1. Electroweak Baryogenesis: Electric dipole moments, the LHC, and the sign of the baryon asymmetry Sean Tulin (Caltech) Collaborators: Daniel Chung Bjorn Garbrecht Michael Ramsey-Musolf (NPAC UW-Madison)

2. Summary of this talk 1.Review electroweak baryogenesis  Basic picture  Requirements for it to work 2.EWB in the MSSM  What is needed  Sign of the baryon asymmetry Sign of EDMs Stop/sbottom mass spectrum Universe made of matter

3. Supersymmetry is super-great! + The minimal supersymmetric standard model (MSSM): + Coupling unification Hierarchy problem Dark matter Stringy motivation

4. Electroweak Baryogenesis Picture We want to explain PDG Dunkley et al [WMAP5] Sakharov conditions: 1.Baryon number violation 2.C- and CP-violation 3.Departure from thermal equilibrium 95% C.L. based on dynamics during the electroweak phase transition. Electroweak sphalerons complex phases 1st order phase transition

5. Electroweak Baryogenesis Picture Higgs potential V( ) T > T c T = T c T =0 First order electroweak phase transition during the early universe High T: EW symmetry restored from thermal corrections to Higgs potential Low T: EW symmetry broken At critical temp T c, degenerate minima. Just below T c, quantum tunneling from to bubble nucleation!     

6. Electroweak Baryogenesis Picture electroweak sphaleron Three Steps: 1. Nucleation and expansion of bubbles of broken EW symmetry 2. CP-violating interactions at bubble wall induces charge density, diffusing outside bubble 3. Sphalerons convert LH asymmetry into B asymmetry diffusion moving bubble wall CP Cohen, Kaplan, Nelson, 1992-1994;Huet, Nelson, 1996 Quark number density

7. electroweak sphaleron Three Steps: 1. Nucleation and expansion of bubbles of broken EW symmetry 2. CP-violating interactions at bubble wall induces charge density, diffusing outside bubble 3. Sphalerons convert LH asymmetry into B asymmetry diffusion moving bubble wall CP Cohen, Kaplan, Nelson, 1992-1994;Huet, Nelson, 1996 Quark number density Electroweak Baryogenesis Picture 4. Baryon asymmetry captured by expanding bubble

8. Requirements for electroweak baryogenesis to work Given a model of electroweak symmetry breaking (e.g. the standard model), what is required? Two requirements: 1.Sufficient CP-violation to explain observed n B 2.A strong first-order electroweak phase transition Neither satisfied in the SM May be satisfied in the MSSM, or in extensions of MSSM (e.g. NMSSM) RH stop 6.5 TeV (to avoid color-breaking phase transition) in MSSM Carena, Nardini, Quiros, Wagner, 2008

9. electroweak baryogenesis requirements Requirement #1: sufficient CP-violation Need to have “sufficient” CP-violation to produce the observed baryon asymmetry 1.Solve Boltzmann equations for particles species in the plasma, with background of expanding bubble of broken EW symmetry diffusion collisions CP-violating source n i = number density for particles — antiparticles

10. stolen from Bjorn Garbrecht

11. electroweak baryogenesis requirements Requirement #1: sufficient CP-violation Need to have “sufficient” CP-violation to produce the observed baryon asymmetry 1.Solve Boltzmann equations for particles species in the plasma, with background of expanding bubble of broken EW symmetry diffusion collisions CP-violating source n i = number density for particles — antiparticles weak sphaleron collision factor 2. Take left-handed fermion charge n L and compute baryon asymmetry

12. Baryon asymmetry CP-violating source collision factor 1.Magnitude of the baryon asymmetry depends on: K C : depends on large fraction of MSSM spectrum CP-violating source: depends on only a few parameters, but still much theoretical uncertainty 2. Sign of baryon asymmetry Depends on CP-violating phase and relatively few other parameters

13. Collision factor What interactions in the plasma are in chemical equilibrium? (i.e. fast compared to diffusion time scale) Previous lore: 1.Gauge/gaugino interactions 2.Top yukawa interactions 3.Strong sphalerons diffusion tLtLtLtL tLtLtLtL tRtRtRtR tRtRtRtR ~ ~ n L left-handed fermion density Cohen, Kaplan, Nelson, 1992-1994;Huet, Nelson, 1996

14. Collision factor What interactions in the plasma are in chemical equilibrium? (i.e. fast compared to diffusion time scale) Previous lore: 1.Gauge/gaugino interactions 2.Top yukawa interactions 3.Strong sphalerons Cohen, Kaplan, Nelson, 1992-1994;Huet, Nelson, 1996 Cirigliano, Lee, Ramsey-Musolf, S.T. (2006) Next, use n i = k i  i Then can express n L = K C n H where K C given in terms of k i ’s ~

15. Collision factor What interactions in the plasma are in chemical equilibrium? (i.e. fast compared to diffusion time scale) Previous lore: 1.Gauge/gaugino interactions 2.Top yukawa interactions 3.Strong sphalerons Cohen, Kaplan, Nelson, 1992-1994;Huet, Nelson, 1996 New Results: 4. Bottom yukawa interactions 5. Tau yukawa interactions (lepton-driven EWB) Chung, Garbrecht, Ramsey-Musolf, S.T. (2008) Cirigliano, Lee, Ramsey-Musolf, S.T. (2006)

16. Collision factor When are bottom Yukawa interactions important? Chung, Garbrecht, Ramsey-Musolf, S.T. (in prep) Time scale for bottom Yukawa interactions vs. diffusion time scale only

17. Collision factor With bottom Yukawa interactions, K C simplifies greatly: n L = K C n H ~ Conversion factor for Higgsinos into LH quarks (3 rd gen) k i = k i (m i /T) largest for small m i K C = 0 for K C < 0 for K C > 0 for Sign of K C (and, in part, n B ) determined by whether RH stop or sbottom is lighter Chung, Garbrecht, Ramsey-Musolf, S.T. (2008) Also, KC -> 0 for

18. Collision factor With bottom Yukawa interactions, K C simplifies greatly: n L = K C n H ~ Physical reason for this effect Which effect wins depends on which degrees of freedom are lighter Chung, Garbrecht, Ramsey-Musolf, S.T. (2008)

19. Focus on case where RH stop < 120 GeV (i.e. MSSM) pp Good: Light stop means large production cross section * Stop at the LHC Decay products: (assume m < 120 GeV) stable (on collider time scales) only if CHAMP searches imply CDF 2007 1. 2. 115 GeV

20. Stop at the LHC Light RH stop at the LHC pp Good: Light stop means large production cross section * Decay products: (assume m < 120 GeV) tends to dominate for Hikasa, Kobayashi (1987) Hiller, Nir (2008) 4. 3.

21. Stop at the LHC Light RH stop at the LHC Low energy QCD (~50 GeV) pp Good: Light stop means large production cross section c Missing energy Bad: Difficult to observe at LHC! * /g Better: radiative decay (signal: missing energy + high p T jet or photon) Carena, Freitas, Wagner (2008)

22. Light RH stop at the LHC Stop at the LHC Radiative stop decay: “LSP” dominant Signal: high P T jet + E T + soft charm jets (tough) Light stop window for strong 1st order phase transition Carena, Freitas, Wagner (2008)

23. Baryon asymmetry CP-violating source collision factor CP-violating source: Two-flavor oscillation problem (a la neutrino oscillations) but with a spacetime dependent Hamiltonian mass matrix What parameters govern the sign of the CP-violating source? relevant phases

24. Carena, Quiros, Seco, Wagner (2000) Lee, Cirigliano, Ramsey-Musolf (2004) Carena, Moreno, Quiros, Seco, Wagner (2002) Konstandin, Prokopec, Schmidt, Seco (2005) CP-violating source Various results: plotted vs. , for M 2 = 200 GeV and

25. CP-violating source How does an expanding bubble of broken EW symmetry produce a CP-asymmetry of particles vs antiparticles? Two-flavor oscillation problem (a la neutrino oscillations) but with a spacetime dependent Hamiltonian H(t) V(t) V(t) * particles anti-particles V(t) rotates flavor states into mass eigenstates (Consider simplified case where Hamiltonian only depends on t) Full treatment requires non-equilibrium, finite temp field theory Quick & dirty explanation: (using elementary QM)

26. CP-violating source Schrödinger Eqn: (flavor basis)  = L, R flavor states Evolution of states: Then rotate to mass basis Schrödinger Eqn is now where Similarly for anti- particle states

27. CP-violating source Evolution of states: Amplitude for mass state |j> to be in flavor state |> after time t CP-violating source: Initial condition: Begin with plasma in equilibrium: ensemble of mass basis states with weight

28. CP-violating source CP-violating source: where Conclusions: 1.Need two nearly degenerate states — otherwise small  and source washed out by oscillations 2.Need spacetime-dependent phase in mixing matrix 3.States not too heavy compared to temp T — otherwise Boltzmann suppressed

29. CP-violating source Example: CP-violating source from Higgsino/Wino oscillations. Flavor states

30. Carena, Quiros, Seco, Wagner (2000) Lee, Cirigliano, Ramsey-Musolf (2004) Carena, Moreno, Quiros, Seco, Wagner (2002) Konstandin, Prokopec, Schmidt, Seco (2005) CP-violating source Various results: plotted vs. , for M 2 = 200 GeV and

31. Implications for EDMs Two-loop EDMs are irreducible: Recently computed in full by Li et al (2008) Two possible CP-violating phases that could drive baryogenesis in MSSM also give rise to EDMs Suppose EDM measured. What are implications for EWB? 1.Assume same phase for both baryon asymmetry and EDM 2.Assume one-loop EDMs suppressed (heavy 1st/2nd gen sfermions)

32. CP-violating phase Li, Profumo, Ramsey-Musolf (2008) Sign of two-loop EDMs mostly correlated wrt CP-violating phases! positive contributions negative contributions

33. Current EDM constraints electron EDM neutron EDM Excluded Li et al (2008)

34. Future EDM searches Very exciting! Future EDM measurements will improve sensitivities by orders of magnitude.

35. Future EDM constraints electron EDM neutron EDM Excluded d e < 3x10 -30 e cm d n < 1x10 -28 e cm Baryogenesis curves made with most optimistic estimates Li et al (2008)

36. Conclusions Sign of baryon asymmetry may be the easiest consistency check for electroweak baryogenesis in the MSSM Under simplest assumptions (EDM and EWB determined by same phase), sign of baryon asymmetry determined by: Collision factor K C : depends on whether RH stop or sbottom is heavier Collision factor K C : depends on whether RH stop or sbottom is heavier Sin of CP-violating phase Sin of CP-violating phase Generalization beyond the MSSM? same collision factor unknown if EDMs correlate with CP-violating phase

37. CP-violating source Discrepency in treatment of diffusion Konstandin et al (2005) Cirigliano, Lee, Ramsey-Musolf, S.T. (2006) n B /s = 3 x (n B /s) WMAP x sin   n B /s = x (n B /s) WMAP x sin   30 nHnHnHnH ~ nHnHnHnH ~