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					           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   29/07/2004               G. Belanger                  1

  • 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   29/07/2004       G. Belanger                        2
•    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

    ALC-Victoria   29/07/2004            G. Belanger                                   3
• 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

  ALC-Victoria   29/07/2004             G. Belanger                       4
                              mSUGRA                     Mh=111
     •   Hardly any “Bulk” region
     •   Coannihilation with stau
     •   Higgs resonance
     •   Higgsino LSP: focus point



ALC-Victoria   29/07/2004            G. Belanger                         5
                 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   29/07/2004             G. Belanger                              6
  NLSP-LSP mass difference and relic density
In the coannihilation region (Ωh2 ≈ .1):

 0.15-0.4GeV precision on
 Δ M (stau-) needed for 2% prediction
 of Ωh2
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   29/07/2004              G. Belanger                                    7
                    The focus point region
Sfermions are heavy : difficult for LHC

Potential for LC in gaugino/Higgsino

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):
                  0.2-0.3% precision on  necessary for 2% prediction of Ω
  ALC-Victoria   29/07/2004               G. Belanger                        8
         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/0312069

     Here light chargino/neutralino mass
        depend sensitively on : expect
        good precision already from
        mass measurement

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                        Heavy Higgs annihilation

•      Heavy Higgs resonance (funnel)                          Mt=175
        –   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
•      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≈300-

    ALC-Victoria    29/07/2004                   G. Belanger     10
                            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   29/07/2004         G. Belanger   11
     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)

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    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   29/07/2004                  G. Belanger                                      13
                    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   29/07/2004              G. Belanger                               14
                    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 

                                                 Allanach et al., Les Houches
ALC-Victoria   29/07/2004          G. Belanger                                  15
        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

•   With expected precision from LC
    Δmt=0.1GeV still large corrections to Ωh2
    ( up to 100%)

•   Need to improve on theoretical

•   In terms of MSSM parameters rather
    than mSUGRA, prediction for Ωh2
    more stable (recall measuring  few
    per-mil is needed to match PLANCK

ALC-Victoria   29/07/2004             G. Belanger   16
                                Some remarks
•    mSUGRA inspired models might seem too                     A0= -1700 GeV
     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 :
                                                               Main channels:
           • 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

    ALC-Victoria   29/07/2004                   G. Belanger                     17
           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                   GB, Boudjema, Cottrant, Pukhov, Semenov
      – Relevant parameter at weak scale:              hep-ph/0407218
      – Important to also consider this

    ALC-Victoria   29/07/2004           G. Belanger                                    18
• 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

ALC-Victoria   29/07/2004     G. Belanger                           19

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