1. CONSTRAINED MSSM AND RECENT ASTROPHYSICAL DATA Alexey Gladyshev (JINR, Dubna & ITEP, Moscow) SEMINAR AT KEK THEORY GROUP November 1, 2004

2. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” CMSSM and recent astrophysical data Various constraints, both theoretical and experimental imposed on model parameters, are discussed. It is shown how each of them restrict allowed regions of the parameter space. The most recent results include the constraints coming from astrophysical data.  Introduction. Motivations for supersymmetry.  Minimal Supersymmetric Standard Model  Constraints on MSSM parameters. Allowed regions of parameter space.  WMAP and EGRET constraints  Conclusions

3. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Problems of the Standard Model  Problem of unification: There is no unification in the Standard Model  Hierarchy problem: Why there are two very different scales: electroweak ( M W  100 GeV ) and Grand Unification ( M GUT  10 15-16 GeV ) or Plank (M Pl  10 19 GeV ) ? Even if one postulates this hierarchy it is destroyed by radiative corrections (or they must cancel with 10 -14 accuracy)

4. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Motivation for Supersymmetry  Grand Unification Theories: real coupling constant unification  Unification of matter and forces  Unification of particle physics and gravity (supergravity)  Solution to the hierarchy problem: add a “superpartner” and quadratic divergencies cancell

5. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Motivation for Supersymmetry  Upper bound on the Higgs boson  Radiative electroweak symmetry breaking  Solution to the Dark Matter problem in the Universe (neutralino)  Superstrings SUSY is the most popular idea beyond the SM Baryonic matter All matter Dark energy

6. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Minimal SUSY Standard Model (MSSM)  Particle content of the Minimal Supersymmetric Standard Model:

7. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Minimal SUSY Standard Model (MSSM)  Lagrangian of the Minimal Supersymmetric Standard Model:  Yukawa interactions

8. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data”  Supersymmetry is a broken symmetry.  Breaking takes place in a hidden sector. Messengers to the visible sector can be gravitino, gauge bosons, gauginos, …  Breaking must be soft (dimension of soft SUSY breaking operators  3) Minimal SUSY Standard Model (MSSM)

9. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM  Free parameters of the Minimal Supersymmetric Standard Model  Gauge and Yukawa coupling constants  Higgs mixing parameter  Soft supersymmetry breaking parameters  Higgs self-interaction coupling constant is not a free parameter, but is fixed by supersymmetry

10. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM  In total one has about a hundred parameters  Main uncertainties come from soft supersymmetry breaking parameters.  Universality hypothesis: soft supersymmetry breaking parameters unify at the scale of Grand Unification

11. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM  As a result one has only 5 free parameters instead of 2 in the Standard Model  Further limitations in parameter space come from constraints both theoretical and experimental  Gauge coupling constants unification  Radiative electroweak symmetry breaking  Yukawa coupling unification  Data on rare processes  Muon anomalous magnetic moment  Neutrality of lightest supersymmetric particle  Dark matter constraint

12. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM  Constraints are used to determine allowed regions in the parameter space by minimizing the  2 -function Experimental data (input) Fit parameters low tan  high tan   1,  2,  3 m t,m b,m  M Z BR(b  s  )  M GUT,  GUT Y t 0,Y b 0,Y  0 m 0,m 1/2 tan   A 0 M GUT,  GUT Y t 0,Y b 0,Y  0 m 0,m 1/2 tan   A 0

13. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM  Fitted parameters m 0 but large m 1/2 and A 0 are initial conditions for the renormalization group equations for superparticle masses  The ratio of v.e.v.’s tan  is highly constrained  Higgs mixing parameter  can be related to other parameters  The role of A is not significant, one cane safely put A 0 =0  In fact one has only a pair (m 0, m 1/2 ) as independent parameters

14. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Unification of gauge coupling constants. This strict constraint fixes the threshold of SUSY breaking M SUSY ~ 1 TeV. Sparticle masses should lie in the TeV range. This fact finds also an indirect support in the high precision LEP data. M SUSY ~ 1 TeV

15. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Unification of Yukawa coupling constants. The b -  unification along with the value of the top mass leads to two possible scenarios determined by the value of tan  Small (low) tan   1 - 3 Large (high) tan   50 Small (low) Large (high) tan  (1-3) tan  (~50)

16. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Unification of Yukawa coupling constants. However, the non-observation of the Higgs boson up to 114 GeV practically exclude the low tan  scenario. The modern limit tan  > 3 - 4 The high tan  scenario still survives and has got another independent confirmation from the Dark Matter problem Small (low) Large (high) tan  (1-5) tan  (~50)

17. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Radiative electroweak symmetry breaking and Z 0 mass. Minimization conditions for the Higgs potential relate the Z 0 -boson mass to model parameters. The sign of  remains undetermined. For large values of tan  This can only take place if m 2 H2 is negative.

18. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Radiative electroweak symmetry breaking and Z 0 mass. This happens at some low energy due to large top Yukawa coupling. The Higgs scalar fields gain non-zero vacuum expectation values and the electroweak symmetry is broken.

19. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Radiative electroweak symmetry breaking and Z 0 mass. The requirement of radiative electroweak symmetry breaking adjust the initial value m 0 In the case of large tan  the situation is even more difficult.

20. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Data on rare processes branching ratios. Flavour changing processes like responsible for the rare B-meson decays can occur at the one-loop level due to virtual W-top pair. In SUSY models there are additional contributing diagrams. In the leading order, contribution from superpartners to the branching ratio may be rather big, exceeding the experimental value by several standard deviations.

21. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Data on rare processes branching ratios. The next-to-leading order corrections are essential and improve the situation. The 95% CL range corresponds to 2  deviation away from the mean value.

22. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Data on rare processes branching ratios. The parameter space is restricted, especially for large tan . Exclusion plots for tan  =35 and 50

23. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Muon anomalous magnetic moment. Recent measurement of the anomalous magnetic moment indicates small deviation from the SM of the order of 2-3 . The deficiency may be easily filled with SUSY contribution, which is proportional to . This requires positive sign of . Sleptons of the second generation are relatively light.

24. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Muon anomalous magnetic moment. Regions excluded by muon anomalous magnetic moment constraint ( tan  = 35, 50 )

25. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  The lightest supersymmetric particle (LSP) is neutral. This constraint is a direct consequence of R-parity conservation and is almost automatic. Excluded regions are shown for tan  =35, 50

26. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Experimental lower limits on Higgs and superparticle masses. In MSSM the couplings in the Higgs potential are the gauge couplings. At the tree level the lightest Higgs boson is lighter than Z 0 ! (if m A  M Z )

27. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Experimental lower limits on Higgs and superparticle masses. However, loop corrections, especially originating from top quark and stops, can increase m h considerably. 1-loop contribution is large and positive 2-loop contribution is small and negative

28. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Experimental lower limits on Higgs and superparticle masses. M asses of other Higgses are always much larger than m h and thus they decouple. The lightest Higgs has the couplings of the SM Higgs within a few per cent. The experimental limits on the SM Higgs M H >114 GeV can be taken. Fit of electroweak data

29. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Experimental lower limits on Higgs and superparticle masses. Regions excluded by Higgs experimental limits provided by LEP2 for tan  = 35, 50

30. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Experimental lower limits on Higgs and superparticle masses. LEP2 collaborations have finished taking data and collected the rich statistics for e + e − CM energies up to √s  208 GeV. Searches for superpartners at LEP2 gave negative results

31. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Cold Dark Matter Constraint. The evidence for the Dark Matter:  Flat rotation curves of spiral galaxies  Gravitational lensing  Motion of galaxies within clusters  Large scale structure formation Flat rotation curves tell that there exist about ten times more mass in the halo around galaxies than in the stars of the disc. The rotation curve of the Milky Way confirms the usual picture.

32. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Cold Dark Matter Constraint. Types of the Dark Matter:  Baryonic dark matter (ten times more than visible matter – 4 %, estimation comes from primordial deuterium abundance). Candidates: MACHOs (whita dwarfs, brown dwarfs, planets)  Non-baryonic “hot” dark matter. Candidates: massive neutrinos. Contribution is comparable with the one of luminous matter.  Non-baryonic “cold” dark matter. Candidates: weakly interacting massive particles (WIMPs)  Particle Physics and Supersymmetry

33. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Cold Dark Matter Constraint. Supersymmetry provide a perfect candidate for dark matter – the neutralino – the mixture of superpartners of photon Z-boson and neutral Higgs bosons  Neutral particle  The lightest supersymmetric particle (LSP)  Stable !!!  Experimental lower mass limit m  > 45 GeV

34. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Favoured regions of parameter space  Pre-WMAP allowed regions in the parameter space. From the Higgs searches tan  >4, from a  measurements  >0 tan  =35 Fit to all constraints tan  =50

35. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Favoured regions of parameter space  Pre-WMAP allowed regions in the parameter space. Inclusion of dark matter constraint strongly limit the parameter space (the neutralino relic density must fall in the allowed range) tan  =35 Fit to Dark Matter constraint tan  =50

36. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Constrained MSSM ( Choice of constraints )  Cold Dark Matter Constraint. Recent WMAP data (2003) on termal fluctuations of CMBR Combination with other cosmic experiments gives

37. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Favoured regions of parameter space  WMAP data leave only very small allowed region as shown by the thin blue line which give acceptable neutralino relic density  Excluded by LSP  Excluded by Higgs searches at LEP2  Excluded by REWSB

38. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Favoured regions of parameter space  Bulk region  The region is characterized by low m 0 and low m 1/2  Typical processes: annihilation of neutralinos through t-channel slepton exchange:  The bulk region is practically excluded by LEP2

39. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Favoured regions of parameter space  Stau-coannihilation region  The region is characterized by low m 0 but large m 1/2  Masses of tau-slepton and neutralino (which has large higgsino component there) almost degenerate  Typical processes: neutralino-stau co-annililation:

40. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Favoured regions of parameter space  Focus point region  The region is characterized by large m 0 and low to large m 1/2  At the boundary of REWSB excluded region  becomes smaller and neutralino is almost higgsino  Typical processes: annihilation of neutralinos to gauge bosons:

41. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Favoured regions of parameter space  A-annihilation funnel region  The region where  Typical processes: resonance annihilation of neutralinos to fermion pairs through exchange of heavy Higgses A (and/or H):  The region reguires large tan 

42. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” EGRET constraint  EGRET data on diffuse galactic gamma ray flux show a clear excess for energies above 1 GeV in comparison with the expectations coming from conventional models  The excess is seen with the same spectrum in all sky directions  Blue dots – EGRET data Yellow area – theoretical expectations

43. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” EGRET constraint  Possible explanation: the excess is due to neutralino (Dark Matter) annihilation  An additional contridution from  Thi limits the neutralino mass to the 50-100 GeV range, thus put limits on the m 1/2 parameter

44. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Favoured regions of parameter space  The region compatible with all electroweak constraints as well as with WMAP and EGRET constraints are rather small  It corresponds to the best fit values of parameters tan  = 51 m 0 = 1400 GeV m 1/2 = 180 GeV A 0 = 0.5 m 0

45. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Superparticle spectrum  Superparticle spectrum for m 0 =1400 GeV, m 1/2 =180 GeV (region where electroweak, WMAP and EGRET constraints are fulfilled) Squarks and sleptons have masses in TeV range Gluinos, charginos and neutralinos are relatively light

46. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Favoured regions of parameter space  Allowed regions in mSUGRA parameter space for tan  = 35, 55

47. A Gladyshev (JINR/ITEP) “Constrained MSSM and recent astrophysical data” Prospects for SUSY searches  The reach of Fermilab TEVATRON, CERN LHC, and 500 and 1000 GeV linear electron-positron colliders for supersymmetry discovery