Mia Schelke, Ph.D. Student

The University of Stockholm, Sweden

Cosmo 03

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 coannihilationsJ. Edsjö, M. Schelke, P. Ullio & P. Gondolo

JCAP 0304 (2003) 001 (hep-ph/0301106)

Broken N=1 SUSY with conserved R-parity

Multiplicatively conserved

even nb of susy’s in vertex

The lightest susy particle (LSP) is stable

susy susy

SMyes

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R : −1 = −1∗1

susy SM

SMno

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R : −1 ≠1∗1

Minimal N=1 Supersymmetric extension of the Standard Model one new particle for each elementary particle

Partners are identical except for the spin, and when SUSY is broken also the mass differ.

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R = (−1)3B +L +2S

R(SM) =1

R(SUSY) = −1

R-parity

LSP = Neutralino = WIMP

The lightest supersymmetric particle (LSP)

will often be a neutralino

But lightest might mean O(100 GeV)

a weakly interacting massive particle (WIMP)

a natural cold dark matter candidate€

i0 = N i1

˜ B + N i2˜ W 3 + N i3

˜ H 10 + N i4

˜ H 20

€ €

Coannihilations and relic densityCoannihilations 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 > v n) #

The comoving relic density will stay constant ever after. NOTE:large small n

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10 + χ 1

0 → τ + τ

χ 10 + ˜ τ → γ + τ

˜ τ + ˜ τ ∗ → γ + γ

˜ τ + ˜ e → τ + e

etc€

i + χ j →σ ij

X + Y

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i, j : any SUSY

X,Y : any SM

Coannihilations*

*Griest & Seckel,1991 Binetruy, Girardi & Salati,1984

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eff v = σ ij v ij

i, j

∑ nieq

nχ 1

0eq

n jeq

nχ 1

0eq

I.e. a coupled system of annihilations/interactions But all `leftover´ susy particles decay into 0

So don’t solve for n1,n2,…., but for ∑ni = n0

#Solve Boltzmann eq. for n0 with

Coannihilation & mass splitting

So eff is large when ij and are large.

m<<T; Boltzmann suppression

small mass splittings

effective coannihilations

lowering (in general) n0 (i.e. CDM)€

nieq

nχ 0eq

= em(χ 0 )−m( i)

T€

nieq

nχ 0eq

n jeq

nχ 0eq

Freeze out:

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T ≈ m(χ 0) 20

JCAP 0304 (2003) 001

Effective coannihilations -- small masssplittings-- another illustration ; p.1/3

•Thermal averaging of all v•Boltzmann suppression of high velocities (fixed T)

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eff v = dpeff

Weff (peff )

4Eeff2

κ (peff ,Teff )0

∞

∫

Effective v

Effective distribution functionLSP-LSP CM

frame

Effective coannihilations -- small masssplittings-- another illustration; p.2/3

p11

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11 v11

p12

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12 v12

p22

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22 v22

p11

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11 v11

p12

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12 v12

p22

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22 v22

p11

Coannihilation processes in individual CM frames (m1<m2<m3….):

Translatation to neutralino annihilations CM frame:

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≈Initial states look like final state thresholds

etc

Effective coannihilations -- small masssplittings-- another illustration; p.3/3

•Thermal averaging of the effective v•Boltmann suppression of heavy initial states

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Mass splitting : m ˜ τ − mχ

mχ

= 6.8%

Coannih. effect : Ωχ ,no coann − Ωχ ,coann

Ωχ ,coann

=100%

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Mass splitting : m ˜ τ − mχ

mχ

= 0.21%

Coannih. effect : Ωχ ,no coann − Ωχ ,coann

Ωχ ,coann

=1000%

Fig: JCAP 0304 (2003) 001

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:• m1/2:GUT unification value of soft susy breaking fermionic mass parameters• m0 :GUT unification value of soft susy breaking bosonic mass parameters• A0 :GUT unification value of soft susy breaking trilinear scalar coupling parameters• tan = v2/v1 : ratio of the Higgs fields vev’s• sign() : 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() (better than 1% accuracy)

The most effective coannihilations (different regions of the parameterspace):

stau ( ): partner of chargino ( ): partners of charged higgs and gauge bosonsstop ( ): partner of top

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˜ τ

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1,2±

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˜ t

The stau coannihilation region:

JCAP 0304 (2003) 001

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˜ τ LSP ⇒ excluded

Neutralino relic density isolevel curves.

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mχ 1

0 GeV[ ]

~400~300~200~100~45

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˜ τ LSP ⇒ excluded

JCAP 0304 (2003) 001

The stau coannihilation region:

Effective coannihilations -- small mass splittings

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mχ 1

0 GeV[ ]~400~300~200~100~45

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˜ τ LSP ⇒ excluded

JCAP 0304 (2003) 001

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For Ωh2 = 0.1

and NO coann.'s included

max(mχ ) ≈100GeV

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For Ωh2 = 0.1

and coann.'s included

max(mχ ) ≈ 400GeV

at mχ 1

0 = m ˜ τ

The stau coannihilation region:

Increasing the upper bound on the neutralino mass.

--- h2 without coannih.

JCAP 0304 (2003) 001

neu

t ralin

o -

- sta

u

The stau coannihilation region:

Increasing the upper bound on the neutralino mass.

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For Ωh2 = 0.1

and NO coann.'s included

max(mχ ) ≈ 700GeV

No REWB

No REWB€

For Ωh2 = 0.1 with coann.'s

max(mχ ) ≈1 TeV

ΔΩ

Ω≈

0.2 − 0.1

0.1=100%

Chargino coannihilation region (high mass focus point region)

Increasing the upper bound on the neutralino mass.

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⇒

Coannihilations in this region had not been discussed in detail before

stau coannihilation region

Coannihilations decrease the lower bound on the neutralino mass in this region

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˜ t LSP

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˜ t LSP

excluded

For m > mt, a light stop

is important even without coann.’s, as it boosts this annih. channel:

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10

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10

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˜ t

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t

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t

Stop coannihilation region

JCAP 0304 (2003) 001

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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 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 are highly correlated

• Efficient coannihilations are found for small mass splittings