Standard Model & Baryogenesisat 50 Years · 2018-11-22 · The Standard Model and Baryogenesisat 50 Years 1967 For the universe to evolve from B= 0 to B¹0, requires: 1.Baryon number

Standard Model & Baryogenesis at 50 Years

The Standard Model and Baryogenesis at 50 Years

Rocky KolbThe University of Chicago


1967

For the universe to evolve fromB = 0 to B ¹ 0, requires:

1. Baryon number violation2. C and CP violation3. Departure from thermal

equilibrium

95% of the Mass/Energy of the Universe is Mysterious


95% of the Mass/Energy of the Universe is Mysterious


BaryonAsymmetry

BaryonAsymmetry

BaryonAsymmetry

99.825% of the Mass/Energyof the Universe is Mysterious


CMB (Planck 2015): ΩB h2 = 0.02230 ± 0.00014

Increasing baryon component in baryon-photon fluid:

• Reduces sound speed.

• Decreases size of sound horizon.

• Peaks moves to smaller angular scales (larger k, larger l).

• Baryon loading increases compression peaks, lowers rarefaction peaks.


13143

BS

ccγ

ρρ

−

= +

( ) ( )0S Sr d cη

η η η′ ′=

PEAKS Sk n rπ=

Wayne Hu

BBN (PDG 2016): 0.021 ≤ ΩB h2 ≤ 0.024

Increasing baryon component in baryon-photon fluid:

• Increases baryon-to-photon ratio η.

• In NSE abundance of species proportional to η A−1.

• D, 3He, 3H build up slightly earlier leading to more 4He.

• Amount of D, 3He, 3H left unburnt decreases.


Discrepancyis fake news

• Why is there an asymmetry between matter and antimatter?

o Initial (anthropic?) conditions: Requires “acausal” initial conditions. Inflation, which seemingly evades acausal issue for density

perturbations, dilutes pre-inflation baryon number by an exponential amount.

o The modern perspective is that reheating after inflation produced a symmetric universe (equal abundances of matter & antimatter).

o Asymmetry developed dynamically after inflation and reheating through a process known as “baryogenesis.”

• Why is it about 10−10 ?

Baryon Asymmetry: nB/s = (0.861 ± 0.005) × 10 −10


Inner Space/Outer Space ConnectionA complete Standard Model of Particle Physics, arising from laboratory experiments and beautiful theoretical ideas, should be applicable to the universe beyond terrestrial laboratories and (in principle) allow the calculation of cosmological parameters such as the baryon number of the universe.

A failure of today’s Standard Model of Particle Physics to account completely for the observed universe (dark matter, dark energy, inflation, baryogenesis) points to the fact that Today’s Standard Model of Particle Physics is not the Final Standard Model of Particle Physics.

Cosmological considerations may point to directions for physics beyond today’sStandard Model. The baryon asymmetry is an example of this.


• Can the standard model of particle physics explain a tiny number in the standard model of cosmology: nB/s = (0.861±0.005) × 10 −10 ?

No, or at least, not yet!

• Can the standard model of particle physics explain an order-unity number in the standard model of cosmology: Dark Matter/Baryons ≈ 5.3?

No, or at least, not yet!

• Starting after inflation/reheating with a symmetric universe, how must the SM be augmented to produce an asymmetric universe?


Baryon Asymmetry: nB/s = (0.861 ± 0.005) × 10 −10

To be discussed:Electroweak BaryogenesisThermal LeptogenesisGUT BaryogenesisAffleck-Dine BaryogenesisSpontaneous Baryogenesis

Other possibilities:Baryogenesis from

• Primordial Cosmic Strings• Primordial Magnetic Fields• Primordial Black Holes

Dissipative BaryogenesisWarm BaryogenesisCloistered BaryogenesisCold BaryogenesisPlanck BaryogenesisPost-Sphaleron BaryogenesisWIMPy BaryogenesisDirac LeptogenesisResonant LeptogenesisNon-Local Electroweak BaryogenesisMagnetic-Assisted EW BaryogenesisSinglet-Assisted EW BaryogenesisVarying Constants Driven Baryogenesis...


Many, Many Models for Baryogenesis

1. Baryon number violating processes :

2. C and CP violating processes:

3. Nonequilibrium conditions:

Sakharov Criteria in the Standard Modelˆ ˆ, 0B H ≠


Zero temperature:Γ ∝ e ≈ 10−171

Non-zero temperature:⟨h⟩ ≠ 0⟨h⟩ = 0





Yes in SM(nonperturbatively)Conserves B − L ( ) ( )sph3 4 E T T

W W WM T M eα −Γ ∝

−16π 2/g2

( )4WTαΓ ∝

Klinkhamer & Manton

’t Hooft








Yes in SM(nonperturbatively)Conserves B − L

Yes in SMDirect CP violation

(CKM)

But Jarlskog invariant very small: CP ∝ (mt

2−mc2) (mt

2−mu2) (mc

2−mu2) (mb

2−ms2) (mb

2−md2) (ms

2−md2) × 2J

J = c12 c132 c23 s12 s13 s23 sinδ

( ) ( )sph3 4 E T TW W WM T M eα −Γ ∝

−16π 2/g2

( )4WTαΓ ∝

Klinkhamer & Manton

’t Hooft






3. Nonequilibrium conditions: Dimopoulos & Susskind




(CKM)


2−mc2) (mt

2−mu2) (mc

2−mu2) (mb

2−ms2) (mb

2−md2) (ms

2−md2) × 2J

J = c12 c132 c23 s12 s13 s23 sinδ


−16π 2/g2

( )4WTαΓ ∝

( )( )

( ) ( )

ˆ ˆ1

ˆ 1

ˆ ˆ ˆB Tr B Tr CPT CPT B

ˆ ˆTr CPT B CPT B

H H

T

H

T

e e

e

β β

β

−− −

−−

= = = = −

Klinkhamer & Manton

’t Hooft


CPT conservedˆCPT, 0H =





3. Nonequilibrium conditions: Dimopoulos & Susskind




(CKM)


2−mc2) (mt

2−mu2) (mc

2−mu2) (mb

2−ms2) (mb

2−md2) (ms

2−md2) × 2J

J = c12 c132 c23 s12 s13 s23 sinδ


−16π 2/g2

( )4WTαΓ ∝

( )( )

( ) ( )

ˆ ˆ1

ˆ 1

ˆ ˆ ˆB Tr B Tr CPT CPT B

ˆ ˆTr CPT B CPT B

H H

T

H

T

e e

e

β β

β

−− −

−−

= = = = −

Klinkhamer & Manton

’t Hooft


No in SM andstandard cosmology CPT conserved

ˆCPT, 0H =

PrimordialPlasma

Electroweak BaryogenesisThe baryon asymmetry is generated at the electroweak phase transition from the seed of CP-violating interactions of particles scattering at the Higgs-field bubble wall.

Assume 1st-order EWK phase transition: nucleate broken-phase bubble in symmetric phase background(phase coexistence → nonequilibrium conditions).

⟨h⟩ ≠ 0 ⟨h⟩ = 0⟨h⟩ = 0

⟨h⟩ = 0

⟨h⟩ = 0


Broken phase expands into unbroken phase.

In broken phase sphalerons suppressed exp(−Esph/T),while in symmetric phase sphalerons unsuppressed.

h

VWall

Kuzmin, Rubakov, Shapashnikov;Cohen, Kaplan, Nelson

⟨h⟩ ≠ 0ΔB H

⟨h⟩ = 0ΔB H

PrimordialPlasma

Electroweak Baryogenesis


⟨h⟩ ≠ 0 ⟨h⟩ = 0⟨h⟩ = 0

⟨h⟩ = 0

⟨h⟩ = 0

1. If CP in Higgs/fermion interactions, different transmission & reflection of left & right-handed quarks at the wall leads to CPasymmetry at wall.




CP

h

VWall


⟨h⟩ ≠ 0ΔB H

⟨h⟩ = 0ΔB H

The baryon asymmetry is generated at the electroweak phase transition from the seed of CP-violating interactions of particles scattering at the Higgs-field bubble wall.



⟨h⟩ ≠ 0 ⟨h⟩ = 0⟨h⟩ = 0

⟨h⟩ = 0

⟨h⟩ = 0

⟨h⟩ ≠ 0ΔB H

⟨h⟩ = 0ΔB H

1. If CP in Higgs/fermion interactions, different transmission & reflection of left & right-handed quarks at the wall leads to CPasymmetry at wall.

2. Sphalerons violate B, they interact with qL(not qR) CP asymmetry converted to baryon asymmetry in front of wall.

3. Baryon asymmetry diffuses into broken phase across wall.




CP

h

VWall

B


PrimordialPlasma

The baryon asymmetry is generated at the electroweak phase transition from the seed of CP-violating interactions of particles scattering at the Higgs-field bubble wall.

Electroweak BaryogenesisProblems:

1. Phase transition not 1st-order in the Standard Model (Higgs mass too large; need mh 72 GeV).

2. too small in the Standard Model (Jarlskog invariant small; n, nuclei EDM).

3. Wall velocity may be too large. As Vwall → 1, wall moves too fast for baryon asymmetry to diffuse into broken-phase bubbles.

CP

Bad News: Electroweak baryogenesis doesn’t work within the Standard Model.

Good News: May point to directions BSM.


Electroweak BaryogenesisHow far BSM to have EWK phase transition 1st-order?

• MSSM initially promising if light right-handed stop (Carena, Quiros, Wagner; Cline & Moore). But increasingly stringent LHC constraints challenge the idea.

• NMSSM is more promising since extra singlet scalar field strengthens phase transition (Menon, Morrissey, Wagner; Huber, Konstandin, Prokopec, Schmidt).

• Two-Higgs models hard to make work since models that might work have very large Higgs self-coupling (Cline, Kainulainen, Trott).

• Most promising (and simplest) is to add a scalar singlet S coupling to Higgs Φ, e.g., V(Φ,S) = μ 2 S 2 + ζ Φ†Φ S 2 to provide cubic term (Choi & Volkas).

Two phase transitions since typically ⟨S⟩¹ 0.

• Lots of work probing models for 1st-order phase transitions at LHC & future colliders.

• 1st-order phase transitions can lead to gravitational waves.


( ) ( )3 22 21,12

V T h T hμ ςπ

Δ = − +

Electroweak BaryogenesisProbe of models with 1st-order phase transitions (Huang, Long, Wang).


V(S) = S 2 + S 3 + S 4 + Φ†Φ S 2 + Φ†Φ S

Points represent models with 1st-order phase transitionorange = too weak for baryogenesisblue = viable baryogenesisred = viable baryogenesis + detectable GWs

eLISA (launch 2034)

Many models with detectable Δ(hZZ) also result in eLISAgravitational wave signal.

real scalar singlet S (mH /2 < mS TeV) interacting with SM through Higgs portal Φ†Φ

(Huang, Long, Wang)(Huang, Long, Wang)

ghhh /ghhh,SM

1 −

g hZZ

/ghZ

Z,SM

Electroweak BaryogenesisProbe of models with 1st-order phase transitions (Huang, Long, Wang).


• Same qualitative results for other models• 2 discrete symmetry S → − S and ⟨S⟩ = 0.• Scalar doublet (squark-like).• New fermions rather than scalars.

• Significant deviations in hZZ-coupling, large (1) deviation in hhh-coupling. Discoverable at future colliders.

• Very strong 1st-order transitions lead to detectable gravitational waves.

• Gravitational waves produced by o Collision of bubbles,o Decay of magnetohydrodynamic turbulence,o Propagation of sound waves.

Electroweak BaryogenesisHow far BSM to have sufficiently large?

• phase in MSSM chargino mass matrix leads to chiral chargino asymmetry →chiral quark asymmetry (Carena, Quiros, Riotto, Vilja, Wagner; Cline, Joyce, Kainulainen). But increasingly stringent LHC constraints, as well as EDM constraints are a problem.

• NMSSM is more promising, extra singlet provides new sources of .

• Ditto for non-SM singlets.

• Multi-Higgs models.

CP

CP

CP



• Doesn’t work in Standard Model, but ingredients in place.

• Need another source of evading FCNC, EDM, and other constraints.

• To have phase transition 1st-order, couple light-ish (mH /2 < m TeV) fields to Higgs.

o Induces non-SM hhh and hZZ couplings which can be probed at colliders.

o Sufficiently strong 1st-order transition could produce gravitational waves detectable by eLISA.

• Many aspects of calculation difficult (wall velocity, transport equations across wall, gravitational wave production, etc.).

CP


• Type-I see-saw model (Gell-Mann, Ramond & Slansky; Yanagida; Mohapatra & Senjanovic; Schecter & Valle) for neutrino masses and mixing enlarges the SM to include a Majorana neutrino N with a large mass which couples to SM leptons and Higgs via = − λ L H N.

• Large Majorana mass for N; small Dirac mass for ν (generated by EWK Higgs mechanism). The see-saw results in light neutrino mass of

mν ≈ 0.3 eV (λ / 0.1)2 (1012 GeV /mN) 2 → so want mN ≈ 1012 GeV.

• N decays to SM leptons + Higgs, violating lepton number by 1:N → L H or N → L H Lepton-number violation.

• Assume Γ(N → L H ) > Γ(N → L H ) CP violation.

• If nonequilibrium conditions, can generate a lepton asymmetry with B − L ¹ 0.

• Sphalerons destroy B + L at T 100 GeV, conserve B − L always.

• If start with initial Li ¹ 0 & Bi = 0, end with Bf = − Li / 2.

(Actually Bf = − 28 Li / 79 Harvey & Turner.)

_ _

_ _

( ) ( )1 12 2

B B L B L= + + −

0

(Fukugita & Yanagida)


Thermal Leptogenesis

• Require interference between tree amplitude and loop corrections, e.g.,

N1

Lj

H

λ1jN1

Lj

H

λ1kλlj

λ∗kl

×

CP violation

( )( )11

1

2 22† 1 31

1 2 21† 2,3 all 11

3 1 3Im16 16

N lHN lH

ii iN

M mMM h

ε λ λπ πλ λ

→→

=→

− ≡ = ≤ M M

M

• Lepton number generated in decay proportional to CP parameterε1:

• If completely out of equilibrium (only drift and decay) nB/s ≈ 10−2ε1

CP violation expressed in terms of microphysics



1. N decay products thermalize; if temperature large enough can washout lepton number through processes like:

2. Efficiency of washout depends on competition between reaction rates (function of model parameters and T ) and expansion rate H ≈ T 2 / MPl.

3. Rates are

Thermal LeptogenesisNonequilibrium conditions

N

L

H

L LN

H HΔL = 2

_

ΔL = 1

Inverse decay, H L → N 2 « 2 scattering, N L ↔ t t

21 1 1

DECAY 28m M M

EhπΓ =

32 2

2 2 42, ,

i

L

i e

T mh ν

μ τπΔ =±

↔=

Γ = ( )1 1

INVERSE DECAY DECAY

/eqN

eqL

n M Tn

Γ = Γ( )

1 11 DECAY2 2 22

/1

eqNL t

eqL

n M TT mnhγ π

Δ =±↔

ΓΓ =

L

N t

H

ΔL = 1

t_

1 1 3m m m< <


≈ exp(−Μ1/Τ )

_2 « 2 scattering, H L ↔ H L

_



Nonequilibrium conditions4. Interesting constraints on neutrino-sector parameters:

o Condition for M1 to decay out-of-equilibrium: 10−3 eV ( ).

o Bound on r.m.s. neutrino mass to avoid ΔL = 2 washout: .

1 1 3m m m< <1m

2

, ,0.3 eV

ii e

mνμ τ=

≤

Thermal Leptogenesis• Leptogenesis is BSM, but motivated by observation of neutrino oscillations (and

masses). Also massive right-handed N fermions present in Grand Unified Theories beyond SU(5), e.g., SO(10).

• Scenario has all the necessary ingredients: L violation from N decay followed by B violation from sphaleron conversion to B asymmetry; CP violation from complex Yukawa couplings; out-of-equilibrium decay for reasonable model parameters.

• Experimental proof of Majorana nature of neutrinos would give a boost to scenario.

• Inner-Space/Outer-Space connection between Baryon Asymmetry (one number) and the richness of the Type-I see-saw model.


GUT Baryogenesis• Explosion of interest shortly after in late 1970s, after Georgi-Glashow 1974 SU(5)

paper.o Yoshimura (1978) used only 2 « 2 processes; no departure from equilibrium.

Doesn’t work.o Toussaint, Trieman, Wilczek, Zee (1979) and Barr (1979) pointed out problem.

Dimopoulos & Susskind (1979) used out-of-equilibrium decay. Weinberg (1979), and later Yoshimura (1979), made quantitative calculations based on out-of-equilibrium decay.

o Full Boltzmann reaction network including inverse decays and 2 « 2 processes by Kolb & Wolfram (1979) and Fry, Olive, Turner (1980).

o Applications to SU(5) and SO(10) by Harvey, Kolb, Reiss, Wolfram in 1982.

• Grand Unified Theories are BSM, but embrace the theoretical underpinnings of the Standard Model (spontaneously broken gauge theories, fundamental quarks and leptons, etc.).

o Ratio of energy scales may not be the most useful metric to measure how far “Beyond the Standard Model.”


GUT Baryogenesis• Theoretical motivation to unify strong with electroweak interactions.

• Expected unification at a mass scale of 1014 – 1016 GeV.

• SU(5) ⊃ SU(3)C ⊗ SU(2)L ⊗ U(1)Y . Gauge bosons in 24V representation. Fermions in 5f + 10f . Higgs in 5H .

• Coupling of fermions to gauge & Higgs:

• in decays of supermassive• Gauge bosons: ΓX ≈ α MX /3 • Higgs bosons: ΓS ≈ λt

2MS /16π

• , again from interference of tree and loop diagrams. Smallish (10−5) but workable.

• Large mass scale enables out-of-equilibrium decays.


CP

B

_

24 5 5 10 10 5 10 10 5 5 10V f f f f U H f f D H f fg λ λ = ⋅ ⋅ + ⋅ + ⋅ ⋅ + ⋅ ⋅

GUT BaryogenesisLarge mass scale enables out-of-equilibrium decays.

• Evolution of number density via decay/inverse-decay: .

• Figure of merit for departure from equilibrium is ratio of decay rate Γ to expansion rate at T = M: H(T = M) ≈ M 2 /M Pl .

• Require to be small.

o Small coupling as in thermal leptogenesis.

o Large mass as in GUT baryogenesis.

• Similar considerations for 2 ↔ 2scatterings & other reactions.


( )2 2EQ3n Hn n n+ = − Γ −

( )PLM

H T M M MΓ Γ≈=

Departure from equilibrium from decay/inverse-decay

Thermal leptogenesis:

GUT baryogenesis:

21 1

DECAY 28m M

hπΓ =

DECAY GUT XMαΓ ≈

12 31 110 GeV; 10 eVM m −= =

1610 GeVXM =

GUT BaryogenesisProblems with GUT Baryogenesis:


• Experimental: proton doesn’t seem to decay at expected level.

• Cosmological:o B − L is a conserved global quantum number in SU(5). Only produce B + L

asymmetry, which is washed out by sphalerons.o Symmetry breaking G → H ⊗ U(1) overproduces magnetic monopoles in phase

transition via Kibble mechanism and thermal production.o Expected temperatures after inflation smaller than unification scale.

• Perhaps unification at larger mass scale (helps with out-of-equilibrium conditions).

• Beyond SU(5): SO(10) has spontaneously broken local B − L so can produce B − L asymmetry (along with B + L). (Massive right-handed neutrino embedded in SO(10).)

• Cosmological issues more problematic.

• Nevertheless, take another look if observation of proton decay at Hyper-Super-Kamiokande.

After SUSY


Affleck-Dine BaryogenesisConsider SUSY GUTs.

Before SUSY breaking there is a many-parameter set of flat directions for the vacuum state.

In general, the states may have a nonzero vacuum expectation value for sleptons and squarks, and . VEV spontaneously breaks CP.

After SUSY breaking the flat directions develop minima with curvature m2 set by SUSY soft breaking scale, and eventually fields relax to , restoring gauge and global symmetries.

0l ≠ 0q ≠

0l q= =

Affleck & Dine

23H mφ φ φ+ = H m φ frozenH m φ relaxes to minimum,

oscillates until Γ = H

After decay at Γ = H

Can easily be (10−10)Can easily be (10+2)!

1/6 1/6 20 GUT 0

CP 2 2GUT GUT 0

B Mns M m M

φ φθφ

+

V(φ)

, ,...l qφ =

Before SUSY

0φ


Affleck-Dine BaryogenesisBaryon isocurvature perturbations.

Curvature perturbations: perturbations in all components are correlated (w = p / ρ):

Baryon Isocurvature perturbations:

Two sources of baryon perturbations: curvature perturbations set by quantum fluctuations in inflaton fieldisocurvature perturbations set by quantum fluctuations in the Affleck-Dine field.

CMB observations place limit on amplitude of baryon isocurvature perturbations (indistinguishable from CDM isocurvature perturbations) of a few percent.

CDM

CDM

1 3 3constant 1 4 4

i B

i i Bwγ ν

γ ν

δρδρ δρ δρδρρ ρ ρ ρ ρ

= → = = =+

ISOCURVATURE

34

B B

B B

γ

γ

δρδρ δρρ ρ ρ

= −

Spontaneous BaryogenesisScalar field φ, which interacts with the baryon-number current: φ−B = .

Field φ nearly homogeneous but evolves in time (rolls) like inflaton field, →φ−B = μB jB

0 = μB (nb – nb) = μB nB .

Interaction term shifts relative baryon and antibaryon spectra by an amount , i.e., dynamically breaks CPT. Effective chemical potential μB leads to net baryon density of nB ≈ μB T 2.

Require B-violating interactions, but system could be in equilibrium since .

True ground state has , so if -reactions effective, nB → 0 .

If -reactions freeze out at TF then final nB is , resulting in .

Many implementations.

Concern: produce isocurvature baryon density fluctuations (Turner, Cohen, Kaplan); at the time a feature, now a bug. Complicated ways to avoid this.

Cohen & Kaplan


1Bjμ

μφ−Λ ∂

0Bφ μΛ ≡ ≠

ˆCPT, 0H ≠

0Bφ μ= = B

B ( ) 2B FF

n Tφ= Λ ( )B Fn s Tφ≈ Λ

−

2φ Λ

Baryogenesis Conclusions• Standard Model of Particle Physics alone, combined with standard cosmological

model, cannot explain nB/s = (0.861 ± 0.005) × 10 −10 , at least so far.

• Perhaps answer will come from completely nonstandard cosmology, or from physics way beyond the Standard Model, for instance the ToE*.

• Or perhaps cosmology pointing directions BSM. o Electroweak Baryogenesis: 1st-order phase transition, new scalars coupled to

Higgs. New sources of .o Thermal Leptogenesis: Exploits BSM physics in neutrino sector.o GUT baryogenesis: Uses concept of unification of forces.


CP

*ToE — Theory omitting Evidence, which solves YUGE problems by pure thought without making boring testable predictions. Who needs observational verification? Sad. EXPERIMENTS ARE FOR LOSERS! MAGA: #MakeAstrophysicsGreekAgain.

Baryogenesis Conclusions• Standard Model of Particle Physics alone, combined with standard cosmological

model, cannot explain nB/s = (0.861 ± 0.005) × 10 −10 , at least so far.

• Perhaps answer will come from completely nonstandard cosmology, or from physics way beyond the Standard Model, for instance the ToE*.

• Or perhaps cosmology pointing directions BSM. o Electroweak Baryogenesis: 1st-order phase transition, new scalars coupled to

Higgs. New sources of . o Thermal Leptogenesis: Exploits BSM physics in neutrino sector.o GUT baryogenesis: Uses concept of unification of forces.


CP

Baryogenesis ConclusionsHoped for disruptions:

• Great new theoretical ideas in cosmology or particle physics are certainly welcome.

• Unexpected discoveries in particle physics or cosmology welcome.• Discovery of low-scale SUSY would open new possibilities for Electroweak

Baryogenesis.• Discovery of non-SM Higgs couplings (e.g., hhh or hZZ) at colliders could mean

EWK transition is 1st-order, pointing to Electroweak Baryogenesis.• Evidence for non-minimal Higgs sector could effect EWK transition and introduce

new CP phases. • Observation of non-SM sources of CP violation, say large neutron EDM. • Proof that neutrinos are Majorana particles would give impetus to Thermal

Leptogenesis.• Observation of proton decay would be evidence for perturbative baryon-number

violation at GUT scales; re-examine GUT Baryogenesis.


Baryogenesis ConclusionsHoped for disruptions:

• Observation of stochastic background of gravitational radiation with eLISA could be evidence for 1st-order phase transitions.

• Observation of a baryon isocurvature component might suggest a rolling field as in Affleck-Dine or Spontaneous Baryogenesis.

• Observation of primordial magnetic fields might point to role in baryogenesis.







Thanks to collaborators on baryogenesis:Dick Bond, Gian Giudice, Jeffrey Harvey, Stuart Raby, David Reiss, Joe Silk, Michael Turner, & Stephen Wolfram.

Benefitted from reviews by: Antonio Riotto; James Cline; Wilfried Buchmüller, Pasquale Di Bari, & Michael Plumacher; …

Benefitted from conversations & communications with:Andrew Long, James Cline, …


Documents

Standard Model & Baryogenesisat 50 Years · 2018-11-22 · The Standard Model and Baryogenesisat 50 Years 1967 For the universe to evolve from B= 0 to B¹0, requires: 1.Baryon number