Temperature dependence of Standard Model CP-violation and Cold Electroweak Baryogenesis

1. Temperature dependence of Standard Model CP-violation and Cold Electroweak Baryogenesis • AleksiVuorinen • Bielefeld University Collaborators: TomášBrauner(Bielefeld) Olli Taanila (Bielefeld) Anders Tranberg (NBI) Reference: Phys.Rev.Lett. 108 (2012) 041601, 1110.6818 [hep-ph] INT, Seattle April 11, 2012

2. Outline • Introduction • Matter/antimatter asymmetry • (Cold) electroweak baryogenesis • CP-violation from the effective action • CP-violation in Standard Model • The SM effective action • Results • Summary and outlook

3. Outline • Introduction • Matter/antimatter asymmetry • (Cold) electroweak baryogenesis • CP-violation from the effective action • CP-violation in Standard Model • The SM effective action • Results • Summary and outlook

4. Matter/antiantimatter asymmetry • Chemical composition of the Universe well-known from BBN

5. Achieving the baryon asymmetry • Asymmetric initial condition? • Problem: Any pre-existing asymmetry gets washed out during inflation • Symmetric initial condition Must generate asymmetry dynamically • ‘Baryogenesis’

6. Sakharov’s conditions • Baryon number violation • Both C- and CP-violation • Departure from thermal/chemical equilibrium Any candidate theory of baryogenesis must incorporate:

7. Condition 1: B violation • Easily accommodated in GUT scenarios • In the Standard Model B is a classical symmetry, but… • …gets violated by an anomaly on the quantum level • Baryon number changes in sphaleron processes • Active at temperatures higher than the electroweak scale

8. Conditions 2 and 3 • C-violation: No problem - weak interactions violate C maximally (absence of right-handed neutrinos) • CP-violation: Present in SM, though suppressed; enters only through the CKM matrix • Departure from thermal/chemical equilibrium: • First order phase transitions • Classical field dynamics (e.g. inflaton oscillations) • Out-of-equilibrium decay of heavy particles (GUT scenarios)

9. Outline • Introduction • Matter/antimatter asymmetry • (Cold) electroweak baryogenesis • CP-violation from the effective action • CP-violation in Standard Model • The SM effective action • Results • Summary and outlook

10. Baryogenesis scenarios • Many different possibilities for baryogenesis • Electroweak baryogenesis (and modifications thereof): Rest of this talk • GUT baryogenesis: B-violation by new interactions; off-equilibrium through decay of heavy particles. Problems: Reheating temperature and proton decay • Leptogenesis: Sphalerons convert leptons to baryons, conserving B-L • If CKM matrix only source of CP-violation, baryogenesis must occur during EW phase transition • No B-violation below electroweak scale • Quark masses degenerate above TEW

11. Electroweak baryogenesis • Theoretically interesting question: Can baryon number be generated during SM electroweak phase transition? • Standard lore: No • Problem 1: • Departure from equilibrium too weak: 1st order transition only if mH<80 GeV, Kajantie et al., PRL 77 (1996) • Problem 2: • For T above EW scale, CP-violation suppressed by • Conclusion: SM cannot explain baryon asymmetry!(?)

12. Cold electroweak baryogenesis • Possible way out: Assume supercooling to T << TEWGarcía-Bellido, Grigoriev, Kusenko, Shaposhnikov, PRD 60 (1999) • Initial condition strongly out of equilibrium • Suppression of CP-violation much less severe than at high T • Typical scenarios involve additional scalars coupled to SM fields Enqvist, Stephens, Taanila, Tranberg, JCAP 1009 (2010) • Solving for baryogenesis dynamics very non-trivial • Need real-time simulations – vastly easier with fermions integrated out, their effects visible only through CP violating bosonic operators

13. Cold electroweak baryogenesis • Classical numerical simulations of SM bosonic effective action produce ~104 times observed baryon asymmetry Tranberg, Hernandez, Konstandin, Schmidt, PLB 690 (2010)

14. Cold electroweak baryogenesis • Classical numerical simulations of SM bosonic effective action produce ~104 times observed baryon asymmetry Tranberg, Hernandez, Konstandin, Schmidt, PLB 690 (2010) • Caveat: Simulations used as the source of CP-violation an operator that • Was evaluated at T=0, i.e. is likely orders of magnitude too large • May not exist at all: Controversial results from different groups • Conclusion: Need to derive full SM bosonic effective action at finite T (~ a few GeV) and perform simulations using it

15. Outline • Introduction • Matter/antiantimatter asymmetry • (Cold) electroweak baryogenesis • CP-violation from the effective action • CP -violation in the Standard Model • The SM effective action • Results • Summary and outlook

16. CP-violation in Standard Model • Originates from difference between quark mass and flavor eigenstates: • Similar structure in the lepton sector; if neutrinos come with Dirac masses, their contribution to CP-violating operators heavily suppressed • CKM matrix source of all observed CP-violation effects

17. CKM matrix and Jarlskog invariant • Kobayashi−Maskawa parameterization of CKM matrix: • CP-violating effects proportional to Jarlskog invariant: • Simplest perturbative CP-violating operator correspondsto the Jarlskog determinant:

18. Outline • Introduction • Matter/antiantimatter asymmetry • CP-violation in the Standard Model • (Cold) electroweak baryogenesis • CP-violation from the effective action • CP -violation in the Standard Model • The SM effective action • Results • Summary and outlook

19. Integrate out quarks; calculate Tr log of Dirac operator with background gauge and Higgs fields Perform expansion in number of external legs/derivatives. Full SM Effective theoryfor SM bosons CP-violatingoperators Numerical simulationon a lattice The agenda

20. Existing results at T=0 • In covariant gradient expansion, external gauge fields count as derivatives • Need at least four W’s to get Jarlskog invariant, hence CP-violation can only start at order four

21. Open questions • Discrepancy of existing order 6 results at T=0: Which one is correct? • How do the T=0 results connect with the expected T-12suppression at high T ? • Up to what temperatures is the cold electroweak baryogenesis scenario still viable?

22. Calculation of chiral determinant • Euclidean Dirac operator in general background field: • Parity-even and -odd parts of Euclidean effective action coincide with its real and imaginary parts • Anomalous Wess-Zumino-Witten term does not contribute to CP violation Smit, JHEP 09 (2004)

23. Application to Standard Model • Quark Dirac operator in chiral basis: • Reduced Dirac operator K=KD+KA: • Expand the trace in powers of derivatives/gauge fields:

24. Method of covariant symbols • Technique to calculate traces of differential operators and perform covariant gradient expansions • For a matrix function M(x) and covariant derivative Dx, makes the expansion manifestly covariant already on the integrand level. García-Recio, Salcedo, JHEP 07 (2009) • Generalization to thermal equilibrium straightforward

25. Outline • Introduction • Matter/antiantimatter asymmetry • CP-violation in the Standard Model • (Cold) electroweak baryogenesis • CP-violation from the effective action • Derivative expansion • The SM effective action • Results • Summary and outlook

26. Order six (T=0) • All contributions depend on a single master integral • Full result for CP-violating effective action: • Complete agreement with García-Recio & Salcedo

27. Order six (T≠0) Lorentz invariant operators at finite temperature: NB1: In Lorentz violating sector, O(100) more terms NB2: All P odd contributions, both Lorentz invariant and violating, vanish identically

28. Order six (T≠0) • Effective couplings drop very fast with temperature • Dependence on Teff=Tv/φ. • ‘Critical’ value 10-5 reached around Teff=0.5-1 GeV

29. Order six (T≠0) • Effective couplings drop very fast with temperature • Dependence on Teff=Tv/φ. • ‘Critical’ value 10-5 reached around Teff=0.5-1 GeV

30. Known issues – work in progress • At finite T, expansion in (covariant) temporal derivatives ill-defined • Spatial derivative part of the result unambiguous • Derivative expansion implies setting momenta of external fields to zero • Expansion argued to be valid up to p~ mc • Computation of next order will help assess convergence of expansion • Optimally, the calculation should be done in an out-of-equilibrium environment • Equilibrium case natural first step

31. Outline • Introduction • Matter/antiantimatter asymmetry • CP-violation in the Standard Model • (Cold) electroweak baryogenesis • CP-violation from the effective action • Derivative expansion • The SM effective action • Results • Summary and outlook

32. Summary • We determined the leading CP-violating operators of the Standard Model bosonic effective action at finite temperature • Result of García-Recio, Salcedo, JHEP 07 (2009) fully confirmed • Result of Hernandez, Konstandin, Schmidt, NPB 812 (2009) questioned • Cold EWBG scenario seems viable if T at most 1 GeV • Order-eight calculation in progress; relevant for estimates of convergence of the derivative expansion • Final step: Perform simulations with our effective action