Neutralino Dark Matter with CP Violation

Sabine Kraml, CERN

GDR matière noir,

Montpellier, 13-14 Feb 2006

in collab. w. G. Bélanger, F. Boudjema, A. Pukhov & A. Semenov

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Relic density of WIMPs

(1) Early Universe dense and hot; WIMPs in thermal equilibrium

(2) Universe expands and cools; WIMP density is reduced through pair annihilation; Boltzmann suppression: n~e-m/T

(3) Temperature and density too low for WIMP annihilation to keep up with expansion rate → freeze out

Final dark matter density: h2 ~ 1/<v>Thermally avaraged cross section of all annihilation channels

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Neutralino LSP of the MSSM

The generic O(100) GeV neutralino LSP has a too large relic density → need specific mechanism(s) for efficient enough annihilation

0.094 < h2 < 0.129 puts strong bounds on the parameter space

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mSUGRA parameter space

GUT-scale boundary conditions: m0, m1/2, A0

4 regions with good h2

bulk (const. by LEP mh limit)

co-annihilation (small M)

Higgs funnel (tan ~ 50)

focus point (higgsino scenario)

Analogous scenarii in the general MSSM

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Neutralino system

Neutralino mass eigenstates

Gauginos

Higgsinos

→ LSP

Gaugino and higgsino mass terms can be complex

→ CP violation ←

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CP violation

In the general MSSM, gaugino and higgsino mass parameters and trilinear couplings can be complex:

Sparticle production and decay rates strongly depend on CPV phases → expect similar influence on <v>

Caution: also the sparticle masses depend on phases

→ disentangle effects from kinematics and couplings

NB1: M2 can also be complex, but its phase can be rotated away.

NB2: CPV phases are strongly constrained by dipole moments;

we set =0 and assume very heavy 1st+2nd generation sfermions

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CP violation: Higgs sector

Non-zero phases induce CP violation in the Higgs sector through loop effects → mixing of h,H,A:

Couplings to neutralinos: scalar and pseudoscalar parts

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Previous studies of relic with CPV

... typically concentrate on some particular aspect;no complete, general analysis so far; no public tools

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CPV with micrOMEGAs

We have implemented the general MSSM Lagrangian with CP-violating phases in CalcHEP/micrOMEGAs

Higgs and sparticle masses and mixing matrices are computed with CPsuperH

Fully automatical computation of the relic density;

all contributing channels automatically included!

Now performing general analysis of CPV-MSSM parameter space ....

micrOMEGAs: G. Bélanger et al., Comput. Phys. Commun. 149 (2002), hep-ph/0112278CPsuperH: J.S. Lee et al., Comput. Phys. Commun. 156 (2004), hep-ph/0307377

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Scan over phases in M1- plane

Blue: WMAP-allowed range in the CP-conserving MSSMGreen: same for the CP-violating case (arbitrary phases of M1 and )

M1 ~

main channel is annihilation into WW

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With increasing (M1), the LSP mass increases; annihilation into WW becomes

less efficient while coannihilation with charginos can set in. Hence h2 ↑ or ↓ ...

()=180°

()=0°

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Scan over phases in M1- plane

mH+ = 500 GeVHiggs funnel

We find the conventional Higgs funnels just above and below 2m=mHi.The allowed bands are again wider than in the CP-conserving case.

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A closer look to the Higgs funnel

M1 = 150, M2 = 300, At = 1200 GeV, tan = 5

masses of 3rd gen: 500 GeV, 1st+2nd gen: 10 TeV

>>M1 → bino-like LSP, m ~ 150 GeV

h2 < 0.129 needs annihilation through Higgs

Scenario 1: = 500 GeV → small mixing in Higgs sector Scenario 2: = 1 TeV → large mixing in Higgs sector

Higgs mixing ~ Im(At)

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Scenario 1, = 500 GeV

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Scenario1: dependence on phase of At

dm2 = mh2−2m

WMAP allowed region follows position of h2 pole, deviation only 4%

0.094 < h2 < 0.129

h2 < 0.094

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When arg(M1) increases, h2 drops This is because m increases and hence dm2 decreases

Scenario1: dependence on phase of M1

0.094 < h2 < 0.129

h2 < 0.094

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Keeping LSP and Higgs masses fixed

gS,P(h2) gS,P(h3)

(M1)=0 (~0, -.06) (-.05, ~0)

(M1)=90° (.05, -.01) (-.002, .04)

Scalar/pseudos. parts of H copuling

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Scenario 2, large Higgs mixing

Smaller mass difference needed

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Order-of-magnitude effects due to t

Green bands: 0.94 < h2 < 0.129

dmi = mhi - 2mLSP, i=2,3

h3 h3

h3

h2

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h3

h3

h2

h2 and h3 interchange scalar-pseudoscalar character

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h3

Not only position but also height of peak varies.

m = −1.5

m = +1.5 GeV

Even for fixed masses order-of-magnitude variation in h2!

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Conclusions

CP-violating phases in the MSSM can have sizeable effects for collider phenomenology as well as for the relic density of the LSP

Implemented the CPV-MSSM into micrOMEGAs found up to order-of-magnitude effects in h2

no generically new features (same channels as in CP-conserving case) but important changes in the couplings; need to disentangle kinematic effects

detailed analysis of Higgs funnel (Higgs CP mixing) general analysis of annihilation is on the way

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Green bands: 0.094 < h2 < 0.129

Yellow region: h2 < 0.094

Phase dependences, scenario 1, = 500 GeV