Neutralino Dark Matter with CP Violation Sabine Kraml, CERN

1. Neutralino Dark Matter with CP ViolationSabine Kraml, CERN GDR matière noir, Montpellier, 13-14 Feb 2006 in collab. w. G. Bélanger, F. Boudjema, A. Pukhov & A. Semenov

2. Relic density of WIMPs • Early Universe dense and hot; WIMPs in thermal equilibrium • Universe expands and cools;WIMP density is reduced through pair annihilation; Boltzmann suppression: n~e-m/T • Temperature and densitytoo low for WIMP annihilation to keep up with expansion rate → freeze out Final dark matter density: Wh2 ~ 1/<sv> Thermally avaraged cross section of all annihilation channels Neutralino dark matter with CP violation

3. 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 < Wh2 < 0.129 puts strong bounds on the parameter space Neutralino dark matter with CP violation

4. mSUGRA parameter space • GUT-scale boundary conditions: m0, m1/2, A0 • 4 regions with good Wh2 • bulk (const. by LEP mh limit) • co-annihilation (small DM) • Higgs funnel (tanb ~ 50) • focus point (higgsino scenario) • Analogous scenarii in the general MSSM Neutralino dark matter with CP violation

5. Neutralino system Gauginos Higgsinos Neutralino mass eigenstates Gaugino and higgsino mass terms can be complex → CP violation ← → LSP Neutralino dark matter with CP violation

6. 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 <sv> • 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 fm=0 and assume very heavy 1st+2nd generation sfermions Neutralino dark matter with CP violation

7. 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 Neutralino dark matter with CP violation

8. Previous studies of  relic with CPV ... typically concentrate on some particular aspect; no complete, general analysis so far; no public tools Neutralino dark matter with CP violation

9. 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/0112278 CPsuperH: J.S. Lee et al., Comput. Phys. Commun. 156 (2004), hep-ph/0307377 Neutralino dark matter with CP violation

10. Scan over phases in M1-m plane M1 ~ m main channel is annihilation intoWW Blue: WMAP-allowed range in the CP-conserving MSSM Green: same for the CP-violating case (arbitrary phases of M1 and m) Neutralino dark matter with CP violation

11. f(m)=180° f(m)=0° With increasing f(M1), the LSP mass increases; annihilation into WW becomes less efficient while coannihilation with charginos can set in. Hence Wh2↑ or↓ ... Neutralino dark matter with CP violation

12. Scan over phases in M1-m plane mH+ = 500 GeV Higgs 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. Neutralino dark matter with CP violation

13. A closer look to the Higgs funnel M1 = 150, M2 = 300, At = 1200 GeV, tanb = 5 masses of 3rd gen: 500 GeV, 1st+2nd gen: 10 TeV • m>>M1→ bino-like LSP, m ~ 150 GeV • Wh2 < 0.129 needs annihilation through Higgs • Scenario 1: m = 500 GeV → small mixingin Higgs sector • Scenario 2: m = 1 TeV → large mixing in Higgs sector Higgs mixing ~ Im(Atm) Neutralino dark matter with CP violation

14. Scenario 1, m = 500 GeV Neutralino dark matter with CP violation

15. Scenario1: dependence on phase of At 0.094 < Wh2 < 0.129 Wh2 < 0.094 dm2 = mh2−2m WMAP allowed region follows position of h2 pole, deviation only 4% Neutralino dark matter with CP violation

16. Scenario1: dependence on phase of M1 0.094 < Wh2 < 0.129 Wh2 < 0.094 • When arg(M1) increases, Wh2 drops • This is because m increases and hence dm2 decreases Neutralino dark matter with CP violation

17. Keeping LSP and Higgs masses fixed Scalar/pseudos. parts of H copuling Neutralino dark matter with CP violation

18. Scenario 2, large Higgs mixing Smaller mass difference needed Neutralino dark matter with CP violation

19. Order-of-magnitude effects due to ft h2 h3 h3 h3 Green bands: 0.94<Wh2<0.129 dmi = mhi - 2mLSP, i=2,3 Neutralino dark matter with CP violation

20. h2 h3 h3 h2 and h3 interchange scalar-pseudoscalar character Neutralino dark matter with CP violation

21. Dm = +1.5 GeV Dm = −1.5 h3 Not only position but also height of peak varies. Even for fixed masses order-of-magnitude variation in Wh2! Neutralino dark matter with CP violation

22. 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 Wh2 • 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 Neutralino dark matter with CP violation

23. Phase dependences, scenario 1, m = 500 GeV Green bands: 0.094 < Wh2 < 0.129 Yellow region: Wh2 < 0.094 Neutralino dark matter with CP violation