Electroweak baryogenesis and beyond the SM (1)

Chang Sub Shin (IBS-CTPU)

at Summer Institute 2019 (Sandpine) Aug 18 – Aug 23, 2019 Outline

Implication of the baryon number for the Standard Model

Ideas of baryogenesis during EW phase transition (including basic of thermal field theory)

EWBG models, constraints and possible new directions Basics of elementary particle for baryogenesis

Baryon (βαρύς: heavy) and Lepton (λε̟τός: thin, small)

Baryon : made by (an odd number of) quarks e.g. proton , neutron Nucleon is heavy because of quark confinement by strong interaction (+uncertainty principle)

939.6 MeV ≃ 938.3 MeV ≃ 20000.5 MeV ≃ 1000 MeV

qu ark (Baryon)

Proton , Neutron gluon (Baryon)

PHYSICAL REVIEW LETTERS 121, 212001 (2018)

Lepton : e lementary fermion which does not feel strong interaction e.g. electron, neutrino (Lepton)

Helium atom Antiparticle

Predicted by theory (unexpectedly) P.A.M. Dirac provides the relativistic Schrödinger equation for electron: “Dirac equation” ⋅ 2 , 2 Solution to the Dirac equation yields

The negative energy solution was interpreted as “Dirac sea”. Excitation of electron from the sea gives the “hole”, the effective particle with the exactly same mass but the opposite charge prediction of After the relativistic Quantum Field Theory (QFT) was developed, the correct interpretation of the hole was made as the anti-particle: equally elementary particle with the same mass but opposite quantum numbers (charges) It turns out that all charged particle has its own antiparticle (e.g. antiquark, antineutrino) Stability of atom ?

Classical electrodynamics for the atom Quantum mechanics for the hydrogen atom

13.6 eV Life time: 0.016ns As the same way, is the positronium stable? No! 0.12ns 139ns

2 6.8 eV/ ≃ MeV → 2 3 23ℎ

Then why is the atom stable? Stability of atom ?

An atom is made by baryons and leptons

1, 0 0 0, 1

If baryon number and lepton number are conserved , between the proton and electron is forbidden. Each particle is also stable: proton is the lightest baryon, electron is the lighted charged lepton.

Atom is stable!

Baryon/Lepton number conservation is essential for life. List of baryon/lepton number

Notation: for a particle, , its antiparticle is denoted as (q: quark, l: lepton)

̅̅ 1/31/3 0 0 0 0 0 0 0 0 1 1 0 0 0 0

2/3, 2/3, 0 0 0 1, 1 0 0 1/3 1/3

, , , ,

110 0 0 0 11 0 0 1 1 0 0 0 0

1,0 1,0 1,0 1,0 0 1,1 0 0

There is NO observed event that violates baryon and lepton number conservation Discrete spacetime (pseudo) symmetry

Is there other symmetry of the theory ? fermions have the spin angular momentum ( ) ℏ/2

⃗ ⃗ ⃗⋅ ⃗ ⃗ helicity || ⃗ ⃗ C : Charge conjugation ( Q ) : Q → → , ⃗→ ⃗, ⃗→ ⃗ P : Parity ( ) : Q ⃗→ ⃗ → , ⃗→ ⃗, ⃗→ ⃗ T : Time reversal ( ) : Q → → , ⃗→ ⃗, ⃗→ ⃗ ↔ ↔ ↔

↔ e.g. Einstein, Maxwell, Dirac equation (so theory) is invariant under the C, P, and T. However the Standard Model is not invariant under the C, P, and T transformation. Evidence of - asymmetry At the present Universe matter + antimatter  fast annihilation into energetic photons

̅, , ̅ …

, , …

Earth is made by (not antiatom, antimolecule) Sun is made by matters. No observation of antimatter in the solar system No evidence of burst between two galaxy induced by intergalactic plasma

Solar wind: energetic , protons The early Universe

The Universe was extremely hot ( ) in the beginning. All particles and antiparticles ≫ ∗ form thermal plasma. As the temperature decreases (cool down) and becomes , ≪ ∗ most of particles and antiparticles with the mass ( ) are annihilated away ∗ HOT Cold e.g. for HOT ≫

1066282746 5 10662827463 14224600201

̅ → ̅ → for ≪ 2 0 35550255127 Cold

1 → 10 Big Bang Nucleosynthesis (BBN)

Light nuclei ( ) in the Universe were made between and . 1 sec 10 sec Input / 2.2 MeV

≡ /

Annual Review of Nuclear and Particle Science, 60:539-568, 2010 Big Bang Nucleosynthesis (BBN)

Light nuclei in the Universe were made between and : primordial abundance 1 sec 10 sec

The final abundances of them are sensitive to the initial baryon abundance . Observation of primordial light nuclei can predict the value of baryon asymmetry around ! 1 sec

The larger the nucleon density, the higher the temperature at which nucleosynthesis began, and so the less time there was for neutron decay before nucleosynthesis, leading to a higher final 4He abundance.

The higher the baryon density, the more complete will be the incorporation of neutrons into 4 , and hence the smaller the resulting He abundance of deuterium. [Weinberg , Cosmology] Cosmic Microwave Background (CMB)

As the temperature becomes lower than the atomic energy ( ), nucleons and eV electrons are bound and form atoms. Photons are decoupled and freely propagate : CMB

→ ̅

≃ 0 gravitational potential from Dark Matter PLANCK Satellite 1 3 1 3 /4

2.7 K Δ 10 Cosmic Microwave Background (CMB)

Baryon abundance is mostly determined by the heights of odd ( ), 2 1 and even ( ) peaks 2 1 2 cos

100 (a) Curvature (b) Dark Energy

80

K) 60 m ( T D 40 Δ 20 Wtot WL PLANCK 2013 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8

100 (c) Baryons (d) Matter 80 Ω ≡

K) 60 m ( T D 40

20 Wbh2 Wmh2

0.02 0.04 0.06 0.1 0.2 0.3 0.4 0.5 10 100 1000 10 100 1000 l l Hu, Dodelson , Ann.Rev.Astron.Astrophys.40:171 - Cosmic Microwave Background (CMB)

Consistent with the value from the BBN!

100 (a) Curvature (b) Dark Energy

80

K) 60 m ( T D 40

20 Wtot WL

0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8

100 (c) Baryons (d) Matter Ω80 ℎ ≡ ℎ

K) 60 m ( T D 40

20 Wbh2 Wmh2

0.02 0.04 0.06 0.1 0.2 0.3 0.4 0.5 10 100 1000 10 100 1000 l l Hu, Dodelson , Ann.Rev.Astron.Astrophys.40:171 - Baryo-genesis

If the baryon asymmetry exists at the early Universe, , as , ≃ MeV 1sec 6 10 the abundance of light nuclei and the shape of the CMB angular power spectrum, and non- observation of anti star, anti galaxy are all explained consistently.

≃ What is the origin of this asymmetry? Is this just an initial condition of the Universe? Is there any dynamical mechanism for ? 0 → 0 Baryon number is the good quantum number for as we observed. BUT it should be 1sec strongly broken at the early Universe 1sec

Big Bang/ 0 0 Inflation  0 1sec 10 year 10 sec 10 year Possibility of baryogenesis in the SM Just an initial condition?

It is commonly accepted that there is super accelerating period of the Universe.

All previous abundance of any particles, asymmetries are diluted away. A new way to generate the asymmetry after inflation is necessary. The Sakharov’s conditions JETP Lett. 5, 24 (1967)

In order to generate the asymmetry ( ) of the Universe from to ≡ ∑ 0 0 1) Baryon number violation: For some initial, final states with different baryon numbers, , . Γ → 0 If , any process gives , so that . No generation → 0 Δ 0 0 2) C and CP violation: for Γ → ⋯ Γ̅ → ⋯ ̅ If the baryon number violating process preserves Charge conjugation, , Therefore . 0 Even if C is violated, if CP is conserved, , Therefore . 0 3) B-violating interactions out-of-thermal equilibrium: Γ → Γ → If the baryon number violating process is in thermal equilibrium,

/ / Tr Tr ↔ ↔ / = / ↔ Tr Tr 0 We used . Any generated asymmetry is washed out. , 0 In other words, if CPT is broken as , → ∝ ↔ In the Standard Model ?

How can we check Sakharov’s conditions in the SM? In the framework of QFT , the evolution of the Universe can be described by the Lagrangian density ℒ

1 ℒ ℒ Δℒ 2

gluons, weak bosons, photons ℒ Higgs

quark, lepton kinetic terms

quark, lepton, Higgs Yukawa ints

There is the possibility to satisfy Sakharov’s three conditions B violation in the SM

1) Baryon number seems conserved in the SM (stability of the atom), but not exactly..

Classical level: baryon current is conserved ⃗ . ⋅ 0 → 0 Quantum level: not conserved 0

2 Tr 32

Nontrivial configuration of the gauge fields can yield the process with such as Δ 0

↔ ̅ ̅ ̅ ̅ ∑ ̅ 2, 0 ↔ 1, 3 How? B violation in the SM

2 Tr Δ Δ 32 The RHS of the equation is total derivative 2 Tr Tr 16 8 3 Change of the Chern-Simons number is the source of baryon number change

2 ⃗ ⃗ Tr intgers for vacua 16 3 Ex) ( ) with 0 ⃗ , ⃗ → 0 , ⃗ , 1 1 Tr 24 Related by large gauge transformation , ⃗ , 0 ⃗ , ⃗ → 0 B violation in the SM

2 Tr Δ Δ 32 The RHS of the equation is total derivative 2 Tr Tr 16 8 3 Change of the Chern-Simons number is the source of baryon number change

2 ⃗ ⃗ Tr intgers for vacua 16 3 Ex) ( ) with 0 ⃗ , ⃗ → 0 , , ⃗ , 1 1 ∼ 1 Δ Tr 24 Related by large gauge transformation , ⃗ , 0 ⃗ , ⃗ → 0 0 1 B violation in the SM

2 Tr Δ Δ 32 At zero temperature, tunneling rate to give ( ) is exponentially suppressed. Δ 1 / Pr tunneling ∝ exp . ∼ ∼ 10 ≪ 1 where is the Euclidean action for the possible tunneling trajectory of the gauge field. The instanton action is given by the condition ( , ). 0 . 0 . . 1 8 . Tr.. 2 (Because SU(2) is broken and gauge bosons get mass of , the dominant contribution of tunneling happens during . For , additional suppression: Δ Δ ≫ expΔ

, , ⃗ , 1 1 ∼ Δ Δ Tr 1 16 tunneling

, ⃗ , 0 / Intuitively , Pr Δ 1 ∼ ∼ 0 1 B violation in the SM

2 Tr Δ Δ 32 At zero temperature, tunneling rate to give ( ) is exponentially suppressed. Δ 1 / Pr tunneling ∝ exp . ∼ ∼ 10 ≪ 1 where is the Euclidean action for the possible tunneling trajectory of the gauge field. The instanton action is given by the condition ( , ). 0 . 0 . . 1 8 . Tr.. 2 (Because SU(2) is broken and gauge bosons get mass of , the dominant contribution of tunneling happens during . For , additional suppression: Δ Δ ≫ expΔ

Such a small probability at zero temperature is good for , stability of baryons. What happens in the early universe? ∼

5 4 3 2 1 0 1 Δ 5 4 3 2 0 Δ B (and C&P) violation in the SM

2 Tr Δ Δ 32 Note that energy barrier is finite. Therefore at the early Universe with finite temperatures, T, There could be enough energy to change the CS number: ˆ tL cˆL ℓe Pr Δ 1 ∝ exp ∼ ˆ cˆ tL L Creation and annihilation of sphalerons at the early Universe provide meaningful baryon number violating interactions uˆ L sphaleron∆ n = 1 uˆ L

cˆL ℓµ

ˆ ℓτ tL , uˆ L Static configuration at this point : sphaleron s (σφαλερός :ready to fall ) 2 ∼

5 4 3 2 1 0 1 Δ 5 4 3 2 0 Δ ** Sphaleorn transition from Sam S.C. Won’s slides sphaleron

0 1/2

1 Static configuration at this point : sphaleron (σφαλερός :ready to fall ) 2 ∼

5 4 3 2 1 0 1 Δ 5 4 3 2 0 Δ B violation in the SM

2 Tr Δ Δ 32

Note: since baryons are fermions, creating baryons cost energy as the figure. Therefore even if the baryon number is created, it could be washed out if CPT is preserved after generation ( ) and sphalerons are in equilibrium ( ): , 0 ≫ 1 ≃ → ∼ i.e. / → Tr 0 Need of sudden decoupling for the sphaleron process

,

5 4 3 2 1 0 1 Δ 5 4 3 2 0 Out-of-equilibrium evolution in the SM

2) Electroweak symmetry is spontaneously broken at T=0.

0 At the early Universe with high temperatures, symmetry could be restored. EW phase transition happens as temperature decreases. This is most significant out-of-eq. process in the SM. e.g. Bubble nucleation/expansion and collision: strong out-of-equilibrium process

0 0

0 0 Out-of-equilibrium evolution in the SM

The Standard Model EWPT of the SM ( ) is not 1 st , 2 nd 130 ry eo 125 GeV th nd n symmetric phase io order but cross-over : similar to the 2 order PT, at 120 rb Symmetric rtu pe but smooth change of Higgs expectation value, Phase st i.e. the correlation length does not jump (1 ) or 110 2nd order nd nd 2endpoint order /GeV c

diverge (2 ) at , just smoothly change /GeV T 100 endpoint ( ) . ≃ 0 90 Out-of-equilibrium process is not so violent. HiggsHiggs phase phase Laine, Rummukainen hep-lat/9809045 80 50 60 70 80 90 multicanonical m /GeV 1 H standard /GeV perturbative

0.8 D’Onofrio, Rummukainen, Tranberg arXiv:1403.3565

2 thermal / 0.6

fluctuation (T)/ T around 2 v

0.4 ∼ 0.2

0

140 150 160 170 180 T / GeV /GeV /GeV Out-of-equilibrium evolution in the SM

Sphaleron rate changes smoothly as the temperature decreases. Considering change of as the one-dimensional random walk, the rate per unit volume is given by Tr 0 1 Γ lim ≃ 20 for ≃ 2/ ,→ 2 1 10 exp for ≃ 2/ 0.03 -10 pure gauge multicanonical Γ 1 1 -15 standard ≃ ≫ 1 perturbative -20 0.8 D’Onofrio, Rummukainen, Tranberg arXiv:1403.3565 2

4 -25 / 0.6 G/T Γ (T)/ T 2 log v ln -30 standard 0.4 multicanonical ∼ fit perturbative -35 0.2 sphaleron decoupling -40 log[ aH(T)/T] 0 ≪ 1 1 -45 140 150 160 170 180 130 140 150 160 170 T / GeV T / GeV /GeV /GeV C & CP violation in the SM

CP transformation in QFT: The quantum field operators,  , , ⃗, , ⃗, , ⃗ transform under the CP as

, ⃗ , ⃗   , ⃗ ̅ , ⃗ , ⃗ ∗, ⃗ Therefore, the interaction terms given by Δℒ , ⃗   ∗ ∗  Δℒ , ⃗ , ⃗ , ⃗ , ⃗ , ⃗ , ⃗ ̅ , ⃗ transform as

∗   ∗  Δℒ , ⃗ , ⃗, ⃗ , ⃗ , ⃗, ⃗ ̅, ⃗ CP is conserved i.e. , Δℒ , ⃗ Δℒ , ⃗ only if the Yukawa couplings,  , are real:  ∗ . Complex couplings are necessary to get CP violation cf) CPT transformation gives  ∗ , . Therefore → , → , if there is not CPT violating background. Δℒ , ⃗ Δℒ , ⃗ C & CP violation in the SM

3) C and CP are violated in the SM: C violation: Only left-handed neutrino exists. ↔ ̅ Gauge interactions of left-handed and right-handed fermions different ↔ ↔  3 2 1 CP violation: Complex couplings (in mass eigen-basis) ↔ ̅  Δℒ , ̅, ̅ ℎ. . 2  Cabibbo–Kobayashi–Maskawa Matrix ( ) 3 3        ∗      ≃ 13 , ≃ 0.2 , ≃ 2.38 , ≃ 68 0 However, the basis independent CP violation ( Jarlskog invariant ) gives too small value

Tr ,  c c s s s sin ∼ 10 The devil is in the detail

Electroweak phase transition in the SM is not strong out-of-equilibrium process

CP violation of the SM is too small

There are all ingredients but NOT enough! New physics is necessary