1. Relic density : dependence on MSSM parameters
B. Allanach, G. Belanger, F. Boudjema, A. Pukhov
Introduction
MSSM parameters in mSUGRA inspired models
mSUGRA parameters and relic density
Some remarks beyond mSUGRA
ALC-Victoria /07/2004
G. Belanger

2. LC-Cosmology
Cosmology (relic density of dark matter) strongly constrains SUSY models, in particular, in mSUGRA, points to specific scenarios for SUSY searches at colliders
With WMAP:
.094 < W h2 < .128 (2 sigma)
PLANCK expects precision of 2%
LHC will test SUSY Dark Matter hypothesis (can also have some LSP signal from direct detection experiments), with LC and precision measurements of SUSY parameters can one match the precision of the relic density measurement by PLANCK hence consistency check on cosmological model
ALC-Victoria /07/2004
G. Belanger

3. A bino LSP annihilates into fermion pairs through
In mSUGRA one must appeal to very specific mechanisms to reach agreement with WMAP. The main reason
The LSP is mostly bino
A bino LSP annihilates into fermion pairs through
t-channel exchange of right-handed slepton
The coupling is U(1) strength  annihilation cross section for neutralino pairs is not efficient enough  too much relic density
Need rather fine adjustment of parameters to meet WMAP
Need very precise determination of parameters for an accurate prediction of relic density
In mSUGRA the only possibilities : coannihilation, Higgs resonance, or Higgsino LSP (in focus point)
In more general MSSM:
Coannihilation can also occur (not necessarily with stau/stop)
Higgs funnel regions are also found (even at low tanbeta)
In addition to scenarios with Higgsino LSP, also possible to have wino LSP
Examples: AMSB, dilaton-dominated/moduli-dominated, non-universal SUGRA ………
Emphasise useful comparison with DAMA region
ALC-Victoria /07/2004
G. Belanger

4. Consider mSUGRA inspired MSSM models
In the WMAP favoured region of mSUGRA the relic density is very sensitive to
ΔM(NLSP-LSP) 
MA-2M 
How precisely do these parameters need to be measured at LHC+LC colliders to have prediction for W h2 competitive with PLANCK
 Consistency check on cosmological model
What is impact on W h2 of uncertainties in evaluation of sparticle spectra in mSUGRA, in particular:
Mt dependence in focus point region, Higgs annihilation
Mb, tan β dependence
Emphasise useful comparison with DAMA region
ALC-Victoria /07/2004
G. Belanger

5. mSUGRA Mh=111 Mt=175 179 Hardly any “Bulk” region
Coannihilation with stau
Higgs resonance
Higgsino LSP: focus point
114
.129 5
.094
ALC-Victoria /07/2004
G. Belanger

6. NLSP-LSP mass difference in coannihilation region
In mass range relevant for LC500,
typical ΔM(stau )= 5-15 GeV, ΔM(e)=12-20 GeV
Scenarios with smaller ΔM allowed but require an additional component for darkmatter
ALC-Victoria /07/2004
G. Belanger

7. NLSP-LSP mass difference and relic density
In the coannihilation region (Ωh2 ≈ .1):
GeV precision on
Δ M (stau-) needed for 2% prediction
of Ωh2
tanβ=10
Important to measure precisely mass of stau in coannihilation region:
LC can make precise measurements of sleptons with small ΔM (Zhang et al, LCWS)
tanβ=35
Allanach et al, LCWS
ALC-Victoria /07/2004
G. Belanger

8. The focus point region Sfermions are heavy : difficult for LHC
Potential for LC in gaugino/Higgsino
sector
LSP has Higgsino component
  is important parameter
for relic density
Coannihilation with charginos and/or
heavier neutralinos are important, mass
difference typically ~50 GeV for relic density
In WMAP range
In the focus point region (mt=172GeV)
(Ωh2 ≈ .128):
% precision on  necessary for 2% prediction of Ω
ALC-Victoria /07/2004
G. Belanger

9. Focus point region - observables
In region where neutralino annihilate to W+W-/ZZ: typically 3 neutralinos+ chargino are accessible at LC500
What precision can be reached on ?
For SPS1a combined LHC-LC analysis : %level on 
Desch et al hep-ph/
Here light chargino/neutralino mass depend sensitively on : expect good precision already from mass measurement
ALC-Victoria /07/2004
G. Belanger

10. Heavy Higgs annihilation
Heavy Higgs resonance (funnel)
Heavy Higgs enhanced coupling to b quarks
Large width
Acceptable relic density if
M(LSP)-MA/2 ~ΓA
Most of Heavy Higgs annihilation region at large tanβ is not accessible to LC500 (or LHC).
Even at low M1/2, important contribution of diagram with heavy Higgs exchange (as well as slepton exchange) possible far from resonance even if M(LSP)<200GeV
Constraint from b->sγ important
What are relevant parameters and how precisely should they be measured to get precise estimate of relic density (MA≈ GeV)
Mt=175
ALC-Victoria /07/2004
G. Belanger

11. MA dependence
For given M0-M1/2 : calculate MSSM spectrum and look at dependence on different MSSM parameters in particular MA,Γ(A), , tanβ
.2% (1GeV) precision on MA needed for 2% prediction of Wh2
This precision can be reached at LHC with
H/A->   (ATLAS-TDR 300fb-1 )
Weaker dependence on , tanβ (also induces shifts in LSP mass)
1% precision on  needed, 5-10% on tanβ
The A width is not an important parameter (far enough from resonance)
ALC-Victoria /07/2004
G. Belanger

12. Moving closer to Higgs resonance
Closer to the Higgs resonance: stronger dependence on MA
MA~700 GeV
Need better than 0.1% measurement of mass
LHC : cannot use   channel for mass determination
Also need tanβ % level and A width (few percent)
ALC-Victoria /07/2004
G. Belanger

13. Elucidating the symmetry breaking mechanism RGE codes and relic density in mSUGRA
In general RGE codes get rather good agreement for the sparticle spectra, but difficult regions are the ones interesting for relic density:
Focus point
Higgsino/gaugino fraction determines coupling of  to Z, fermions… and determines main annihilation cross-section (  ff, WW)
Large tanβ (mass of Higgs)
Coannihilation (need precise mass difference)
Coannihilation channels are suppressed by factor
ALC-Victoria /07/2004
G. Belanger

14. Large tan β : mSUGRA Within mSUGRA very strong
dependence on input parameters :
top/bottom quark mass, tanβ
With expected precision from LC
( Δmt =.1GeV) can predict Ω h2 with
2-3% precision within mSUGRA
But no hope of reaching sufficient accuracy on mb(mb) or on tanβ
2% accuracy on Ω would require determination of tanβ at per-mil level  main problem: shifts in tanβ induce shifts in MA / M(LSP)
Precise predictions of relic density within this mSUGRA scenario not possible
Much more reliable predictions after determination of MSSM parameters
ALC-Victoria /07/2004
G. Belanger

15. Focus point region and Mt
Strong dependence on the top quark mass
Increasing Mt pushes focus point towards heavier M0
Dependence on the code used for evaluation of supersymmetric spectrum: critical parameter is 
Isajet7.69
Allanach et al., Les Houches
ALC-Victoria /07/2004
G. Belanger

16. Relic density and MSSM parameters
With expected precision from hadron Collider ΔMt=1-2 GeV, prediction for Ω can vary by more than one order of magnitude
With expected precision from LC Δmt=0.1GeV still large corrections to Ωh2 ( up to 100%)
Need to improve on theoretical predictions
In terms of MSSM parameters rather than mSUGRA, prediction for Ωh2 more stable (recall measuring  few per-mil is needed to match PLANCK accuracy)
ALC-Victoria /07/2004
G. Belanger

17. Some remarks
A0= GeV
mSUGRA inspired models might seem too restrictive but even in other scenarios relic density from WMAP often imposes coannihilation /Higgs funnel/ Higgsino LSP Results presented are valid in more general MSSM models
Other cases not considered yet
stop NLSP, e.g. in mSUGRA with large A0
ΔM~30-50GeV
Mass difference should be critical parameter for relic density prediction
In mSUGRA stop NLSP only consistent with b->sγ and Mh for large negative mixing
Wino LSP :
scenario that cannot be realized in mSUGRA
much easier to satisfy relic density constraint if LSP not bino,
One example: changing the gaugino mass relations at GUT scale
Main channels:
ALC-Victoria /07/2004
G. Belanger

18. Relaxing universality :the wino LSP
M1>M2 at GUT scale : increasing the wino content of the LSP makes for more efficient annihilation  relic density constraint is easily satisfied
Preferred channels: WW
M1~1.8M2 at GUT scale M1~M2 at weak scale
LSP is mixed wino/bino
M(LSP)~600GeV in WMAP range
Relevant parameter at weak scale: M1,M2,
Important to also consider this scenario
GB, Boudjema, Cottrant, Pukhov, Semenov
hep-ph/
ALC-Victoria /07/2004
G. Belanger

19. Summary
Precision measurement of NLSP-LSP mass difference at LC essential to be competitive with PLANCK precision on relic density in coannihilation region
In focus point region, need high precision determination of  .
At large tanβ need precise determination of MA AND tanβ .
To go back to origin of supersymmetry breaking mechanism, high-precision determination of mt is needed in focus point region (also improvement in precision in RGE) and in heavy Higgs annihilation region. Also mb(mb) is needed.
In progress: sensitivity on various parameters in non-mSUGRA inspired models
Update
ALC-Victoria /07/2004
G. Belanger