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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
€
R : −1 = −1∗1
susy SM
SMno
€
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.
€
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
€
€
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
€
i, j : any SUSY
X,Y : any SM
Coannihilations*
*Griest & Seckel,1991 Binetruy, Girardi & Salati,1984
€
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:
€
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)
€
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
€
11 v11
p12
€
12 v12
p22
€
22 v22
p11
€
11 v11
p12
€
12 v12
p22
€
22 v22
p11
Coannihilation processes in individual CM frames (m1<m2<m3….):
Translatation to neutralino annihilations CM frame:
€
≈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
€
Mass splitting : m ˜ τ − mχ
mχ
= 6.8%
Coannih. effect : Ωχ ,no coann − Ωχ ,coann
Ωχ ,coann
=100%
€
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
€
˜ τ
€
1,2±
€
˜ t
The stau coannihilation region:
JCAP 0304 (2003) 001
€
˜ τ LSP ⇒ excluded
Neutralino relic density isolevel curves.
€
mχ 1
0 GeV[ ]
~400~300~200~100~45
€
˜ τ LSP ⇒ excluded
JCAP 0304 (2003) 001
The stau coannihilation region:
Effective coannihilations -- small mass splittings
€
mχ 1
0 GeV[ ]~400~300~200~100~45
€
˜ τ LSP ⇒ excluded
JCAP 0304 (2003) 001
€
For Ωh2 = 0.1
and NO coann.'s included
max(mχ ) ≈100GeV
€
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.
€
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.
€
⇒
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
€
˜ t LSP
€
˜ t LSP
excluded
For m > mt, a light stop
is important even without coann.’s, as it boosts this annih. channel:
€
10
€
10
€
˜ t
€
t
€
t
Stop coannihilation region
JCAP 0304 (2003) 001
€
⇒
€
⇒
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