Probing the Early Universe with Baryogenesis & Inflation - - PowerPoint PPT Presentation

Probing the Early Universe with Baryogenesis & Inflation

Wilfried Buchmüller DESY, Hamburg ICTP Summer School,Trieste, June 2015

• When and how was the baryon asymmetry generated?
• What caused inflation, and at which energy scale?
• How are inflation, baryogenesis and dark matter related?

[adapted from Schmitz ’12]

Outline

• BARYOGENESIS
• 1. Electroweak baryogenesis
• 2. Leptogenesis
• 3. Other models
• INFLATION
• 1. The basic picture
• 2. Recent developments

BARYOGENESIS

What is the origin of matter, i.e., the baryon-to-photon ratio

ηB = nB

nγ = (6.1 ± 0.1) × 10−10

? ? ? ? Key references

• A. D. Sakharov, JETP Lett. 5 (1967) 24
• G. ‘t Hooft, Phys. Rev. Lett. 37 (1976) 8
• V. A. Kuzmin,
• V. A. Rubakov and M. E. Shaposhnikov, Phys. Lett. B 155 (1985) 36
• J. A. Harvey and M. S. Turner, Phys. Rev. D 42 (1990) 3344

Sakharov’s conditions

Necessary conditions for generating a matter-antimatter asymmetry:

• baryon number violation
• C and CP violation
• deviation from thermal equilibrium

Alternative mechanisms: dynamics of scalar fields, e.g. Affleck-Dine baryogenesis, heavy moduli decay, ... Check of 3rd condition: hBi = Tr(e−βHB) = Tr(ΘΘ−1e−βHB) = Tr(e−βHB) , Θ = CPT

Sphaleron processes

Baryon and lepton number not conserved in Standard Model, JB

µ = 1

3 X

generations

• qLγµqL + uRγµuR + dRγµdR
• ,

JL

µ =

X

generations

• lLγµlL + eRγµeR
• ,

divergence given by triangle anomaly, ∂µJB

µ = ∂µJL µ

= Nf 32π2 ⇣ −g2W I

µνf

W Iµν + g02Bµν e Bµν⌘ ; Nf: number of generations; W I

µ, Bµ: SU(2) and U(1) gauge fields,

gauge couplings g and g0.

Change in baryon and lepton number related to the change in topological charge the gauge field, B(tf) − B(ti) = Z tf

ti

dt Z d3x@µJB

µ

= Nf[Ncs(tf) − Ncs(ti)] , with Ncs(t) = g3 96⇡2 Z d3x✏ijk✏IJKW IiW JjW Kk

−1 1

T=0, sphaleron T=0, instanton E / W Esph

Non-abelian gauge theory: ∆Ncs = ±1, ±2, . . .. Jumps in Chern-Simons asso- ciated with changes of baryon and lepton number, ∆B = ∆L = Nf∆Ncs .

Sphaleron

cL

τ

L

e

µ

L

s

L

s t b b ν ν ν u d d

L L L L L

In SM, effective 12-fermion interaction OB+L = Y

i

(qLiqLiqLilLi) , ∆B = ∆L = 3 uc+dc + cc → d + 2s + 2b + t + νe + νµ + ντ

Sphaleron rate crucially depends on temperature, only relevant in early universe:

zero temperature: Γ ⇠ e−Sinst = e− 4π

α = O

• 10−165

EW phase transition: ΓB+L V = κ M 7

W

(αT)3 exp (βEsph(T)) , with Esph(T) ' 8π g v(T) high temperature phase: ΓB+L V = κsα5T 4 ⇠ 10−6

“consensus” among theorists: B+L violating processes in thermal equilibrium in temperature range:

TEW ∼ 100 GeV < T < Tsph ∼ 1012 GeV

... but no direct experimental evidence for instanton or sphaleron processes ...

Chemical potentials

In SM, with Higgs doublet H and Nf generations, there are 5Nf + 1 chemical potentials (qi, `i, ui, di, ei); for non-interacting gas of massless particles µi give asymmetries in particle and antiparticle number densities, ni − ni = gT 3 6 8 < : µi + O ⇣ (µi)3⌘ , fermions 2µi + O ⇣ (µi)3⌘ , bosons

Relations between the various chemical potentials: SU(2) instantons: X

i

(3µqi + µli) = 0 QCD instantons: X

i

(2µqi − µui − µdi) = 0

vanishing hypercharge of plasma: X

i

✓ µqi + 2µui − µdi − µli − µei + 2 Nf µH ◆ = 0 Yukawa interactions: µqi − µH − µdj = 0 , µqi + µH − µuj = 0 , µli − µH − µej = 0

Relations determine B and L in terms of B-L :

B = X

i

(2µqi + µui + µdi) , L = X

i

(2µli + µei) B = cs(B − L) , L = (cs − 1)(B − L) , cs = 8Nf + 4 22Nf + 13

Electroweak baryogenesis and leptogenesis fundamentally different! In EWBG B-L conserved, generation of B in strong phase transition; in LG generation of B from initial generation of B-L (then unaffected by sphaleron processes)

• I. Electroweak Baryogenesis

Key references

• D. A. Kirzhnits and A. D. Linde, Phys. Lett. B 42 (1972) 471
• A. G. Cohen, D. B. Kaplan and A. E. Nelson, Phys. Lett. B 336 (1994) 41

Reviews

• W. Bernreuther, Lect. Notes Phys. 591 (2002) 237
• D. E. Morrissey and M. J. Ramsey-Musolf, New J. Phys. 14 (2012) 125003
• T. Konstandin, Physics - Uspekhi 56 (8) 747 (2013)

φ

crit

φ

T = T

C

V

eff

T = T < T

C 1

T = T > T

C 2

φ V

eff

T

1

TC T

2

2nd order vs 1st order (electroweak) phase transition, as universe cools

• down. What determines the shape of the effective potential? How does the

phasetransition proceed in an expanding universe? How can the complicated nonequilibrium process be calculated, where all masses are generated?

Finite-temperature effective potential

Massive scalar field: Euclidean field theory with finite time range β; add source term, calculate free energy (constant source, volume Ω):

Sβ = Z

β

✓1 2(∂τφ)2 + 1 2(∂iφ)2 + V (φ) ◆ V (φ) = 1 2µ2 + λ 4 φ4 , Z

β

= Z β dτ Z d3x , β = 1 T

Zβ[j] = Z

β

Dφ exp (Sβ[φ] Z

β

jφ) = exp (βΩWβ(j)) , ∂Wβ ∂j = 1 βΩh Z

β

φ(x)i ⌘ ϕ

Legendre transformation yields effective potential: explicit calculation, high temperature expansion: 2nd term is free energy of massless boson; thermal bath generates “thermal mass” of boson; usefull concept to understand some effects in thermal field theory qualitatively, but different from kinematic mass; in gauge theories problem of gauge invariance ...

Vβ(ϕ) = VT =0(ϕ) π2 90T 4 + 1 24m2(ϕ)T 2 1 12π m3(ϕ)T + . . . m2(ϕ) = m2 + 3λϕ2 , m(ϕ) T ⌧ 1 = 1 2(m2 + λ 4 T 2)ϕ2 + λ 4 ϕ2 + . . . Vβ(ϕ) = Wβ(j) − ϕj , j = −∂Vβ ∂φ

Higgs model & symmetry breaking

In (Abelian) Higgs symmetry “broken” in ground state: finite-temperature potential (with “barrier temperature”, where the barrier dissappears):

Sβ = Z

β

• (Dµφ)∗Dµφ + µ2|φ|2 + λ|φ|4

, Dµ = ∂µ + igAµ , µ2 < 0 , Re φ0 =

• −µ2/λ

1/2 ≡ ϕ0/ √ 2 , mA = gϕ0 , mH = √ 2λ ϕ0

Vβ(ϕ) = a 2(T 2−T 2

b )ϕ2 − b

3Tϕ3 + λ 4 ϕ4 + . . . ∂2Vβ ∂2ϕ

• ϕ=0 = 0 : T 2

b = −µ2

a , a = 3g2 16 + λ 2

Cooling down, at critical temperature, Higgs vev jumps to critical vev: phase transition weak for large Higgs mass (small coupling λ); Standard model and extensions: “a” and “b” in effective potential more complicated functions of gauge and Yukawa couplings. Much work on effective potential (mostly mid-nineties): loop corrections, gauge dependence, infrared divergencies, treatment of Goldstone bosons, resummations, nonperturbative effects (gap equations, rigorous lattice studies!), beautiful work ... Baryogenesis needs strong phase transition: not possible in SM, but possible in extensions ...

Vβc(ϕc) = Vβc(0) : T 2

c T 2 b

T 2

c

' b2 aλ > 0 , ϕc Tc = 2b 3λ

ϕc Tc > 1

Nonperturbative effects change 1st order transition to crossover at critical Higgs mass:

[Csikor, Fodor, Heitger ’98] [Jansen ’96]

critical endpoint, lattice: RHW = mH mW , mc

H = 72.1 ± 1.4 GeV

gap equations, magnetic mass: mc

H =

✓ 3 4πC ◆1/2 ' 74 GeV , mSM = Cg2T , C ' 0.35

Phase diagram

Bubble nucleation & growth

bubbles form

and expand

liquid T < TC ~

_

T T C

t = t0 t > t0

nucleation rate per volume: Γ V = A exp (−Γeff[Φ]) , Φ : saddle point of effective action, interpolating between the two phases , Langer’s theory, ...

no 1st-order phase transition in SM, but in extensions (singlet model, 2HDM,...)

broken phase becomes our world unbroken phase

v Wall = 0

φ

>> H

CP CP

_

~

Γ B + L

Sph

Γ B + L

Sph

q _ q q q _ q _ q q q _

CP violating scatterings at bubble wall (one-dimensional approximation):

Lf = − X

ψ

yψ ¯ ψLψRφ , φ(z) = ρ(z) √ 2 eiθ(z) , ρ(z) = vc 2 ✓ 1 − tanh z Lw ◆

Calculating the baryon asymmetry

very difficult, series of approximations: Schwinger-Keldysh → Boltzmann equations → diffusion equations ... ; CP violating interactions with bubble wall generate in front of wall excess of left-handed “tops”, converted to baryon asymmetry by sphaleron processes; in frame of wall chemical potentials only depend on distance from wall: important parameters: critical Higgs vev, bubble wall velocity, bubble wall width, diffusion parameters, ...

chemical potentials: µqL(z) = 3(µq1(z) + µq2(z) + µq3(z)) baryon number density: ∂nB ∂t = 3 2 Γsph T ⇣ µqL − κcs nB T 2 ⌘ diffusion equations: vw∂zµi − X

j

Γijµj + · · · = Si final result: nB = 3 2 Γsph vwT Z ∞ µqL(z)e−kBz , kB = 3κcs 2vw Γsph T 3

Example 1: 2 Higgs-doublet model (2HDM)

V (H1, H2) = −µ2

1H† 1H1 − µ2 2H† 2H2 − µ2 3(eiαH† 1H2 + h.c.)

+ λ1 2 (H†

1H1)2 + λ2

2 (H†

2H2)2 + λ3(H† 1H1)(H† 2H2)

+ λ4|H†

1H2|2 + λ5

2 ⇣ (H†

1H2)2 + h.c.

⌘ LY = yH2q3tc + h.c. + . . . approximate Z2 symmetry, broken by µ3; measure for size of couplings, one-loop corrections: ∆ = max|δλi/λi|

Recent work: Dorsch, Huber, No ’13: mH± . mH0 < mA0 , mA0 & 400 GeV , Rγγ = Γ(h0 ! γγ)/Γ(h0 ! γγ)SM 6= 1 Blinov, Profumo, Stefanik ’15: Inert Doublet Model OK, predictions: (MH, MA, MH±, Rγγ) = (66, 300, 300, 0.90), (200, 400, 400, 0.93), (5, 265, 265, 0.90)

300 320 340 360 380 400 120 130 140 150 160 170 180 190 ηB=5 ηB=10 ηB=20 ηB=40 ηB=60

mH mh

ξ=1

[Fromme, Huber, Seniuch ’06]

ηB in units of 10−11; large enough baryon asymmetry requires ξ = vc/Tc & 1.5 and ∆ ∼ 0.5, i.e. 2HDM is strongly coupled! Watch electric dipole moments!

Example 2: Standard Model with singlet

Motivation: non-minimal composite Higgs models, additional singlet in low energy effective Lagrangian; strong first-order phase transition from tree-level potential, thermal instability for singlet and Higgs; CP violation via additional dim5-operator:

V (h, s, T) = λh 4  h2 − v2

c + v2 c

w2

c

s2 2 + κ 4 s2h2 + 1 2(T 2 − T 2

c )(ch h2 + cs s2)

mh ms vc f/b Lwvc vc/Tc S1 120 GeV 81 GeV 188 GeV 1.88 TeV 7.1 2.0 S2 140 GeV 139.2 GeV 177.8 GeV 1.185 TeV 3.5 1.5

Light singlet scalar in principle observable at LHC; problem: coupling only via Higgs! Dedicated searches needed; also modification of Higgs properties, electroweak precision observables, ...

[Espinosa, Gripaios, Konstandin, Riva ’12]

s h t t t e e e

LtHs = s f H ¯ qL3(a + ibγ5)tR + h.c.

CP violation for baryogenesis implies EDMs for electron and neutron; predictions close to upper experimental bound! Energy scale f/b ~ 1 TeV, i.e. low compositeness scale - other resonances due to compositeness should be in LHC range! Note: baryogenesis in MSSM popular for many years, but stop lighter than stop required ... ! Possibility in NMSSM ... ?

Summary: electroweak baryogenesis

• Very interesting topic in nonequilibrium QFT, huge activity during the past

past 30 years since closely related to Higgs mechanism

• Theoretical uncertainty considerable:
• Strong interactions and new particles are unavoidable; 2 HDM: charged

Higgs bosons,... ; SM with singlet: light neutral scalar; ...

• Dedicated searches at the LHC, stronger bounds on dipole moments

and electroweak precision tests should settle the issue of EWBG

nB s ⇠ Γsph T 4 1 LwTc δCP 4π e−mψ/Tc ✓ vc Tc ◆γ κd . 10−9 , Γsph/T 4 ⇠ 10−6 , γ = 3 . . . 4 , κd = 10−2 . . . 10−1 ' 6.2 · 10−10