Temperature dependence of Standard Model CP-violation and Cold Electroweak Baryogenesis Aleksi Vuorinen Bielefeld University Aleksi Vuorinen Bielefeld University INT, Seattle April 11, 2012 INT, Seattle April 11, 2012 Collaborators: Tomáš Brauner (Bielefeld) Olli Taanila (Bielefeld) Anders Tranberg (NBI) Reference: Phys.Rev.Lett. 108 (2012) , [hep-ph] Collaborators: Tomáš Brauner (Bielefeld) Olli Taanila (Bielefeld) Anders Tranberg (NBI) Reference: Phys.Rev.Lett. 108 (2012) , [hep-ph]

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

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

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

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’

Sakharov’s conditions 1) Baryon number violation 2) Both C- and CP-violation 3) Departure from thermal/chemical equilibrium Any candidate theory of baryogenesis must incorporate:

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

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)

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

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 T EW

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: 1 st order transition only if m H <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!(?)

Cold electroweak baryogenesis Possible way out: Assume supercooling to T << T EW García-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

Cold electroweak baryogenesis Classical numerical simulations of SM bosonic effective action produce ~10 4 times observed baryon asymmetry Tranberg, Hernandez, Konstandin, Schmidt, PLB 690 (2010)

Cold electroweak baryogenesis Classical numerical simulations of SM bosonic effective action produce ~10 4 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

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

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

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

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

The agenda Full SM Effective theory for SM bosons CP-violating operators Numerical simulation on a lattice Integrate out quarks; calculate Tr log of Dirac operator with background gauge and Higgs fields Perform expansion in number of external legs/derivatives.

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 order 4 Smit, JHEP 09 (2004) no CP-odd terms at this order! order 6 García-Recio, Salcedo, JHEP 07 (2009) only CP-odd P-even operators order 6 Hernandez, Konstandin, Schmidt, NPB 812 (2009) also CP-odd P-odd operators

Open questions 1)Discrepancy of existing order 6 results at T=0: Which one is correct? 2)How do the T=0 results connect with the expected T -12 suppression at high T ? 3)Up to what temperatures is the cold electroweak baryogenesis scenario still viable?

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)

Application to Standard Model Quark Dirac operator in chiral basis: Reduced Dirac operator K=K D +K A : Expand the trace in powers of derivatives/gauge fields:

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 D x, makes the expansion manifestly covariant already on the integrand level. García-Recio, Salcedo, JHEP 07 (2009) Generalization to thermal equilibrium straightforward

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

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

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

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

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

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~ m c ‣ 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

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

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