# Presentation: 175545

## Neutralino Dark Matter in the GUT-less CMSSM

- Pearl Sandick
- University of Minnesota

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## First Glimpse of Dark Matter

- 1933:  Fritz Zwicky
- Used Doppler shift to measure the
- 	peculiar velocities of galaxies at the edge of the Coma Cluster
- Assuming virial equilibrium, found that most of the mass of the cluster must not be visible
- Analysis has been repeated many times:
- Different clusters, same (qualitative) result!

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## Rotation Curves

- Newtonian Mechanics:
-                      So outside of the luminous disk, expect
- Instead, observe

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

**Notes:**
Orbital velocity of stars/gas in galaxy
Most robust evidence for dark matter
Vera Rubin?

## State of the Art

- X-ray measurements (Chandra)
- [weak] gravitational lensing
- Bullet Cluster
- WMAP

- Clowe *et al.* (2006)

- NASA/WMAP Science Team

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

**Notes:**
Bullet Cluster:  stars (visible) mostly passed right through in collision (slowed), hot gas (red, seen in x-rays by Chandra) slows more substantially because it interacts both gravitationally and electromagnetically, dark matter (blue, inferred from lensing of background objects) is less perturbed than hot gas because it only interacts gravitationally

## What could it be?

- Candidates include:
- 	neutrinos, axions, KK excitations, Q-balls, gravitinos, neutralinos, axinos, Chaplygin gas, primordial black holes, branons, mirror matter, WIMPzillas...

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

**Notes:**
Neutrinos:  oscillations -> have mass
Axions:  solve Strong CP Problem (Why does QCD not break CP?)
KK:  viable DM candidate in models with UEDs, KK thoeries unify gravitation and electromagnetism.
Q-ball:  non-topological (stable, gauranteed by charge conservation) soliton (local field configuration) that arises in SUSY field theories
Chaplygin gas:  unifies dark matter and dark energy
Primordial black holes:  can’t explain all of dark matter (ostriker), produced during reheating or from primordial density perturbations
Branons:  come from extra dimensions
Mirror Matter:  restores parity to universe (violated by weak interaction)
WIMPzillas:  might be created at the end of inflation

## What makes a good DM candidate?

- Stable, Neutral
- From WMAP *et al.*  DMh2  0.1
-                                            and

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

**Notes:**
Charged dark matter would for bound states with normal matter – strong bounds from heavy isotope abundances
10^(-36) cm^2 = picobarn (typical weak interaction cross section)
Check assumptions for 2nd formula (nonrelativistic?)

## Why study SUSY?

- Haag, Lopuszanski and Sohnius (1975):
- Supersymmetry is the only graded Lie algebra that generates symmetries of the S-matrix consistent with relativistic quantum field theory.

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

**Notes:**
HLS theorem is extension to Coleman-Mandula theorem (“loophole”)
Poincare symmetry is full symmetry of a relativistic quantum field theory (product of Lorentz transformations with translations)
Internal symmetries are any symmetries of the theory not involving spacetime (color transformations of quarks, isospin, ...)

## Why study SUSY?

- Classical Higgs Potential:  V = mH2 ||2 + ||4
- SM requires <>  0, so
- <> = (-mH2 / 2 )1/2  174 GeV
-  -mH2  (100 GeV)2

- But mH2 gets quantum corrections from particles that interact with the Higgs field!

**Why study SUSY?**

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

**Notes:**
In the susy case, corrections go like abs{mstop^2-mtop^2} times log cutoff (see Keith or Hitoshi)
in order to give gauge bosons mass, need higgs field
2 aspects to hierarchy problem:  why scales different and how to keep them different

## Why study SUSY?

- Unification of the Gauge Couplings

- Near miss!

- Running (*b*’s) depends only on particle content of the model.

**SM**

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## SUSY Algebra

- Field theory definition:  SUSY generators transform under the spinor representations.  SUSY algebra describes bosons (commute) and fermions (anticommute) with one algebra:  {Q,Qbar} = blah
- This means that each SM particle has a partner with the same quantum numbers (except boson/fermion) that we haven’t seen yet!

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## Particle Zoo

- MSSM:
- Minimal Supersymmetric Standard Model
- Has the *minimal particle content* possible
- in a SUSY theory.

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## Particle Zoo

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## Another reason to study SUSY:

- Neutralinos are an excellent dark matter candidate!
- The lightest one may be a stable WIMP with h2  DMh2

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## Another reason to study SUSY:

- Neutralinos are an excellent dark matter candidate!
- The lightest one may be a stable WIMP with h2  DMh2

- Note: Properties of neutralino LSP will depend on its composition!

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## SUSY Breaking

- Explicitly add [soft] SUSY-breaking terms to the theory
- Masses for all gauginos and scalars
- Couplings for scalar-scalar and scalar-scalar-scalar interactions

- CMSSM (similar to mSUGRA)
- Assume universality of soft SUSY-breaking parameters at MGUT
- 	Free Parameters: m0, m1/2, A0, tan(), sign()

- 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

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

**Notes:**
Virtues of CMSSM: easy to calculate! Generic features can be understood...
Add a slide here about difference between CMSSM and mSUGRA?

## Neutralino Relic Density

- 1.  Assume neutralinos were once in thermal equilibrium
- Solve the Boltzmann rate equation to find abundance now

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

**Notes:**
Omega = nm/rhocrit
What is “t” in Boltzmann eq.?

## 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)

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

**Notes:**
Add better pictures?

## Constraints

- mh > 114 GeV
- m± > 104 GeV
- BR(b  s )            HFAG
- BR(Bs  +--)        CDF
- (g -- 2)/2            g-2 collab.

- LEP

- 0.09  h2  0.12

- Apply constraints from colliders and cosmology:

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## CMSSM

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

**Notes:**
Relic density restricts mo and m1/2 to thin strips of parameter space for any value of tan beta (conclusion)

## CMSSM

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## tan()

- CMSSM with >0 and A0=0
- 0.094 < h2 < 0.129
- tan() = 5,10,15,20,25,30,
-               35,40,45,50,55

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

**Notes:**
Shaded region is compatible with g-2 at 2 sigma
Note:  focus point region not shown
Add ref!

## 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.

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## 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 new parameter!
- Scale of universality of the soft breaking parameters:  Min

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## Sparticle Mass Evolution

- First look at gaugino and scalar mass evolution.
- _Gauginos (1-Loop):_

- Running of gauge couplings identical to CMSSM case, so low scale gaugino masses are all closer to m1/2 as Min is lowered.

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## Sparticle Mass Evolution

- First look at gaugino and scalar mass evolution.
- _Scalars (1-Loop):_

- As Min   low scale Q, expect low scale scalar masses to be closer to m0.

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## Sparticle Mass (parameter) Evolution

- Higgs mass parameter,  (tree level):

- As Min   low scale Q, expect low scale scalar masses to be closer to m0.
- ___2__ becomes generically smaller as M__in__ is lowered_.

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## Mass Evolution with Min

- m1/2 = 800 GeV
- m0= 1000 GeV
- A0 = 0
- tan() = 10
- > 0

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## Neutralinos and Charginos

- Must properly include coannihilations involving all three lightest neutralinos!

- m1/2 = 800 GeV
- m0= 1000 GeV
- A0 = 0
- tan() = 10
- > 0

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

**Notes:**
Is (800,1000) right?

## Lowering Min

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## Lowering Min – large tan()

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## 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

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## Direct Detection

- Effective 4-fermion lagrangian for neutralino-nucleon scattering (velocity-independent pieces):

- If neutralinos are DM, they are present locally, so will occasionally bump into a nucleus.

- spin dependent

- spin independent
- (scalar)

-   Fraction of nucleus participates
-   Important for capture & annihilation   rates in the sun

-   Whole nucleus participates
-   Best prospects for direct detection

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

**Notes:**
Assume pi-nucleon Sigma term is 64 MeV

## Neutralino-Nucleon Scattering

- tan  = 10, Min = MGUT

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

**Notes:**
Green is fail relaxed Higgs constraint (but pass chargino mass)
Xenon10 is 3 *10^-8 at about 30 GeV

## Neutralino-Nucleon Scattering

- tan  = 10, Min = 1012 GeV

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

## Neutralino-Nucleon Scattering

- tan  = 50, Min = MGUT

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

**Notes:**
Green is fail relaxed Higgs constraint (but pass chargino mass)
Xenon10 is 3 *10^-8 at about 30 GeV

## Neutralino-Nucleon Scattering

- tan  = 50, Min = 1014 GeV

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

**Notes:**
Green is fail relaxed Higgs constraint (but pass chargino mass)
Xenon10 is 3 *10^-8 at about 30 GeV

## 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!

- Fermilab Theoretical Astrophysics Seminar

- September 17, 2007

**Notes:**
Consequences for neutralino dark matter:  allowed regions of parameter space as well as direct detection prospects