Temperature dependence of Standard Model
CP-violation and Cold Electroweak Baryogenesis
Aleksi Vuorinen
Bielefeld University
Collaborators:
Tomáš Brauner (Bielefeld)
Olli Taanila (Bielefeld)
Anders Tranberg (NBI)
Reference: Phys.Rev.Lett. 108 (2012) 041601, 1110.6818 [hep-ph]
INT, Seattle
April 11, 2012
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
F}_ {\m u \ n u} \ quad \ Righ t arro w \ quad \ frac{n _ B - n _ {\bar{B} }}{n _ \ gam m a} = - (0 .3 2 \ p m 0 .0 4 ) \ t im es1 0 ^ {-4 } \ t im es \ delt a_ {cp } \ n o n um ber
•
Symmetric initial condition
Must generate asymmetry dynamically
•
‘Baryogenesis’
Sakharov’s conditions
Any candidate theory of baryogenesis must incorporate:
1) Baryon number violation
2) Both C- and CP-violation
3) Departure from thermal/chemical equilibrium
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:
‣
•
Problem 2:
‣
•
Departure from equilibrium too weak: 1st order
transition only if mH<80 GeV, Kajantie et al., PRL 77 (1996)
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 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
Integrate out quarks; calculate
Tr log of Dirac operator with
background gauge and Higgs fields
Effective theory
for SM bosons
Perform expansion in number
of external legs/derivatives.
CP-violating
operators
Numerical simulation
on a lattice
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=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-ofequilibrium 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