Cosmo 03

Mia Schelke

, Ph.D. Student The University of Stockholm, Sweden

Outline

• SUSY DM phenomenology highlights • What are coannihilations • Why can coannihilations control the relic neutralino density • When are coannihilations important • The SUSY model used in our work:mSUGRA • Results of relic density calculations including all coannihilations J. Edsjö, M. Schelke, P. Ullio & P. Gondolo

JCAP 0304 (2003) 001 (

hep-ph/0301106)

Broken N=1 SUSY with conserved R-parity

 M inimal N=1 S upersymmetric extension of the S tandard M odel one new particle for each elementary particle Partners are identical except for the spin , and when SUSY broken also the mass differ. susy susy R-parity

R

 (  1) 3

B



L

 2

S R

:  1   1  1 SM

R

(

SM

)  1 is

R

(

SUSY

)   1 susy SM yes no SM Multiplicatively conserved even nb of susy’s in vertex 

R

:  1  1  1 The

l

ightest

s

usy

p

article (

LSP

) is stable 

LSP = Neutralino = WIMP



The lightest supersymmetric particle ( LSP ) will often be a neutralino

c 0 c

i

0 

N i

1 ˜ 

N i

2 ˜ 3 

N i

3 ˜ 1 0 

N i

4 ˜ 2 0

But lightest might mean O(100 GeV) a

w

eakly

i

nteracting

m

assive

p

article ( WIMP ) a natural cold dark matter candidate



Coannihilations and relic density

Coannihilations processes in the early Universe determine the relic density of neutralinos : The neutralinos freeze out of thermal equilibrium approx. when: The Hubble expansion rate > the effective neutralino annihilation rate (H > s v n) # The comoving c 0 relic density will stay constant ever after. NOTE:large s small n c 1 0    c 1 0      c 1 0               

e etc

 Coannihilations * c

i

 c

j

s

ij



X



Y

c

i

,

j

:

any SUSY X

,

Y

:

any SM

 *Griest & Seckel,1991 Binetruy, Girardi & Salati,1984 I.e. a coupled system of annihilations/interactions But all `leftover´ susy particles decay into c 0 So don’t solve for n 1 ,n 2 ,…., but for ∑n i = n c 0 # Solve Boltzmann eq. for n c 0 with s

eff v

 

i

,

j

s

ij v ij n i eq eq n

c 1 0

n eq j eq n

c 1 0  

Coannihilation & mass splitting

So

s eff

is large when

s ij

eq eq n

c 0

n eq

and are large.

n

c 0

n i eq n

c

eq

0 

e m

( c 0 ) 

m

(

i

)

T

 Freeze out:

T



m

( c 0 ) 20 m<

small mass splittings



effective coannihilations lowering

(in general)

n

c 0

(i.e.

W CDM

)

Effective coannihilations -- small masssplittings -- another illustration ; p.1/3 •Thermal averaging of all s v •Boltzmann suppression of high velocities (fixed T) LSP-LSP CM frame Effective distribution function s

eff v

 0  

dp eff W eff

(

p eff

) 4

E eff

2  (

p eff

,

T eff

) Effective s v  JCAP 0304 (2003) 001

Effective coannihilations -- small masssplittings -- another illustration; p.2/3 Coannihilation processes in individual CM frames (m 1

v

11 s 12

v

12 s 22

v

22     p 11  p 12 Translatation to neutralino annihilations CM frame: p 22 s 11

v

11 s 12

v

12 s 22

v

22   p 22 p 11 p 12 p 11 Initial states look like final state thresholds etc 

Effective coannihilations -- small masssplittings -- another illustration; p.3/3 •Thermal averaging of the effective s v •Boltmann suppression of heavy initial states Fig: JCAP 0304 (2003) 001  Mass splitting :

m

˜ 

m

c  6.8%

m

c Coannih. effect : W c ,no coann  W W c ,coann c ,coann  100%  Mass splitting :

m

˜ 

m

c

m

c  0.21% Coannih. effect : W c ,no coann  W c ,coann W c ,coann  1000%

Our work in mSUGRA

• • • J. Edsjö, M. Schelke, P. Ullio & P. Gondolo JCAP 0304 (2003) 001 (hep-ph/0301106) We include

all coannihilations

and use the

DarkSUSY

package: Gondolo, Edsjö, Ullio, Bergström, Schelke and Baltz http://www.physto.se/~edsjo/darksusy/ • DarkSUSY is a public fortran package for

accurate

calculations of neutralino relic density and detection rates. DarkSUSY solves the Boltzmann equation accurately (including resonances and thresholds).

Minimal supergravity

• N=1 local susy with gravity mediated breakdown of susy • Effective model:N=1 global susy (MSSM) plus soft susy breaking terms • • • • • • The five free mSUGRA parameters: m 1/2 :GUT unification value of soft susy breaking fermionic mass parameters m 0 :GUT unification value of soft susy breaking bosonic mass parameters A 0

tan

b :GUT unification value of soft susy breaking trilinear scalar coupling parameters = v 2 /v 1

sign

( m ) : m : ratio of the Higgs fields vev’s is the Higgs superfield parameter

All coannihilations are included

The DarkSUSY code includes all channels of all 2 -> 2 tree-level coannihilation processes (Except initial state gluinos) To gain computational speed: Only include initial state sparticles with m<1.5m( c 0 ) (better than 1% accuracy)  The most effective coannihilations (different regions of the parameterspace): stau stop  chargino ˜ c 1,2  higgs and gauge bosons  

The stau coannihilation region: Neutralino relic density isolevel curves.

JCAP 0304 (2003) 001   LSP  excluded

The stau coannihilation region: Effective coannihilations -- small mass splittings JCAP 0304 (2003) 001  LSP  excluded  ~45 ~100 ~200  ~300 m c 1 0  GeV ~400 

The stau coannihilation region: Increasing the upper bound on the neutralino mass.

JCAP 0304 (2003) 001 For W h 2  0.1

and coann.' s included max(

m

c ) at

m

c 0 1  

m

˜ 400GeV  LSP  excluded  For W h 2  0.1

and NO coann.' s included max(

m

c )  100GeV  

---

W h 2 without coannih. ~45 ~100 ~200  ~300 m c 1 0  GeV ~400 

The stau coannihilation region: Increasing the upper bound on the neutralino mass.

JCAP 0304 (2003) 001

Chargino coannihilation region (high mass focus point region) Increasing the upper bound on the neutralino mass.

For W h 2  0.1 with coann.' s max(

m

c ) W W  0.2

 1 TeV  0.1

0.1

 100% No REWB   W h 2  0.1

and NO coann.' s included max(

m

c )  700GeV  Coannihilations in this region had not been discussed in detail before

Stop coannihilation region Coannihilations decrease the lower bound on the neutralino mass in this region JCAP 0304 (2003) 001 ˜  excluded    For m c > m t , a light stop  ˜ LSP is important even without coann.’s, as it boosts this annih. channel: c 1 0 c 1 0

t t

  stau coannihilation region  

Conclusions

• The relic neutralino density can be wrong by as much as 100s or 1000s percent if coannihilations are not included • Coannihilations open up new regions of parameter space where the density is otherwise too high • In the stau and chargino coannihilation regions the upper mass bound to the c 0 mass is increased, while its lower bound is decreased in the stop coann. region • The efficiency of the coannihilation with a certain sparticle and the mass splitting between this sparticle and the c 0 are highly correlated • Efficient coannihilations are found for small mass splittings