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