[PPT] - The serendipity of EW baryogenesis Graldine SERVANT DESY/U.Hamburg PowerPoint Presentation

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DESY/U.Hamburg

Géraldine SERVANT

Higgs Cosmology workshop,

Kavli Royal Society Centre, March 28 2017

DESY

The serendipity of EW baryogenesis

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Aim: Exploring the cosmological interplay between Flavour dynamics and EW baryogenesis A rich programme

Baldes, Konstandin, Servant, 1608.03254 Baldes, Konstandin, Servant, 1604.04526 Bruggisser, Konstandin, Servant, to appear

Effect of varying Yukawas on EW phase transition

Implementation in Froggatt-Nielsen
Natural realisation of Yukawa variation in Randall-Sundrum
Calculation of baryon asymmetry in models of variable Yukawas
Von Harling, Servant, 1612.02447

2

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η = nB − n ¯

B

nγ ≡ η10 × 10−10

Matter Anti-matter asymmetry of the universe

: R R

5.7 ≤ η10 ≤ 6.7 (95%CL)

3

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Gavela, P. Hernandez, Orloff, Pene ’94 Konstandin, Prokopec, Schmidt ’04 Tranberg, A. Hernandez, Konstandin, Schmidt ’09

so far, no baryogenesis mechanism that

works with only SM CP violation (CKM phase) double failure:

lack of out-of-equilibrium condition

remains unexplained within the Standard Model

η

proven for standard EW baryogenesis attempts in cold EW baryogenesis Brauner, Taanila,Tranberg,Vuorinen ’12

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5

Baryogenesis at a first-order EW phase transition

[image credit:1304.2433]

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6 3) In symmetric phase,<Φ>=0, very active sphalerons convert chiral asymmetry into baryon asymmetry Chirality Flux in front of the wall

Baryon asymmetry and thf EW scale

Electroweak baryogenesis mechanism relies on a first-order phase transition satisfying

1) nucleation and expansion of bubbles of broken phase

broken phase

<Φ>≠0

Baryon number is frozen

2) CP violation at phase interface responsible for mechanism

f charge separation

CP Q U Q U H

hΦ(Tn)i Tn & 1

Kuzmin, Rubakov, Shaposhnikov’85 Cohen, Kaplan, Nelson’91

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The Electroweak Baryogenesis Miracle:

6
4
2

2 4 6

Broken Symmetric

Γws = 10−6 T e−

Esph T φ(T ) v

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The Electroweak Baryogenesis Miracle:

Γws = 10−6 T e−

Esph T φ(T ) v

ηB ∼ Γws µL Lw g∗ T

Lw ∼ 1 T

µL ∼ M

00M ∼ δCP

L2

w T

ηB ∼ Γws δCP g∗ Lw T 2

B ∼ 10−6 δCP

g∗ ∼ 10−8δCP

All parameters fixed by electroweak physics. If new CP violating source of order 1 then we get just the right baryon asymmetry.

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Objective # I Strong 1st-order EW phase transition

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50 100 150 200 250 300

Φ GeV

0.005 0.0025 0.0025 0.005 0.0075 0.01

VΦv4

first-order or cross over

50 100 150 200 250 300

Φ GeV

0.02 0.01 0.01 0.02

VΦv4

⤵ T →

In the SM, a 1rst-order phase transition can occur due to thermally generated cubic Higgs interactions:

for MH > 72 GeV, no 1st order phase transition

Sum over all bosons which couple to the Higgs

In the SM: not enough

In the MSSM: new bosonic degrees of freedom with large coupling to the Higgs Main effect due to the stop

V (φ, T) ≈ 1 2(−µ2

h + cT 2)φ2 + λ

4 φ4 −ETφ3

−ETφ3 ⊂ − T 12π

i

m3

i (φ)

i

≃

W,Z

10

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11

A strong 1st order PT leads to sizable deviations in hgg and hƔƔ couplings and therefore in Higgs production rate and decays in ƔƔ e.g: Light stop scenario in Minimal Supersymmetric Standard Model The most common way to obtain a strongly 1st order phase transition by inducing a barrier in the effective potential is due to thermal loops of BOSONIC modes.

Higgs Field @ h D Effective Potential @ Veff D

I. Thermally HBECL Driven

+ H-m 2 + c T 2L h 2

T Hh 2L3ê2

+ h 4 @ h D

eff D

Driven

2 4 6

Very constrained by LHC !

One adds new scalar coupled to the Higgs

Katz, Perelstein ’14

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12

The (former) EW baryogenesis window in the Minimal Supersymmetric Standard Model: A Stop-split supersymmetry spectrum

3

t , f

L 1,2 1,2 u,d

~ ~

λ 0.1 TeV 1 TeV 10 TeV

R

~

h , t , h ,

~

λ

from EDM bounds from Higgs mass bound for strong 1st order phase transition for sufficient CP violation

bounds get relaxed when adding singlets or in BSSM The light stop scenario: testable at the LHC

− →

γ χ 0 f ~ f f ~

∝ Im(µM2)

γ γ χ h, H, A

e x c l u d e d b y h i g g s m e a s u r e m e n t s a n d s t

p

s e a r c h e s see 1207.6330

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13

Easily seen in effective field theory approach:

Add a non-renormalizable Φ6 term to the SM Higgs potential and allow a negative quartic coupling

“strength” of the transition does not rely on the one-loop thermally generated negative self cubic Higgs coupling

V (Φ) = µ2

h|Φ|2 − λ|Φ|4 + |Φ|6

Λ2

〈〉

complete one-loop potential

1 4 3 2 2000 1750 1500 1250 1000 750 500 250 100 125 150 175 200 225 250 275

mh (GeV) 〈φn〉 Tn

Λ (GeV)

region where EW phase transition is 1st order

strong enough for EW baryogenesis if Λ 1.3 TeV

Delaunay-Grojean-Wells ’08

Grojean-Servant-Wells ’04

Higgs mass measurement does not constrain the nature of the EW phase transition

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14

at a Hadron Collider at an e

but Typically large deviations to the Higgs self-couplings

where

deviations between a factor 0.7 and 2

The dotted lines delimit the region for a strong 1rst

rder phase transition

µ = 3m2

H

v0 η = 3m2

H

v2

+ 36 v2 Λ2 + 6 v3 Λ2

L = m2

H

2 H2 + µ 3!H3 + η 4!H4 + ...

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example: the SM+ a real scalar singlet

g

V (H, S)

EW preserving min. EW broken min.

from F. Riva

> Espinosa et al, 1107.5441

e.g 1409.0005

S has no VEV today: no Higgs-S mixing-> no EW precision tests , tiny modifications of higgs couplings at colliders

V0 = µ2|H|2 + λ|H|4 + 1 2µ2

SS2 + λHS|H|2S2 + 1

4λSS4. p

The easiest way: Two-stage EW phase transition

Poorly constrained

Cold Baryogenesis

main idea: During quenched EWPT, SU(2) textures can be produced. They can lead to B-violation when they decay.

Turok, Zadrozny ’90 Lue, Rajagopal, Trodden, ‘96

vacua sphaleron Higgs winding gauge dressing

by thermal fluctuations by classical dynamics by classical dynamics

N N

CS H

∆B = 3∆NCS.

Garcia-Bellido, Grigoriev, Kusenko, Shaposhnikov, ’99 Tranberg et al, ’06

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1) large Higgs quenching to produce Higgs winding number in the first place 2) unsuppressed CP violation at the time of quenching so that a net baryon number can be produced 3) a reheat temperature below the sphaleron freese-out temperature T ~ 130 GeV to avoid washout of B by sphalerons Requirements for cold baryogenesis

can occur during supercooled EW phase transition, 1407.0030

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LHC

LHC TEV LEP

LHC

model A model B

200 400 600 800 1000 100 200 500 1000 2000 m[GeV] f [GeV]

[1410.1873] LHC constraints on the scale of conformal symmetry breaking (dilaton) VEV of dilaton

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Summary of this part

SM+ 1 singlet scalar: the most minimal and easiest way to get a strong 1st order EW phase transition

Dilaton-like potentials: a class of well-motivated and naturally

strong 1st order phase transitions, with large supercooling

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Objective # II New large sources of CP violation

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6
4
2

2 4 6

Broken Symmetric

Γws = 10−6 T e−

Esph T φ(T ) v

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Kinetic equations

✓ kz∂z − 1 2 ⇣h V † m†m 0 V i⌘

ii ∂kz

◆ fL,i ≈ C + S ✓ kz∂z − 1 2 ⇣h V † m†m 0 V i⌘

ii ∂kz

◆ fR,i ≈ C − S

collisions source

Cline, Joyce, Kainulainen ’00 Konstandin, Prokopec, Schmidt ’04

Kinetic equations

Huber Fromme ’06

ηB = X

i

Z +1

1

dy Ki(y) ¯ Si(y) (

diffusion effects & sphalerons CP-violating source

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Usual CP-violating sources in EW baryogenesis:

Chargino mass matrix (MSSM)
Varying phase in effective Top quark Yukawa

SM+singlet, Composite Higgs, 2-Higgs doublet model

two recent alternatives: strong CP (QCD axion)

and CP in DM sector (see Cline talk)

Espinosa, Gripaios, Konstandin, Riva, ‘11 Konstandin et al, Cline et al Fromme-Huber Cline et al, Carena et al…

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∆CP ∼

M 6

W T 6 c

−1 Y

i>j u,c,t

m2

i − m2 j

Y

i>j d,s,b

m2

i − m2 j

JCP

ηB . 10−2∆CP

Gavela, et al. ’93 Huet, Sather ’94

Jarlskog constant In the SM:

Farrar, Shaposhnikov ‘93

Based solely on reflection coefficients

the CKM matrix as the CP-violating source

28

J = s2

1s2s3c1c2c3 sin(δ) = (3.0 ± 0.3) × 10−5,

If large masses during EW phase transition

>no longer suppression of CKM CP violation

Berkooz, Nir, Volansky ’04

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S ∼ Im h V †

CKMm†00mVCKM

i m = y(z) · φ(z) √ 2 For constant y: S ∼ Im h V †

CKMy†yVCKM

i | {z }

=0

φ00φ

New idea: Varying SM Yukawas as CP violating source

29

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S ∝ Im h V †m†00mV i =

|m|2θ00

m = |m|eiθ

1-Flavour case requires variation of phase More than 1 flavour: no need for variation of phase

30

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Flavour-EW symmetry breaking cosmological interplay

31

Baldes, Konstandin, Servant, 1608.03254 Baldes, Konstandin, Servant, 1604.04526 Bruggisser, Konstandin, Servant, to appear Von Harling, Servant, 1612.02447

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Origin of the fermion mass hierarchy?

interactions between boson, yijf

i LΦ(c)f j R,

rder 1 at the beginning

EWPT to their hΦi = v/ p 2,

rder PT.

There are three main mf = yfv/ p 2: metries as originally

fermion Yukawas fermion masses

the mass spectrum of the fermions is intriguing

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33

1) Spontaneously broken abelian flavour symmetries as originally proposed by Froggatt and Nielsen 2 ) Localisation of the profiles of the fermionic zero modes in extra dimensions 3) Partial fermion compositeness in composite Higgs models

There are three main mf = yfv/ p 2: metries as originally

There are three main mechanisms to describe fermion masses

may be related by holography

}

The scale at which the flavour structure emerges is not known. Usually assumed to be high but could be at the EW scale.

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Origin of the fermion mass hierarchy?

interactions between boson, yijf

i LΦ(c)f j R,

rder 1 at the beginning

Fermion Yukawas

yij ⇠ (hχi/M)−qi+qj+qH,

In Froggatt Nielsen constructions, the Yukawa couplings are controlled by the breaking parameter of a flavour symmetry. A scalar field “flavon” carrying a negative unit of the abelian charge develops a vacuum expectation value (VEV) and:

the field χ vac-

flavor charges of the fermions

34

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Froggatt-Nielsen

interactions between boson, yijf

i LΦ(c)f j R,

rder 1 at the beginning

Fermion Yukawas

yij ⇠ (hχi/M)−qi+qj+qH,

The scale M is usually assumed close to the GUT scale flavor charges of the fermions

hχi/M ⇠ 0.22,

described. In most

Yt ∼ 1, Yc ∼ λ3, Yu ∼ λ7, Yb ∼ λ2, Ys ∼ λ4, Yd ∼ λ6, s12 ∼ λ, s23 ∼ λ2, s13 ∼ λ3.

λ=

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36

There are good motivations to consider that the flavour structure could emerge during electroweak symmetry breaking

For Example, if the “Flavon” field dynamics is linked to the Higgs field

Emerging Flavour during Electroweak symmetry breaking

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0.2 0.4 0.6 0.8 1.0ϕ/v 0.2 0.4 0.6 0.8 1.0

y(1,0,ϕ,n)

n = 10 n = 2 n = 1 n = 0.5 n = 0.1

Yukawa coupling variation across the bubble wall

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0.2 0.4 0.6 0.8 1.0ϕ/v 0.2 0.4 0.6 0.8 1.0

y(1,0,ϕ,n)

n = 10 n = 2 n = 1 n = 0.5 n = 0.1

40
20

20 40 z·Tc

6.×10-6
5.×10-6
4.×10-6
3.×10-6
2.×10-6
1.×10-6

K(z)

Kernel for n=10

40
20

20 40 z·Tc

0.00006
0.00004
0.00002

S(z)

Source for n=10

40
20

20 40 z·Tc

6.×10-6
5.×10-6
4.×10-6
3.×10-6
2.×10-6
1.×10-6

K(z)

Kernel for n=0.1

40
20

20 40 z·Tc

1.×10-7
5.×10-8

5.×10-8 S(z)

Source for n=0.1

38

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Baryon asymmetry for random distribution of n_i

10-13 10-12 10-11 10-10 |ηB| 1 2 3 4 Counts (arbitrary units )

e Lw = 5 · Tc, vw = 0.1 and ξ = 1.5.

Y (n1, n2, n3, n4) = ✓ ei3.17y(1, 0, φ, n1) ei4.92y(1, 0, φ, n2) ei5.29y(1, 0, φ, n3) ei2.04y(1, 0, φ, n4) ◆ 39

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40

A first-order Electroweak Phase Transition in the Standard Model from Varying Yukawas

Baldes, Konstandin, Servant, 1604.04526

The new result: The nature of the EW phase transition is completely changed when the Standard Model Yukawas vary at the same time as the Higgs is acquiring its vacuum expectation value.

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41

Mass of fermionic species for varying Yukawas

y(φ) = ( y1 ⇣ 1 − h

φ v

in⌘ + y0 for φ ≤ v, y0 for φ ≥ v.

mf = y(φ)φ √ 2 y0: Yukawa value today

y1: Yukawa value before

the EW phase transition

constant Yukawa case with y0=1 (Top quark)

FLAVOUR COSMOLOGY

SLIDE 42

High Temperature Effective Higgs Potential

Veff = Vtree(φ) + V 0

1 (φ) + V T 1 (φ, T) + VDaisy(φ, T).

At one-loop:

tree level piece 1-loop T=0 piece 1-loop T≠0 piece Daisy resummation piece

42

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2) Barrier from the T 6= 0 one-loop potential: loop finite temperature correction is given by

V T

1 (φ, T) =

X

i

gi(1)F T 4 2π2 ⇥ Z ⇣ X Z ∞ y2Log ⇣ 1 (1)F e−p

y2+m2

i (φ)/T 2⌘

dy.

V T

f (φ, T) = gT 4

2π2 Jf ✓mf(φ)2 T 2 ◆

Jf(x2) ⇡ 7π4 360 π2 24x2 x4 32Log  x2 13.9

δV ⌘ V T

f (φ, T) V T f (0, T) ⇡ gT 2φ2[y(φ)]2

96 .

High-T expansion: Fermionic fields create a barrier!

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50 100 150 200 250 300 0.0 0.2 0.4 0.6 0.8 1.0 1.2 f @GeVD Veffâ10-8 @GeV4D

This leads to a cubic term in φ, e.g. for y(φ) = y1(1 φ/v): δV ⇡ gy2

1φ2T 2

96 ✓ 1 2φ v + φ2 v2 ◆ (10)

__ full potential _ _ _ thermal contribution only

- -thermal contribution
nly with high-T

expansion

44

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VDaisy(φ, T) = X

i

giT 12π n m3

i (φ)

⇥ m2

i (φ) + Πi(T)

⇤3/2o (11)

sum is

ver

bosons Consider the contribution from the Higgs: The novelty is the dependence of the thermal mass on Φ, which comes from the Φ-dependent Yukawa couplings

3) Effects from the Daisy correction: tion comes from resumming the Matsubara

V φ

Daisy(φ, T) =

T 12π n m3

φ(φ)

⇥ m2

φ(φ) + Πφ(φ, T)

⇤3/2o , (12)

Πφ(φ, T) = ✓ 3 16g2

2 + 1

16g2

Y + λ

2 + y2

t

4 + gy(φ)2 48 ◆ T 2. (13)

come from resumming Matsubara zero- modes for the bosonic degrees of freedom thermal mass

45

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50 100 150 200 250 300

1.0
0.5

0.0 0.5 1.0 f @GeVD Veffâ10-8 @GeV4D

3) Effects from the Daisy correction: tion comes from resumming the Matsubara

The effect is to lower the effective potential at Φ =0, with respect to the broken phase minimum. By lowering the potential at Φ =0, the phase transition is delayed and strengthened.

__ full potential _ _ _ full potential minus Daisy contribution

- - Daisy contribution
nly

46

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47

Full one-loop effective Higgs potential with Daisy Resummation

Standard Case (Constant Yukawas) With varying Yukawas

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48

Variation of the Yukawas of SM fermions from O(1) to their present value during the EW phase transition leads to a strong first-order EW phase transition

This offers new routes for generating the baryon asymmetry at the electroweak scale, strongly tied to flavour models.

Summary

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Naturally varying Yukawas: The Froggatt-Nielsen case

Baldes, Konstandin, Servant, 1608.03254

In simplest implementation: Tension between requirement of very light flavon (for sufficient Yukawa variation) and Flavour constraints (meson oscillations) But: We did not take into account dynamics of Froggatt- Nielsen fermion. Follow-up study more promising.

Baldes, Servant, Suresh, in progress.

49

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Von Harling, Servant ’16

Naturally varying Yukawas: The Randall-Sundrum case

(0)

e Aµ

(0) (0)

t ) UV (M

P

H IR (TeV)

ds2 = e

2ky

dx dx dy2

AdS_5 metric

S d4x H H e

2kyIRM2 P H 2 +

H 4

n radion

e

kyIR!

50

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y( ) = 1 2cL 1

1 2cL

1 2cR 1

1 2cR

UV IR

y

rh. charm wf.

UV IR

y

rh. charm wf.

UV IR

y

rh. charm wf.

S d5x g c k

CONSTANT bulk fermion mass term:

In minimal Randall-Sundrum models, Yukawas decrease across the bubble wall

resulting 4D effective Yukawas:

51

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f Yukawas across the bubbl

σ

dir. perp. to bubble wall

broken phase unbroken phase

3
2
1

1 2 3 4 5.×10-16 1.×10-15 1.5×10-15 2.×10-15 2.5×10-15

charm Yukawa

dir. perp. to bubble wall
3
2
1

1 2 3 4 0.0020 0.0025 0.0030 0.0035

Yukawas decrease along bubble wall not enough CP-violation from SCP Im V M M V

52

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UV IR

y

rh. charm wf.

UV IR

y

rh. charm wf.

UV IR

y

rh. charm wf.

Now, assume following natural possibility: bulk fermion mass term comes from Yukawa coupling with Goldberger-Wise scalar:

S d5x g

y( ) = k

(0) ˜ cL (0) ˜ cR 1 e

(˜ cL+˜ cR )

Position-dependent mass term!

resulting 4D effective Yukawas:

53

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f Yukawas across the bubble

σ

dir. perp. to bubble wall

broken unbroken phase phase

10
8
6
4
2

2 4 5.×10-16 1.×10-15 1.5×10-15 2.×10-15 2.5×10-15

charm Yukawa

dir. perp. to bubble wall
10
8
6
4
2

2 4 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Yukawas increase along bubble wall more CP-violation from SCP Im V M M V

54

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5 10 15 20 25 30 0.005 0.010 0.050 0.100 0.500 1 ky eky/2 fR

(0)

10 20 30 40 50 10-5 10-4 0.001 0.010 0.100 1 ky eky/2 fR

(0)

20 40 60 80 100 10-19 10-14 10-9 10-4 10 ky eky/2 fR

(0)

5 10 15 20 25 30 0.2 0.4 0.6 0.8 1.0 1.2 ky c loc 10 20 30 40 50 0.0 0.2 0.4 0.6 0.8 1.0 1.2 ky c loc 20 40 60 80 100 0.0 0.2 0.4 0.6 0.8 1.0 1.2 ky c loc

Wave function when going back in time Bonus: Modified wave functions give suppression of CP-violating processes which are very constraining in the standard case

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Constraint for standard case of constant bulk mass terms: m(1) & 3 (22 6) TeV e

kyIRk & 3 (9

3) TeV In our scenario instead: m(1) & 3 (7 2) TeV e

kyIRk & 3 (3

1) TeV Significant improvement!

sL dL Gμ

(1)

ur model

5 10 15 20 25 30 10-7 10-4 10-1 ky wavefunctions

sL dL Gμ

(1)

standard case

5 10 15 20 25 30 0.005 0.010 0.050 0.100 0.500 1 ky wavefunctions

Suppression of overlap integral

G(1)

A

dL sR sL dR

CP violation in K-Kbar mixing

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Neutron EDM

Important constraint on IR scale e

kyIRMP also from neutron EDM.

Dominant contribution:

dL dR D(n)

R

Q(m)

L

γ H v

Constraint for standard case of constant bulk mass terms: m(1) & 3 26 TeV e

kyIRk & 3 11 TeV

Again expect that constraints eased in our scenario since first fermionic KKs are heavier than for constant bulk mass terms

57

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Summary

Minimal modification of RS: Yukawa coupling between Goldberger-Wise scalar and bulk fermions naturally large yukawas and enhanced CP violation in bubble walls during EW phase transition eases constraints from CP violation n K Kbar mixing

bubble wall

H Y σ

z

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Gravity wave signals from 1st order cosmological phase transitions

Stochastic background of gravitational radiation

EW phase transition

> mHz -> LISA!

[eLISA Cosmology Working group, 1512.06239] [Credit:David Weir] Fluid flows Magnetic fields turbulence

10-5 10-4 0.001 0.01 0.1 10-16 10-14 10-12 10-10 10-8 f@HzD h2WGWHfL

), β/H∗ = 100

d T∗ = 100 GeV, α = 0.5, vw = 0.95,

s e e D . W e i r ’ s t a l k

59

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60

Conclusion

The possibility of time-dependent CP-violating sources allows to make EW baryogenesis compatible with Electric Dipole Moment constraints and can be well-motivated

theoretically. We provided 2 examples:

1) strong CP from QCD axion, 2) weak CP from dynamical Yukawas 2) —> Flavour cosmology! New window of opportunities Beautiful Dynamical interplay between flavour and electroweak symmetry breaking.

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Annexes

SLIDE 62

strong sector

G→H⊃SO(4)

︴︴

━━━━

W a

µ , Bµ

Ψ

Lint = AµJµ + ¯ ΨO + h.c.

New strong sector endowed with a global symmetry G spontaneously broken to H → delivers a set of Nambu Goldstone bosons

G H NG NGBs rep.[H] = rep.[SU(2) × SU(2)] SO(5) SO(4) 4 4 = (2, 2) SO(6) SO(5) 5 5 = (1, 1) + (2, 2) SO(6) SO(4) × SO(2) 8 4+2 + ¯ 42 = 2 × (2, 2) SO(7) SO(6) 6 6 = 2 × (1, 1) + (2, 2) SO(7) G2 7 7 = (1, 3) + (2, 2) SO(7) SO(5) × SO(2) 10 100 = (3, 1) + (1, 3) + (2, 2) SO(7) [SO(3)]3 12 (2, 2, 3) = 3 × (2, 2) Sp(6) Sp(4) × SU(2) 8 (4, 2) = 2 × (2, 2), (2, 2) + 2 × (2, 1) SU(5) SU(4) × U(1) 8 45 + ¯ 4+5 = 2 × (2, 2) SU(5) SO(5) 14 14 = (3, 3) + (2, 2) + (1, 1)

[Mrazek et al, 1105.5403]

> Agashe, Contino, Pomarol’05

custodial SO(4)

to avoid large corrections to the T parameter

Easy to motivate additional scalars, e.g:

SLIDE 63

SU(2)L × SU(2)R

SU(2)V

SU(3)c

QCD: global symm.

n u,d

strong int.

U(1)Q

⊃ 6 - 3 = 3 PNGB π±, π0 global symm. on techniquarks

SO(6) × U(1)x

SO(5) × U(1)Y

SU(Nc)

Composite Higgs: ⊃ SU(2) × U(1)Y 16 - 11 = 5 PNGB H, S SO(5)/SO(4) -> SM SO(6)/SO(5) -> SM + S SO(6)/SO(4) -> 2 HDM associated LHC tests

Higgs scalars as pseudo-Nambu-Goldstone bosons of new dynamics above the weak scale

SLIDE 64

22

vw K1 µ0 + vw(m2)0 K2 µ + u0 − Γinel X

i

µi = 0 −K4 µ0 + vw ˜ K5 u0 + vw(m2)0 ˜ K6 u + Γtotu = ±vwK8 Im h V †m†00mV i

Source Interactions: Couple different particle species together

Yukawa interactions
Helicity flip
W-scattering
Higgs number violation
Strong sphaleron

Γy,q = 4.2 × 10−3 y2

q T

Γm,q =

m2

q

63T

ΓW = T

60

Γh = m2

W

50T

Γss = 4.9 × 10−4T e.g. tL ↔ tR + h

e.g. tL ↔ tR e.g. tL ↔ bL h ↔ 0 all L ↔ all R m = y(z) · φ(z) √ 2

e.g. Fromme, Huber ’06 hep-ph/0604159

SLIDE 65

V 0

1 (φ) =

X

i

gi(1)F 64π2 ⇢ m4

i (φ)

✓ Log m2

i (φ)

m2

i (v)

3

2 ◆

⇢

✓  + 2m2

i (φ)m2 i (v)

1) Effects from the T = 0 one-loop potential:

loop zero temperature correction is given by

A large fermionic mass significantly lowers between Φ=0 and Φ=v. This can lead to weaker

rather than stronger - phase transitions.

In addition, it can lead to the EW minimum no longer being the global minimum.

) + V 0

1 ( Baldes, Konstandin, Servant, 1604.04526

SLIDE 66

66

Contours of Φc/Tc=1 for different choices of y1 and y0, areas above these lines allow for EW baryogenesis. Φc/Tc=1 Φc/Tc=1 Φc/Tc=1

Dashed lines: areas above these lines are disallowed (for the indicated choices of y1 and y0 due to the EW minimum not being the global one.

n characterizes how fast the Yukawa variation is taking place. Depending on the underlying model, the Higgs field variation will follow the flavon field variation at different speeds. Large n means the Yukawa coupling remains large for a greater range of phi away from zero. It strengthens the phase transition.

Baldes, Konstandin, Servant, 1604.04526

The serendipity of EW baryogenesis

Baryogenesis at a first-order EW phase transition

Cold Baryogenesis

Kinetic equations

S ∝ Im h V †m†00mV i =

m = |m|eiθ

}

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