1. Dark Matter Phenomenology of the GUT-less CMSSM
Pearl Sandick
University of Minnesota
Ellis, Olive & PS, Phys. Lett. B 642 (2006) 389
Ellis, Olive & PS, JHEP 06 (2007) 079

2. Why we like SUSY Solves the Naturalness Problem
Gauge coupling unification (GUTs)
Predicts a light Higgs boson
R-Parity
conservation
Dark Matter
Candidate!
Pearl Sandick, UMN

3. Parameter Soup
Don’t observe boson-fermion degeneracy, so SUSY must be broken (How?)
Most general case (MSSM) has > 100 new parameters!
Make some assumptions about SUSY breaking at a high scale, and evolve mass parameters down to low scale for observables
Explicitly add [soft] SUSY-breaking terms to the theory
Masses for all gauginos and scalars
Couplings for scalar-scalar and scalar-scalar-scalar interactions
Virtues of CMSSM: easy to calculate! Generic features can be understood…
CMSSM (similar to mSUGRA)
Assume universality of soft SUSY-breaking parameters at MGUT
Free Parameters: m0, m1/2, A0, tan(), sign()
Pearl Sandick, UMN

4. SUSY Dark Matter
1. Assume neutralinos were once in thermal equilibrium
2. Solve the Boltzmann rate equation to find abundance now
Pearl Sandick, UMN

5. Be Careful!
Situations when care must be taken to properly calculate (approximate) the relic density:
1. s - channel poles
2 m  mA
2. Coannihilations
m  mother sparticle
3. Thresholds
2 m  final state mass
Griest and Seckel (1991)
Pearl Sandick, UMN

6. Constraints Apply constraints from colliders and cosmology:
mh > 114 GeV
m± > 104 GeV
BR(b  s ) HFAG
BR(Bs  +--) CDF
(g -- 2)/ g-2 collab.
LEP
0.09  h2  0.12
Pearl Sandick, UMN

7. CMSSM Focus Point Coannihilation Strip LEP Higgs mass
Relaxed LEP Higgs
LEP chargino mass
g--2 suggested region
2 < 0
(no EWSB)
stau LSP
Coannihilation Strip
Pearl Sandick, UMN

8. Rapid annihilation funnel 2m  mA
CMSSM
Rapid annihilation funnel m  mA
bs
B+--
Pearl Sandick, UMN

9. tan() CMSSM >0 and A0=0 0.094 < h2 < 0.129
35,40,45,50,55
Shaded region is compatible with g-2 at 2 sigma
Note: focus point region not shown
Pearl Sandick, UMN

10. CMSSM Summary
(If DM consists mainly of neutralinos), the constraint on the relic density of neutralinos restricts m1/2 and m0 to thin strips of parameter space.
tan() provides leverage.
Most of parameter space is not compatible with measured DM density.
Pearl Sandick, UMN

11. Scale of universality of the soft breaking parameters: Min
GUT-less CMSSM
What if SUSY breaking appears below the GUT scale?
Should the soft breaking parameters be universal below the SUSY GUT scale?
Mixed modulus-anomaly mediated SUSY breaking with KKLT type moduli stabilization (mirage mediation models), warped extra dimensions, …
SUSY broken in a hidden sector (communication to observable sector?)
Add one new parameter!
Scale of universality of the soft breaking parameters: Min
Pearl Sandick, UMN

12. Evolution of the Soft Mass Parameters
M1/2 = 800 GeV
First look at gaugino and scalar mass evolution.
Gauginos (1-Loop):
Results shown later use full 2-loop expressions.
a = 1,2,3 (bino, wino, gluino)
Running of gauge couplings identical to CMSSM case, so low scale gaugino masses are all closer to m1/2 as Min is lowered.
Pearl Sandick, UMN

13. Evolution of the Soft Mass Parameters
m0 = 1000 GeV
First look at gaugino and scalar mass evolution.
Scalars (1-Loop):
…reduced energy range over which running occurs for soft breaking parameters, so they end up more similar to their input (high) scale values as M_in is lowered.
As Min  low scale Q, expect low scale scalar masses to be closer to m0.
Pearl Sandick, UMN

14. Evolution of the Soft Mass Parameters
Higgs mass parameter,  (tree level):
M1 an m2 are the soft Higgs masses associated with H1 and H2. For fixed m_1/2, mu^2 becomes negative (unphysical) at lower m_0.
As Min  low scale Q, expect low scale scalar masses to be closer to m0.
2 becomes generically smaller as Min is lowered.
Pearl Sandick, UMN

15. Mass Evolution with Min
m1/2 = 800 GeV
m0= 1000 GeV
A0 = 0
tan() = 10
> 0
Pearl Sandick, UMN

16. Neutralinos and Charginos
Must properly include coannihilations involving all three lightest neutralinos!
m1/2 = 800 GeV
m0= 1000 GeV
A0 = 0
tan() = 10
> 0
Pearl Sandick, UMN

17. Lowering Min
h2
too small!
Pearl Sandick, UMN

18. Lowering Min – large tan()
h2
too small!
Pearl Sandick, UMN

19. Direct Detection Plot all cross sections not forbidden by constraints
If neutralinos are DM, they are present locally, so will occasionally bump into a nucleus.
Effective 4-fermion lagrangian for neutralino-nucleon scattering (velocity-independent pieces):
Plot all cross sections not forbidden by constraints
If calc < CDMWMAP, scale by calc/CDMWMAP
Assume pi-nucleon Sigma term is 64 MeV
spin independent
(scalar)
spin dependent
Fraction of nucleus participates
Important for capture & annihilation rates in the sun
Whole nucleus participates
Best prospects for direct detection
Pearl Sandick, UMN

20. Neutralino-Nucleon Scattering
tan = 10, Min = MGUT
Green is fail relaxed Higgs constraint (but pass chargino mass)
4 curves are current CDMS II and XENON10 limits, and projected SuperCDMS at Soudan and projected XENON100 sensitivities
Pearl Sandick, UMN

21. Neutralino-Nucleon Scattering
tan = 10, Min = 1012 GeV
Pearl Sandick, UMN

22. Summary/Conclusions
Relaxed the standard CMSSM assumption of universality of soft breaking parameters at the GUT scale
Examined the impact of lower Min on the constraints from colliders and cosmology
Specific attention to consequences for neutralino dark matter
In GUT-less CMSSM, constraint on dark matter abundance changes dramatically with Min
Below critical Min, neutralinos can not account for the measured relic density!
Pearl Sandick, UMN

23. EXTRA SLIDES
Pearl Sandick, UMN

24. Non-zero Trilinear Couplings
A0 > 0  larger weak-scale trilinear couplings, Ai
Large loop corrections to  depend on Ai, so  is generically larger over the plane than when A0 = 0.
Also see stop-LSP excluded region
Pearl Sandick, UMN

25. Neutralino-Nucleon Scattering
tan = 50, Min = MGUT
Green is fail relaxed Higgs constraint (but pass chargino mass)
Xenon10 is 3 *10^-8 at about 30 GeV
Pearl Sandick, UMN

26. Neutralino-Nucleon Scattering
tan = 50, Min = 1014 GeV
Pearl Sandick, UMN