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Temperature dependence of Standard Model
CP-violation and Cold Electroweak Baryogenesis
Temperature dependence of Standard Model
CP-violation and Cold Electroweak Baryogenesis
Aleksi VuorinenBielefeld UniversityAleksi Vuorinen
Bielefeld University
INT, SeattleApril 11, 2012INT, Seattle
April 11, 2012
Collaborators: Tomáš Brauner (Bielefeld) Olli Taanila (Bielefeld) Anders Tranberg (NBI)
Reference: Phys.Rev.Lett. 108 (2012) 041601, 1110.6818 [hep-ph]
Collaborators: Tomáš Brauner (Bielefeld) Olli Taanila (Bielefeld) Anders Tranberg (NBI)
Reference: Phys.Rev.Lett. 108 (2012) 041601, 1110.6818 [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’
nonumber\delta_{cp}\times\{-4}times10^ \0.04) pm\(0.32- = gamma}\}}{n_n_{\bar{B}-frac{n_B \quad\Rightarrow \quad \nu}\F}_{\muwidetilde{\nu}\F_{\mu tr}{\rm phi\;\rphi^\dagge\}pi)^2m_W^2\}{(4delta_{cp}\frac{3\&=O}_{cp}& {\mathcal
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 TEW
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!(?)
Cold electroweak baryogenesis
• Possible way out: Assume supercooling to T << TEW 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 ~104 times observed baryon asymmetry Tranberg, Hernandez, Konstandin, Schmidt, PLB 690 (2010)
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
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 correspondsto 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 theoryfor SM bosons
CP-violatingoperators
Numerical simulationon 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 6García-Recio,
Salcedo, JHEP 07 (2009)
only CP-odd P-even
operators
order 6Hernandez,
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=KD+KA:
• 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 Dx, 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 Teff=Tv/φ.• ‘Critical’ value 10-5 reached around Teff=0.5-1 GeV
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
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
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