larger thanñ ñ

final states for

åçæ è éçò ó

î î

FINAL STATE fits the AMS+HEAT data as well as the

ï ð

final states

Super symmetr y is an excellent candidate to explain the cold Dark Matterin the univer se. Its signal could be the positr ons and antipr otons fromneutralino annihilation into

î îfinal states

Wim de Boer ICHEP, Amster dam, July, 2002 19