1. REHEATING TEMPERATURE IN GAUGE MEDIATION MODELS AND COMPRESSED PARTICLE SPECTRUM Olechowski, SP, Turzynski, Wells (ABOUT RECONCILING SUPERSYMMETRIC DARK MATTER WITH THE THERMAL HISTORY OF THE UNIVERSE)

2. DARK MATTER AND MATTER/ANTI-MATTER ASYMMETRY: TWO EXPERIMENTAL FACTS THAT HAVE NO EXPLANATION IN THE STANDARD MODEL LOOKING FOR AN EXPLANATION IN A SINGLE BSM THEORY, HOPEFULLY TOGETHER WITH A DYNAMICAL EXPLANATION OF THE ORIGIN OF THE FERMI SCALE BEST CHANCE: SUPERSYMMETRY BUT NOT EASY TO RECONCILE… Ellis, Linde, Nanopoulos, Sarkar, Kim..

3. BARYOGENESIS AT THE EW SCALE-DIFFICULT BARYOGENESIS VIA THERMAL LEPTOGENESIS? GENERIC CONCLUSION MANY WAYS TO WEAKEN THE BOUND BUT…. The problem: reheating temperature after inflation

4. BUT HIGH REHEATING TEMPERATURE MAY HAVE DANGEROUS IMPLICATIONS FOR BIG BANG NUCLEOSYNTHESIS! THERE MAY BE PRODUCED TOO MANY LONG-LIVED PARTICLES WHOSE DECAY PRODUCTS WOULD DESTROY SUCCESSFUL BBN E.G. (UNSTABLE) GRAVITINOS THE BOUNDS FORVERSUS (FOR SUCH PARTICLES)

5. BROKEN SUPERSYMMETRY --  SUPERGRAVITY TO EAT GOLDSTINO BY GRAVITINO (TO SAY THE LEAST) Invariance of the Lagrangian for the gravitino-goldstino system under local supersymmetric transformations, in the flat space, implies where F is the susy breaking vev

6. MODELS WITH CONSERVED R-PARITY; GRAVITY MEDIATION; NEUTRALINO AS LSP IS A DARK MATTER CANDIDATE  UNSTABLE GRAVITINO

7. Gravitinos are produced by scatterings of e.g. gauge bosons in the thermal bath

9. GRAVITINO PROBLEM (UNSTABLE GRAVITINOS) Gravitino decays with life time of the order of 10^7 sec or longer, so it decays long after BBN FOR GRAVITINO MASSES IN THE 10 TeV RANGE (Mirage mediation?) THE REHEATING TEM CAN GO ABOVE 10^9 GeV

10. GAUGE MEDIATION MODELS  STABLE GRAVITINO

11. MINIMAL GAUGE MEDIATION: A (SM) SINGLET FIELD X, COUPLED TO MESSENGERS IN REP OF SU(5) SUPERPOTENTIAL GAUGINO MASES SCALAR MASSES

12. STABLE GRAVITINO (LSP), AS IN GAUGE MEDIATION MODELS THE NLSP PRODUCED WITH SOME „THERMAL RELIC ABUNDANCE” (SOLVE BOLTZMAN EQUATION), HAD IT NOT DECAYED DECAYS ONLY INTO GRAVITINO and a SM PARTICLE, AND CAN BE LONG-LIVED; ITS DECAY PRODUCTS CAN DESTROY BBN

13. NLSP LIFE-TIME DEPENDS ON THE NLSP MASS (MAINLY) AND ON THE REST OF THE SUPERPARTNER SPECTRUM (WEAKLY) THE BBN BOUNDS CAN BE PRESENTED IN THE PLANE

14. LET’S LOOK AT BBN BOUNDS FOR SNEUTRINO OR STAU TAKEN AS THE NLSP (least hadronic decay products) BUT NEUTRALINO NLSP, FOR MIXED HIGGSINO-WINO AND BINO-HIGGSINO, CAN ALSO BE INTERESTING (for a recent complete analysis, see Laura Covi et al.)

15. WATCH THE GRAVITINO MASS!

16. IF THE STABLE GRAVITIONO IS THE ONLY CONSTITUENT OF DARK MATTER : THE GRAVITINO DENSITY IS A FUNCTION OF REHEATING TEMPERATURE AND PROPORTIONAL TO A FACTOR DEPENDING ON THE SUPERPARTNER SPECTRUM

17. THE GRAVITINO DENSITY IS A FUNCTION OF REHEATING TEMPERATURE M_r – gluino, wino, bino masses at T_R m_3/2 enters also the BBN bounds, and the PHYSICAL gaugino masses are Larger than m_3/2

18. LET’s LOOK AT THE GRAVITINO PRODUCTION FROM THE POINT OF VIEW OF MAXIMIZING THE REHEATING TEMPERATURE, BUT CONSITENTLY WITH THE BBN BOUNDS REMEMBER (PHYSICAL) IT IS THEN USEFUL TO STUDY THE QUESTION OF MAXIMIZING T_R AS A FUNCTION OF THE PHYSICAL NLSP MASS AND PHYSICAL GAUGINO MASSES

19. FIXED m_NLSP: T_R MAXIMIZED FOR 1) ALL M_R=m_NLSP (gauginos cannot then be universal at the GUT scale) 2) FOR m_3/2 that minimize the squared bracket, but consistently with the BBN bound (for a given value of the m_NLSP

21. STABLE GRAVITINO AS DARK MATTER AND MAXIMAL REHEATING TEMPERATURE (for stau/sneutrino NLSP) GRAVITINO MASS AROUND 1-10 GeV GAUGINO (IN PARTICULAR GLUINO) AND NLSP MASSES CLOSE TO EACH OTHER AND LIGHT (200 GEV- 1 TEV) HEAVY STOPS, FOR THE HIGGS TO BE ABOVE THE LEP BOUND AND FOR THE ELECTROWEAK BREAKING (WITH A LIGHT GLUINO) WHAT IS THE SCALE OF MEDIATION? (MESSENGER SCALE IN GAUGE MEDIATION MODELS) HOW TO GET IT IN SUPERSYMMETRY BREAKING MEDIATION MODELS?

22. FOR GRAVITINOS IN THE 1- 10 GeV RANGE AND WITH SFERMION MASSES OF A FEW HUNDREDS GeV, WE NEED WHERE

23. THUS, LARGE MESSENGER SCALE, CLOSE TO THE GUT SCALE HYBRID MODELS OF MEDIATION - GAUGE, WITH NON-NEGLIGIBLE GRAVITY MEDIATION CONTRIBUTION COMMENTS: RG EVOLUTION IMPORTANT FOR THE MAPPING OF THE PHYSICAL SOFT MASSES TO THEIR INITIAL LARGE SCALE VALUES

24. TYPICAL SPECTRA CONISTENT WITH THE MAXIMAL TEMPERATURE AND RG EVOLUTION

25. A LOOK AT THE EFFECTS OF RG RUNNING TO LARGE SCALES 1) RG FOR RIGHT STAU(NLSP): VERY SMALL INITIAL HYPERCHARGE SCALAR MASSES 2) RUNNING OF THE GAUGINO MASSES: NON-UNIVERSAL GAUGINO MASSES AT THE LARGE SCALE 3) HEAVY STOP MASSES: LARGE INITIAL “COLOURED” SCALAR MASSES

26. MINIMAL GAUGE MEDIATION VERSUS GENERALIZED GAUGE MEDIATION -- SEVERAL SINGLET FIELDS WITH VEVS, BROKEN SU(5) SYMMETRY IN THEIR COUPLINGS TO MESSENGER MULTIPLETS, MESSENGERS IN LARGER REPRESENTATIONS OF SU(5) THAT DECOMPOSE INTO REP OF SM SUBGROUPS

27. GENERALIZED GAUGE MEDIATION -6 PARAMETRS IN MODEL BUILDING, ONE HAS TO ARRANGE FOR LARGE CONTRIBUTIONS TO THE SCALAR MASSES OF COLOURED PARTICLES WHILE SUPPRESSING THE DOUBLET AND HYPERCHARGE CONTRIBUTIONS AND LIGHT GAUGINOS! CONSTRAINTS ON THE MESSENGER REPRESENTATIONS E.G. 3x24, 40+40*, 75..

28. SUMMARY MAXIMAL REHEATING TEMPERATURE WITH STABLE GRAVITINO (LSP) AS DARK MATTER IS REACHED FOR „SPECIAL” (PARTIALLY COMPRESSED) SPECTRUM; IT CAN BE INTERESTING PHENOMENOLOGICALLY (DEGENERATE STATES) COMPARED TO A GENERIC SPECTRUM, THE GAIN IN T_R IS ABOUT ONE ORDER OF MAGNITUDE; SUCH SCENARIOS BRING US CLOSER TO THE „LEPTOGENESIS-FRIENDLY” RANGE OF TEMPERATURES MESSENGER MASSES MUST BE CLOSED TO THE GUT SCALE (hybrid gauge – gravity mediation) GENERALIZED GAUGE MEDIATION MODELS CAN EASILY ACCOMODATE SUCH SCENARIOS

30. BUT, IT REQUIRES GENERALIZED GAUGE MEDIATION, WITH 1) non-universal gaugino masses (light gluino) 2) heavy “coloured” scalars 3) very light “hypercharge” scalars

35. THE SMALLER THE HADRONIC BRANCHING RATIOS THE WEAKER THE BOUNDS

47. S is the supercurrent of the visible (MSSM) sector; this sector is thermalized while the gravitionos are not