SUSY SO(10) and its implications for colliders and cosmology

1. SUSY SO(10) and its implications for colliders and cosmology Tomáš Blažek Comenius Univ, Bratislava CERN, 9 Aug 2007

2. Contents • Why SO(10) • Main Experimental Constraints and Their Effects • Examples of Best Fits from the Global Top-Down Analysis • Implications for SUSY searches

3. Well-Known SO(10) Virtues • SM fermionic multiplets of one family × 3 colours + fit nicely into the 16 of SO(10): • the 16 is a chiral rep -> there’s no singlet in 16×16 -> it is massless at the SO(10) level • anomaly canceled automatically, since SO(10) is anomaly free, unlike SU(3)c×SU(2)L×U(1)Y or SU(5) • the extra 16th state has quantum numbers of νR, and is not protected against geting massive below MGUT setting stage for the L number violation and see-saw mechanism after EWSB • Similarly the two Higgs doublets fit into a massless 10 • Gauge couplings unify

4. Well-Known SO(10) Virtues cont’d • The 16310163 operator gives order one yukawa coupling: • get a heavy top quark • EW symmetry broken radiatively (for universal scalar masses) • prediction • yt ≈ yb ≈ ytau ≈ yνtau • includes successful idea of b-tau unification • The see-saw mechanism then predicts about the right hierarchy between the charged fermions and much lighter neutrinos • ... and there is more that is less well-known and is coming in this talk

5. SO(10) Troubles • Have you seen a proton decaying lately? (dim 5 operator due to the coloured triplet higgs vs. the sign of the MGUT correction to αs ) • The 16310163 operator gives order one yukawa coupling: • Prediction • yt ≈ yb • implies large amount of fine tuning at EWSB scale: must get vd≈3GeV, as mt(MZ)/mb(MZ)≈50, • i.e., need large tanβ • Moreover, scalar higgs masses run very steep – Fig. • Since mc/mt« ms/mb, mmu/mtau and also • mu/mc« md/ms, • different higher-dimensional operators generate fermion masses of the two lighter generations • UV completion ?

6. Running MSSM mass parameters

7. SO(10) studies • Approach 1: study a particular model, which can be more or less complete, generating higher dimensional operators, and filling in the 3×3 yukawa matrices at MGUT by reading out the individual entries from the Frogatt-Nielsen diagrams OR • Approach 2: be less specific and study „SO(10)-like models“ in an MSSM analysis below MGUT which just takes into account the large yukawa couplings of the third generation

8. SO(10) studies Approach 1: Implemented in • and a number of follow-up papers. • Strategy: Do pure top-down global analysis evaluating χ2from the comparison with the available low energy data. See Table. • Important details: • Include GUT threshold correction to αs • Gravity mediated SUSY breaking with non-universal scalar higgs masses • Face fine tuning with an embedded minimisation procedure, separately minimising χ2using the non-universal higgs masses for each set of the GUT parameters

9. Table of Low Energy Observables

10. Table of Low Energy Observables MSSM analysis only

11. BR(b sγ) Constraint Effective Hamiltonian: ~ where η= αs(MZ) / αs(μ) Contributions to C7(MZ): chargino diagram enhanced by tanβ picks up the sign of the μ parameter SUSY CKM contrib non-negligible C7 or

12. mb(mb) Constraint Large SUSY Threshold Contributions to mb(MZ): • both diagrams enhanced by tanβ and proportional to μ • must be of opposite signs: need negative At • still potentially too large: pushes μ to low values ... get low mass higgsino-like charginos and neutralinos • for the same reason the global analysis best fits prefer heavy gluino. That means rather large M1/2 which through the RGEs feeds into large scalar masses.

13. Constraint from the muon anomalous magn moment SUSY Contributions to aμ: • both diagrams enhanced by tanβ and proportional to μ, chargino contribution typically greater • no freedom to choose the sign: could have gone the opposite way than the BNL measurement, but it has not • the low value of μ and heavy scalar masses tend to prefer lesser contribution than what is measured in the e+e- exp. • If the result stays, it could be a hint for a non-universal SUSY breaking mechanism.

14. Constraint from non-observation of Bs to μ+μ- SUSY contributions to this decay amplitude are enhanced by (tanβ)3. In this amplitude the process is mediated by the pseudoscalar higgs exchange. • need pseudoscalar higgs mass typically greater than 300 GeV

15. Examples of Global Analysis Best Fits

16. Examples of Global Analysis Best Fits

17. Examples of Global Analysis Best Fits

18. Another Example of Global Analysis Best Fits

19. Implications from the SO(10)-like models best fits • the lightest CP even higgs very close to the current limit mh ≈ 115-120 GeV • the rest of the higgs spectrum above ≈ 250-300 GeV • light higgsino-like charginos and neutralinos close to 100 GeV, the LSP is most of the times a higgsino-like neutralino • possibly a light stop and stau (and maybe sbottom) due to the large left-right splittings • the rest of the MSSM sparticle spectrum at/above the TeV scale • CDM is formed by a mixture of bino/higgsino-like neutralino LSP and should be observed in the near future, or the LSP is higgsino-like LSP that annihilates too rapidly to form the dominant CDM component