Z-ino-driven electroweak baryogenesis Eibun Senaha (Nagoya U, E-ken) - - PowerPoint PPT Presentation

Z’-ino-driven electroweak baryogenesis

Oct 6, 2013

Eibun Senaha (Nagoya U, E-ken)

@7th Toyama Higgs meeting

• Ref. PRD88,055014 (2013) [arXiv:1308.3389]

Higgs physics and cosmology

❒ Higgs-cosmology connections

• dark matter ⟺ inert Higgs, Higgs portal etc.
• cosmic baryon asymmetry ⟺ EW baryogenesis

It is possible to get the baryon asymmetry at the EW scale. ❒ 126 GeV Higgs boson was discovered.

What’ s the cosmological implication?

• etc

However, the region where the baryon asymmetry can arise within the SM was excluded due to “no strong 1st-order PT, no sufficient CPV . ”

Current status

SUSY: SM+extended Higgs sector:

Next-to-MSSM (NMSSM), nearly-MSSM (nMSSM), U(1)’-MSSM (UMSSM), triplet-MSSM (TMSSM) etc.

strong 1st-order PT CPV(Higgs sector) real singlet OK X complex singlet OK OK MHDM (M≥2) OK OK real triplet OK X complex triplet OK X ❒ SM EWBG was excluded.

strong 1st-order EWPT is OK, CPV is OK In this talk, we discuss a possibility of the EWBG in the UMSSM. MSSM EWBG (light stop scenario) looks dead.

Outline

Introduction EWBG in the U(1)’-extended MSSM (UMSSM) strong 1st-order EW phase transition (PT) sphaleron decoupling condition (baryon asymmetry) Summary

U(1)’-extended MSSM (UMSSM)

superpotential:

2 Higgs doublets (Hd, Hu) + 1 Higgs singlet (S)

V0 = VF + VD + Vsoft,

VF = ||2 |ijΦi

dΦj u|2 + |S|2(Φ† dΦd + Φ† uΦu)

• ,

VD = g2

2 + g2 1

8 (Φ†

dΦd − Φ† uΦu)2 + g2 2

2 (Φ†

dΦu)(Φ† uΦd)

+ g2

1

2 (QHdֆ

dΦd + QHuΦ† uΦu + QS|S|2)2,

Vsoft = m2

1Φ† dΦd + m2 2Φ† uΦu + m2 S|S|2 − (ijAλSΦi dΦj u + h.c.).

Higgs potential Q’ s: U(1)’ charges, QHd + QHu + QS = 0.

Φd =

• 1

√ 2(vd + hd + iad)

φ−

d

• ,

Φu = eiθ

• φ+

u 1 √ 2(vu + hu + iau)

• ,

S = 1 √ 2(vS + hS + iaS).

M.Cvetic et al, PRD56:2861 (’97) D.Suematsu et al, Int.J.Mod.Phys.A10 (‘95) 4521.

WUMSSM ijSHi

uHj d

g

1 =

• 5/3g1

U(1)’-extended MSSM (UMSSM)

superpotential:

2 Higgs doublets (Hd, Hu) + 1 Higgs singlet (S)

V0 = VF + VD + Vsoft,

VF = ||2 |ijΦi

dΦj u|2 + |S|2(Φ† dΦd + Φ† uΦu)

• ,

VD = g2

2 + g2 1

8 (Φ†

dΦd − Φ† uΦu)2 + g2 2

2 (Φ†

dΦu)(Φ† uΦd)

+ g2

1

2 (QHdֆ

dΦd + QHuΦ† uΦu + QS|S|2)2,

Vsoft = m2

1Φ† dΦd + m2 2Φ† uΦu + m2 S|S|2 − (ijAλSΦi dΦj u + h.c.).

Higgs potential Q’ s: U(1)’ charges, QHd + QHu + QS = 0.

Φd =

• 1

√ 2(vd + hd + iad)

φ−

d

• ,

Φu = eiθ

• φ+

u 1 √ 2(vu + hu + iau)

• ,

S = 1 √ 2(vS + hS + iaS).

M.Cvetic et al, PRD56:2861 (’97) D.Suematsu et al, Int.J.Mod.Phys.A10 (‘95) 4521.

WUMSSM ijSHi

uHj d

U(1)’-D term g

1 =

• 5/3g1

1 vd ∂V0 ∂hd

• = m2

1 + g2 2 + g2 1

8 (v2

d − v2 u) − Rλ

vuvS vd + |λ|2 2 (v2

u + v2 S) + g2 1

2 QHd∆ = 0, 1 vu ∂V0 ∂hu

• = m2

2 − g2 2 + g2 1

8 (v2

d − v2 u) − Rλ

vdvS vu + |λ|2 2 (v2

d + v2 S) + g2 1

2 QHu∆ = 0, 1 vS ∂V0 ∂hS

• = m2

S − Rλ

vdvu vS + |λ|2 2 (v2

d + v2 u) + g2 1

2 QS∆ = 0, 1 vu ∂V0 ∂ad

• = 1

vd ∂V0 ∂au

• = IλvS = 0,

1 vS ∂V0 ∂aS

• = Iλ

vdvu vS = 0,

∆ = QHdv2

d + QHuv2 u + QSv2 S,

Rλ = Re(λAλeiθ) √ 2 = |λAλ| √ 2 cos(δAλ + δλ + θ) ≡ |λAλ| √ 2 cos(δAλ + δ

λ),

Iλ = Im(λAλeiθ) √ 2 = |λAλ| √ 2 sin(δAλ + δλ + θ) ≡ |λAλ| √ 2 sin(δAλ + δ

λ).

Tadpole (minimization) conditions

where vd = vu = vS = 0 is assumed.

CP is conserved at the tree level.

Iλ = 0.

1 vd ∂V0 ∂hd

• = m2

1 + g2 2 + g2 1

8 (v2

d − v2 u) − Rλ

vuvS vd + |λ|2 2 (v2

u + v2 S) + g2 1

2 QHd∆ = 0, 1 vu ∂V0 ∂hu

• = m2

2 − g2 2 + g2 1

8 (v2

d − v2 u) − Rλ

vdvS vu + |λ|2 2 (v2

d + v2 S) + g2 1

2 QHu∆ = 0, 1 vS ∂V0 ∂hS

• = m2

S − Rλ

vdvu vS + |λ|2 2 (v2

d + v2 u) + g2 1

2 QS∆ = 0, 1 vu ∂V0 ∂ad

• = 1

vd ∂V0 ∂au

• = IλvS = 0,

1 vS ∂V0 ∂aS

• = Iλ

vdvu vS = 0,

∆ = QHdv2

d + QHuv2 u + QSv2 S,

Rλ = Re(λAλeiθ) √ 2 = |λAλ| √ 2 cos(δAλ + δλ + θ) ≡ |λAλ| √ 2 cos(δAλ + δ

λ),

Iλ = Im(λAλeiθ) √ 2 = |λAλ| √ 2 sin(δAλ + δλ + θ) ≡ |λAλ| √ 2 sin(δAλ + δ

λ).

Tadpole (minimization) conditions

where vd = vu = vS = 0 is assumed.

CP is conserved at the tree level.

Iλ = 0.

Higgs boson masses

m2

H1 ≤ m2 Z cos2 2β + |λ|2

2 v2 sin2 2β + g2

1 v2(QHd cos2 β + QHu sin2 β)2.

At the tree level, the lightest Higgs mass is bounded as

In the limit QHd = QHu ≡ Q, tan β = 1, one gets

m2

H1,2 = 1

2

• m2

S + |λ|2v2 + 6g2 1 Q2v2 S

• m2

S + 2g2 1 Q2(3v2 S v2)

2 + 4v2 Rλ (|λ|2 2g2

1 Q2)vS

2

• ,

m2

H3 = m2 Z |λ|2

2 v2 + 2RλvS,

CP-even Higgs: CP-odd Higgs:

m2

A = 2RλvS

sin 2β

• 1 + v2

4v2

S

sin2 2β

• charged Higgs:

m2

H± = m2 W + 2Rλ

sin 2β vS − |λ|2 2 v2.

Heavy Higgs boson masses are controlled by Rλ (Aλ).

Higgs boson masses

m2

H1 ≤ m2 Z cos2 2β + |λ|2

2 v2 sin2 2β + g2

1 v2(QHd cos2 β + QHu sin2 β)2.

At the tree level, the lightest Higgs mass is bounded as

In the limit QHd = QHu ≡ Q, tan β = 1, one gets

m2

H1,2 = 1

2

• m2

S + |λ|2v2 + 6g2 1 Q2v2 S

• m2

S + 2g2 1 Q2(3v2 S v2)

2 + 4v2 Rλ (|λ|2 2g2

1 Q2)vS

2

• ,

m2

H3 = m2 Z |λ|2

2 v2 + 2RλvS,

CP-even Higgs: CP-odd Higgs:

m2

A = 2RλvS

sin 2β

• 1 + v2

4v2

S

sin2 2β

• charged Higgs:

m2

H± = m2 W + 2Rλ

sin 2β vS − |λ|2 2 v2.

Heavy Higgs boson masses are controlled by Rλ (Aλ).

Higgs boson masses

m2

H1 ≤ m2 Z cos2 2β + |λ|2

2 v2 sin2 2β + g2

1 v2(QHd cos2 β + QHu sin2 β)2.

At the tree level, the lightest Higgs mass is bounded as

In the limit QHd = QHu ≡ Q, tan β = 1, one gets

m2

H1,2 = 1

2

• m2

S + |λ|2v2 + 6g2 1 Q2v2 S

• m2

S + 2g2 1 Q2(3v2 S v2)

2 + 4v2 Rλ (|λ|2 2g2

1 Q2)vS

2

• ,

m2

H3 = m2 Z |λ|2

2 v2 + 2RλvS,

CP-even Higgs: CP-odd Higgs:

m2

A = 2RλvS

sin 2β

• 1 + v2

4v2

S

sin2 2β

• charged Higgs:

m2

H± = m2 W + 2Rλ

sin 2β vS − |λ|2 2 v2.

Heavy Higgs boson masses are controlled by Rλ (Aλ).

Vacuum structures

V0(ϕd, ϕu, ϑ, ϕS) = 1 2m2

1ϕ2 d + 1

2m2

2ϕ2 u + 1

2m2

Sϕ2 S − RλϕdϕuϕS + g2 2 + g2 1

32 (ϕ2

d − ϕ2 u)2

+ |λ|2 4 (ϕ2

dϕ2 u + ϕ2 dϕ2 S + ϕ2 uϕ2 S) + g2 1

8 (QHdϕ2

d + QHuϕ2 u + QSϕ2 S)2.

EW : v = 246 GeV, vS = 0; I : v = 0, vS = 0; II : v = 0, vS = 0; SYM : v = vS = 0.

V0(ϕ = vEW) < V0(ϕ = vEW),

m2

H± < m2 W + m2 Z cot2 2β + 2|λ|2v2 S

sin2 2β + g2

1 ∆2

v2 sin2 2β ≡ (mmax

H± )2.

Tree-level effective potential We require

various vacua:

V (EW) (vd, vu, θ, vS) < 0 gives an upper bound on mH±

V (EW) (vd, vu, θ, vS) = −g2

2 + g2 1

32 (v2

d − v2 u)2 + 1

2RλvdvuvS − |λ|2 4 (v2

dv2 u + v2 dv2 S + v2 uv2 S) − g2 1

8 ∆2,

Energy of EW vacuum is

1000 2000 3000 4000 5000 6000 200 400 600 800 1000

• Smallest mmax

H± is realized for tan β = 1.

• In this case, mH± 1 TeV for vS 640 GeV.

mmax

H±

|λ| = 0.8, QHd = −0.5, QHu = QHd/ tan2 β

Z’ boson mass:

Input parameters

mH1 = 126 GeV

mH±

mZ λ Aλ

tan β vS

QHd QHu

• QHd

QHu

M2

ZZ =

• 1

4(g2 2 + g2 1)v2 g

1

2

• g2

2 + g2 1(QHdv2 d − QHuv2 u) g

1

2

• g2

2 + g2 1(QHdv2 d − QHuv2 u)

g2

1 (Q2 Hdv2 d + Q2 Huv2 u + Q2 Sv2 S)

• .

QHd = QHu = −0.5 tree level: 1-loop level:

m2

Z = g2 1 (Q2 Hdv2 d + Q2 Huv2 u + Q2 Sv2 S).

Neutral gauge boson masses

(QS = −QHd − QHd = 1)

stop loop

αZZ < O(10−3) = ⇒ tan β =

• QHd

QHu

From EW precision tests,

m˜

q = m˜ tR = 1.5 TeV, At = m˜ q + |µeff|/ tan β, (µeff = λvS/

√ 2).

Z’ boson mass:

Input parameters

mH1 = 126 GeV

mH±

mZ λ Aλ

tan β vS

QHd QHu

• QHd

QHu

M2

ZZ =

• 1

4(g2 2 + g2 1)v2 g

1

2

• g2

2 + g2 1(QHdv2 d − QHuv2 u) g

1

2

• g2

2 + g2 1(QHdv2 d − QHuv2 u)

g2

1 (Q2 Hdv2 d + Q2 Huv2 u + Q2 Sv2 S)

• .

QHd = QHu = −0.5 tree level: 1-loop level:

m2

Z = g2 1 (Q2 Hdv2 d + Q2 Huv2 u + Q2 Sv2 S).

Neutral gauge boson masses

(QS = −QHd − QHd = 1)

stop loop

= 1

αZZ < O(10−3) = ⇒ tan β =

• QHd

QHu

From EW precision tests,

m˜

q = m˜ tR = 1.5 TeV, At = m˜ q + |µeff|/ tan β, (µeff = λvS/

√ 2).

Z’ boson mass:

Input parameters

mH1 = 126 GeV

mH±

mZ λ Aλ

tan β vS

QHd QHu

• QHd

QHu

M2

ZZ =

• 1

4(g2 2 + g2 1)v2 g

1

2

• g2

2 + g2 1(QHdv2 d − QHuv2 u) g

1

2

• g2

2 + g2 1(QHdv2 d − QHuv2 u)

g2

1 (Q2 Hdv2 d + Q2 Huv2 u + Q2 Sv2 S)

• .

QHd = QHu = −0.5 tree level: 1-loop level:

m2

Z = g2 1 (Q2 Hdv2 d + Q2 Huv2 u + Q2 Sv2 S).

Neutral gauge boson masses

(QS = −QHd − QHd = 1)

stop loop

= 550 GeV

= 1

αZZ < O(10−3) = ⇒ tan β =

• QHd

QHu

From EW precision tests,

m˜

q = m˜ tR = 1.5 TeV, At = m˜ q + |µeff|/ tan β, (µeff = λvS/

√ 2).

Electroweak phase transition

Veff(ϕd, ϕu, ϕS; T) = V0 + V1 + V T

1

V1 =

• i

ci ¯ m4

i

64π2

• ln ¯

m2

i

¯ µ2 − 3 2

• ,

IB,F (a2) = ∞ dx x2 ln

• 1 e−

√ x2+a2

.

V T

1 = T 4

2π2

• i=bosons

ciIB ¯ m2

i

T 2

• +
• i=fermions

ciIF ¯ m2

i

T 2

• ,

❒ TC and Higgs VEVs at TC are determined by Veff. Effective potential: ❒ gauge bosons, top/bottom, stop/sbottom loops are taken into account.

❒ sphaleron energy gives the dominant effect.

Esph = 4πvE/g2 (g2: SU(2) gauge coupling),

After the EWPT, the sphaleron process has to be decoupled.

Γ(b)

B (T) (prefactor)e−Esph/T < H(T) 1.66g∗T 2/mP

❒ log corrections are subleading. (typically 10% correction)

g∗ massless dof, 106.75 (SM) mP Planck mass ≃ 1.22x1019 GeV

Sphaleron decoupling

v T > g2 4πE

• 42.97 + log corrections
• ≡ ζsph

B-changing rate in the broken phase < Hubble constant

1st and 2nd order EWPTs

❒ order parameter

= Higgs VEV

[From K. Funakubo’ s slide]

❒ EWBG requires

“1st-order” PT This is what the 1st- and 2nd-order PTs look like.

1st and 2nd order EWPTs

❒ order parameter

= Higgs VEV

[From K. Funakubo’ s slide]

❒ A negative

contributions is necessary.

❒ EWBG requires

“1st-order” PT This is what the 1st- and 2nd-order PTs look like.

1st and 2nd order EWPTs

❒ order parameter

= Higgs VEV

[From K. Funakubo’ s slide]

❒ A negative

contributions is necessary.

❒ EWBG requires

“1st-order” PT This is what the 1st- and 2nd-order PTs look like.

e.g.

Bosonic thermal loop

V (boson)

1

|const| · |m(v)|3T

Veff(ϕ; T) = 1 2M 2(T)ϕ2 + 1 2m2

Sϕ2 S − ˜

Rλϕ2ϕS + |λ|2 4 ϕ2ϕ2

S +

˜ λ2 4 ϕ4,

M 2(T) = m2

1 cos2 β + m2 2 sin2 β + GT 2,

˜ Rλ = Rλ sin β cos β, ˜ λ2 = g2

2 + g2 1

8 cos2 2β + |λ|2 4 sin2 2β,

1st-order EWPT

where After eliminating φS using the minimization condition w.r.t. φS, one gets Let us consider the g1’=0 case, 1st-order PT may be realized if ˜

λ <

• 2

m2

S

| ˜ Rλ|

Veff(ϕ; T) = 1 2M 2(T)ϕ2 ˜ R2

λϕ4

2(m2

S + |λ|2ϕ2/2) +

˜ λ2 4 ϕ4 1 2M 2(T)ϕ2 + 1 4

• ˜

λ2 2 ˜ R2

λ

m2

S

• ϕ4 + |λ|2 ˜

R2

λ

4m4

S

ϕ6.

vC/TC⤴ if Aλ⤴ and/or vS⤵

TC and Higgs VEVs

vC = lim

T ↑TC

• v2

d(TC) + v2 u(TC),

vSC = lim

T ↑TC vS(TC),

vsym

SC = lim T ↓TC vS(TC).

TC: T at which Veff has degenerate minima.

❒ Such a Z’ must be leptophobic to be phenomenologically viable. ❒ In the light Z’ (small vS) region, the EWPT can be strong 1st order due to the doublet-singlet Higgs mixing effects.

100 200 300 400 500 600 180 200 220 240 260 100 200 300 400 500 600 700 170 180 190 200 210 220 230 240

TC and Higgs VEVs

vC = lim

T ↑TC

• v2

d(TC) + v2 u(TC),

vSC = lim

T ↑TC vS(TC),

vsym

SC = lim T ↓TC vS(TC).

TC: T at which Veff has degenerate minima.

❒ Such a Z’ must be leptophobic to be phenomenologically viable. ❒ In the light Z’ (small vS) region, the EWPT can be strong 1st order due to the doublet-singlet Higgs mixing effects.

100 200 300 400 500 600 180 200 220 240 260

TC and Higgs VEVs

vC = lim

T ↑TC

• v2

d(TC) + v2 u(TC),

vSC = lim

T ↑TC vS(TC),

vsym

SC = lim T ↓TC vS(TC).

TC: T at which Veff has degenerate minima.

❒ Such a Z’ must be leptophobic to be phenomenologically viable. ❒ In the light Z’ (small vS) region, the EWPT can be strong 1st order due to the doublet-singlet Higgs mixing effects.

100 200 300 400 500 600 180 200 220 240 260

TC and Higgs VEVs

vC = lim

T ↑TC

• v2

d(TC) + v2 u(TC),

vSC = lim

T ↑TC vS(TC),

vsym

SC = lim T ↓TC vS(TC).

TC: T at which Veff has degenerate minima.

❒ Such a Z’ must be leptophobic to be phenomenologically viable. ❒ In the light Z’ (small vS) region, the EWPT can be strong 1st order due to the doublet-singlet Higgs mixing effects.

100 200 300 400 500 600 180 200 220 240 260 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 170 180 190 200 210 220 230 240

1 2 3 4 180 200 220 240 260 1.6 1.7 1.8 1.9 2 2.1 2.2 180 200 220 240 260

sphaleron energy vC/TC vs. ζsph

Sphaleron decoupling (cont)

For simplicity, we evaluate sphaleron energy at T=0. Also, U(1)Y and U(1)’ contributions are neglected.

Esph = 4πv g2 E

❒ sphaleron decoupling condition is satisfied for mZ’≲220 GeV .

0.5 0.5 1 1 1.5 2 2.5 3 350 400 450 500 550 170 180 190 200 210 220 230 240 0.5 0.6 0.7 0.7 0.8 0.9 350 400 450 500 550 170 180 190 200 210 220 230 240

Scan analysis

vC/TC |λ|

• Strong 1st-order EWPT requires relatively large |λ|.
• Smaller mH± (|Aλ|) gives weaker vC/TC.

Using the CTP formalism, we evaluate SCPV and Γ

BAU

nB = 3 2Γ(s)

B

SCPV √ Γ Lw √ ¯ D v2

w

r1

Under the reasonable assumptions, one may get

Γ(s)

B : B-changing rate in the symmetric phase

SCPV : CP-violating source terms Γ : CP-conserving chirality changing terms

Lw : wall width ¯ D : diffusion constant r1 : numerical factor

vw

Lw

Using the CTP formalism, we evaluate SCPV and Γ

BAU

nB = 3 2Γ(s)

B

SCPV √ Γ Lw √ ¯ D v2

w

r1

Under the reasonable assumptions, one may get

Γ(s)

B : B-changing rate in the symmetric phase

SCPV : CP-violating source terms Γ : CP-conserving chirality changing terms

Lw : wall width ¯ D : diffusion constant r1 : numerical factor

vw

Lw

Z’-ino driven EWBG

❒ If M’1≃μeff, BAU can be explained by the Z’-ino effect.

YB = nB s

1 2 3 4 5 180 200 220 240 260 280

tan β = 1, mH1 = 126 GeV, mH± = 550 GeV, mZ = 200 GeV, QHd = QHu = −0.5, δM

1 = π/2, δλ = 0, ∆β = 0.01, vw = 0.4.

Z’-ino driven EWBG

❒ If M’1≃μeff, BAU can be explained by the Z’-ino effect.

YB = nB s

1 2 3 4 5 180 200 220 240 260 280

tan β = 1, mH1 = 126 GeV, mH± = 550 GeV, mZ = 200 GeV, QHd = QHu = −0.5, δM

1 = π/2, δλ = 0, ∆β = 0.01, vw = 0.4.

Summary

❒ We have revisited the possibility of EWBG in the UMSSM in light of mh=126 GeV . ❒ Doublet-singlet Higgs mixings existing in the tree-level Higgs potential can induce the strong 1st-order EWPT, which predict ❒ Sufficient BAU may be generated by the Z’-ino effects.

• leptophobic light Z’ boson
• utlook
• precise knowledge of bubble wall profiles (wall velocity&width)
• collider phenomenology

Next step is

• reduction of HVV coupling

backup slides

100 200 300 400 500 600 700 170 180 190 200 210 220 230 240 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 170 180 190 200 210 220 230 240

Higgs boson masses and couplings

• H1 and H2 are mixtures of the doublet and singlet Higgs bosons.
• Strong 1st-order PT inevitably leads to the reduction of H1VV coupling.

Experimental constraints on light leptophobic Z’

❒ Z’ boson (<200 GeV) is constrained by the UA2 experiment.

0.8 ~

UA2

0.6 0.4 0.2

‘

I,,,,I,,,H

I,, 140 160 180 200 220 240 260 280 300

M~/(GeV)

• Fig. 5. Excluded region to 90% for Z’ —. ~q, (excluded region is hatched). The branching ratio is

given as a fraction of standard model branching ratio. The solid line shows a branching ratio of 1 for Z’ —~c~qwhilst the dashed line shows a branching ratio of 0.7.

UA2 bounds on mZ’

UA2 Collaborations,NPB400: (1993) 3

• M. Buckley et al,PRD83:115013 (2011)

❒ Electroweak precision tests (see e.g. Umeda,Cho,Hagiwara, PRD58 (1998) 115008)

• > In our case, no constraint since Z-Z’ mixing is assumed to be small.

❒ All dijet-mass searches at Tevatron/LHC are limited to Mjj>200 GeV .

gffZ ¯ fL,RγµfL,RZ

µ