Testing Higgs Relaxation Leptogenesis: Why Isocurvature Is More - - PowerPoint PPT Presentation

Testing Higgs Relaxation Leptogenesis: Why Isocurvature Is More Promising Than CP Violation

Lauren Pearce

University of Illinois, Urbana-Champaign Based on: Alexander Kusenko, LP, Louis Yang, Phys.Rev.Lett. 114 (2015) no.6, 061302 Masahiro Kawasaki, LP, Louis Yang, Alexander Kusenko, Phys.Rev. D95 (2017) no.10, 103006

Lauren Pearce (UIUC) 1 / 23

Outline

Outline

Briefly review Higgs relaxation leptogenesis

Lauren Pearce (UIUC) 2 / 23

Outline

Outline

Briefly review Higgs relaxation leptogenesis Focus on CP violation:

Lauren Pearce (UIUC) 2 / 23

Outline

Outline

Briefly review Higgs relaxation leptogenesis Focus on CP violation:

◮ An effective O6 operator obscures source of CP violation Lauren Pearce (UIUC) 2 / 23

Outline

Outline

Briefly review Higgs relaxation leptogenesis Focus on CP violation:

◮ An effective O6 operator obscures source of CP violation ◮ Therefore CP constraints are not very restrictive Lauren Pearce (UIUC) 2 / 23

Outline

Outline

Briefly review Higgs relaxation leptogenesis Focus on CP violation:

◮ An effective O6 operator obscures source of CP violation ◮ Therefore CP constraints are not very restrictive

Test via cosmological isocurvature measurements?

Lauren Pearce (UIUC) 2 / 23

Higgs Relaxation

The Higgs Potential

The LHC has found a Higgs boson with mass ∼ 125 GeV

Lauren Pearce (UIUC) 3 / 23

Higgs Relaxation

The Higgs Potential

The LHC has found a Higgs boson with mass ∼ 125 GeV If we evolve the Standard Model RGE equation out to high scales, the Higgs potential becomes shallow, and even appears to have a second minimum

Lauren Pearce (UIUC) 3 / 23

Higgs Relaxation

The Higgs Potential

The LHC has found a Higgs boson with mass ∼ 125 GeV If we evolve the Standard Model RGE equation out to high scales, the Higgs potential becomes shallow, and even appears to have a second minimum

V (φ) φ

Lauren Pearce (UIUC) 3 / 23

Higgs Relaxation

Bunch & Davies (1978), Linde (1982) Hawking & Moss (1982)

Inflation and the Higgs Potential

During inflation, scalar fields with a shallow potential develop large VEVs:

Lauren Pearce (UIUC) 4 / 23

Higgs Relaxation

Bunch & Davies (1978), Linde (1982) Hawking & Moss (1982)

Inflation and the Higgs Potential

During inflation, scalar fields with a shallow potential develop large VEVs: VEV fluctuates to a large values (due to quantum fluctuations)

V (φ) φ

Lauren Pearce (UIUC) 4 / 23

Higgs Relaxation

Bunch & Davies (1978), Linde (1982) Hawking & Moss (1982)

Inflation and the Higgs Potential

During inflation, scalar fields with a shallow potential develop large VEVs: VEV fluctuates to a large values (due to quantum fluctuations) Hubble friction from expansion of universe prevents from rolling back down ¨ φ + 3H ˙ φ + V ′

φ = 0 V (φ) φ H

Lauren Pearce (UIUC) 4 / 23

Higgs Relaxation

Higgs Relaxation

During reheating, the Hubble parameter decreases.

V (φ) φ H

Lauren Pearce (UIUC) 5 / 23

Higgs Relaxation

Higgs Relaxation

During reheating, the Hubble parameter decreases. When H(t) ∼ curvature of potential, Hubble friction no longer prevents the VEV from rolling down.

V (φ) φ

Lauren Pearce (UIUC) 5 / 23

Higgs Relaxation

Higgs Relaxation

During reheating, the Hubble parameter decreases. When H(t) ∼ curvature of potential, Hubble friction no longer prevents the VEV from rolling down.

V (φ) φ

Lauren Pearce (UIUC) 5 / 23

Higgs Relaxation

Higgs Relaxation

During reheating, the Hubble parameter decreases. When H(t) ∼ curvature of potential, Hubble friction no longer prevents the VEV from rolling down.

V (φ) φ

Lauren Pearce (UIUC) 5 / 23

Higgs Relaxation

Higgs Relaxation

During reheating, the Hubble parameter decreases. When H(t) ∼ curvature of potential, Hubble friction no longer prevents the VEV from rolling down. Naturally have an epoch with an evolving scalar VEV.

V (φ) φ

Lauren Pearce (UIUC) 5 / 23

Higgs Relaxation Leptogenesis Higgs relaxation leptogenesis ≈ Higgs relaxation + Spontaneous baryogenesis

Lauren Pearce (UIUC) 6 / 23

Higgs Relaxation Leptogenesis Higgs relaxation leptogenesis ≈ Higgs relaxation + Spontaneous baryogenesis

Where is CP violation hidden?

Lauren Pearce (UIUC) 6 / 23

Higgs Relaxation Leptogenesis Higgs relaxation leptogenesis ≈ Higgs relaxation + Spontaneous baryogenesis

Where is CP violation hidden? One of the differences between Higgs relaxation leptogenesis and spontaneous baryogenesis

Lauren Pearce (UIUC) 6 / 23

Spontaneous Baryogenesis

Dine et. al., Phys.Lett. B257 (1991) 351-356 Cohen, Kaplan, Nelson Phys.Lett. B263 (1991) 86-92

Spontaneous Baryogenesis

Spontaneous baryogenesis models use an evolving VEV to produce a net particle asymmetry:

Lauren Pearce (UIUC) 7 / 23

Spontaneous Baryogenesis

Dine et. al., Phys.Lett. B257 (1991) 351-356 Cohen, Kaplan, Nelson Phys.Lett. B263 (1991) 86-92

Spontaneous Baryogenesis

Spontaneous baryogenesis models use an evolving VEV to produce a net particle asymmetry: Consider the coupling: L ⊇ (a/f )W ˜ W

Lauren Pearce (UIUC) 7 / 23

Spontaneous Baryogenesis

Dine et. al., Phys.Lett. B257 (1991) 351-356 Cohen, Kaplan, Nelson Phys.Lett. B263 (1991) 86-92

Spontaneous Baryogenesis

Spontaneous baryogenesis models use an evolving VEV to produce a net particle asymmetry: Consider the coupling: L ⊇ (a/f )W ˜ W

a: Axion field, W : SU(2) gauge field, f : Axion coupling strength

Lauren Pearce (UIUC) 7 / 23

Spontaneous Baryogenesis

Dine et. al., Phys.Lett. B257 (1991) 351-356 Cohen, Kaplan, Nelson Phys.Lett. B263 (1991) 86-92

Spontaneous Baryogenesis

Spontaneous baryogenesis models use an evolving VEV to produce a net particle asymmetry: Consider the coupling: L ⊇ (a/f )W ˜ W

a: Axion field, W : SU(2) gauge field, f : Axion coupling strength

Using electroweak anomaly equation: (a/f )∂µjµ

B+L

Lauren Pearce (UIUC) 7 / 23

Spontaneous Baryogenesis

Dine et. al., Phys.Lett. B257 (1991) 351-356 Cohen, Kaplan, Nelson Phys.Lett. B263 (1991) 86-92

Spontaneous Baryogenesis

Spontaneous baryogenesis models use an evolving VEV to produce a net particle asymmetry: Consider the coupling: L ⊇ (a/f )W ˜ W

a: Axion field, W : SU(2) gauge field, f : Axion coupling strength

Using electroweak anomaly equation: (a/f )∂µjµ

B+L

Integration by parts: (∂µa/f )jµ

B+L

Lauren Pearce (UIUC) 7 / 23

Spontaneous Baryogenesis

Dine et. al., Phys.Lett. B257 (1991) 351-356 Cohen, Kaplan, Nelson Phys.Lett. B263 (1991) 86-92

Spontaneous Baryogenesis

Spontaneous baryogenesis models use an evolving VEV to produce a net particle asymmetry: Consider the coupling: L ⊇ (a/f )W ˜ W

a: Axion field, W : SU(2) gauge field, f : Axion coupling strength

Using electroweak anomaly equation: (a/f )∂µjµ

B+L

Integration by parts: (∂µa/f )jµ

B+L

When a has a time-dependent VEV a: L ⊇ (∂t a /f )nB+L

Lauren Pearce (UIUC) 7 / 23

Spontaneous Baryogenesis

Dine et. al., Phys.Lett. B257 (1991) 351-356 Cohen, Kaplan, Nelson Phys.Lett. B263 (1991) 86-92

Spontaneous Baryogenesis

L ⊇ (∂t a /f )nB+L

Lauren Pearce (UIUC) 8 / 23

Spontaneous Baryogenesis

Dine et. al., Phys.Lett. B257 (1991) 351-356 Cohen, Kaplan, Nelson Phys.Lett. B263 (1991) 86-92

Spontaneous Baryogenesis

L ⊇ (∂t a /f )nB+L If scatterings in plasma are rapid on the VEV evolution timescale:

Lauren Pearce (UIUC) 8 / 23

Spontaneous Baryogenesis

Dine et. al., Phys.Lett. B257 (1991) 351-356 Cohen, Kaplan, Nelson Phys.Lett. B263 (1991) 86-92

Spontaneous Baryogenesis

L ⊇ (∂t a /f )nB+L If scatterings in plasma are rapid on the VEV evolution timescale:

◮ Treat VEV as a classical background when constructing Hamiltonian Lauren Pearce (UIUC) 8 / 23

Spontaneous Baryogenesis

Dine et. al., Phys.Lett. B257 (1991) 351-356 Cohen, Kaplan, Nelson Phys.Lett. B263 (1991) 86-92

Spontaneous Baryogenesis

L ⊇ (∂t a /f )nB+L If scatterings in plasma are rapid on the VEV evolution timescale:

◮ Treat VEV as a classical background when constructing Hamiltonian ◮ Effective chemical potential µ ∼ ∂t a /f for B + L charge Lauren Pearce (UIUC) 8 / 23

Spontaneous Baryogenesis

Dine et. al., Phys.Lett. B257 (1991) 351-356 Cohen, Kaplan, Nelson Phys.Lett. B263 (1991) 86-92

Spontaneous Baryogenesis

L ⊇ (∂t a /f )nB+L If scatterings in plasma are rapid on the VEV evolution timescale:

◮ Treat VEV as a classical background when constructing Hamiltonian ◮ Effective chemical potential µ ∼ ∂t a /f for B + L charge Lauren Pearce (UIUC) 8 / 23

Spontaneous Baryogenesis

Dine et. al., Phys.Lett. B257 (1991) 351-356 Cohen, Kaplan, Nelson Phys.Lett. B263 (1991) 86-92

Spontaneous Baryogenesis

L ⊇ (∂t a /f )nB+L If scatterings in plasma are rapid on the VEV evolution timescale:

◮ Treat VEV as a classical background when constructing Hamiltonian ◮ Effective chemical potential µ ∼ ∂t a /f for B + L charge

Leads to ℓ, q ¯ ℓ, ¯ q

Lauren Pearce (UIUC) 8 / 23

Spontaneous Baryogenesis

Dine et. al., Phys.Lett. B257 (1991) 351-356 Cohen, Kaplan, Nelson Phys.Lett. B263 (1991) 86-92

Spontaneous Baryogenesis

L ⊇ (∂t a /f )nB+L If scatterings in plasma are rapid on the VEV evolution timescale:

◮ Treat VEV as a classical background when constructing Hamiltonian ◮ Effective chemical potential µ ∼ ∂t a /f for B + L charge ◮ Scatterings with B- or L-number violation lead to asymmetry Lauren Pearce (UIUC) 8 / 23

Spontaneous Baryogenesis

Dolgov & Freese Phys.Rev. D51 (1995) 2693-2702 hep-ph/9410346

Spontaneous Baryogenesis

L ⊇ (∂t a /f )nB+L If scatterings in plasma are rapid on the VEV evolution timescale:

◮ Treat VEV as a classical background when constructing Hamiltonian ◮ Effective chemical potential µ ∼ ∂t a /f for B + L charge ◮ Scatterings with B- or L-number violation lead to asymmetry

If not, analyze asymmetric particle production using Bogoliubov analysis

Lauren Pearce (UIUC) 8 / 23

Higgs Relaxation Leptogenesis

Higgs Relaxation Leptogenesis

Consider instead the operator: L ⊇ ϕ2 Λ2

n

W ˜ W , ϕ : Higgs field

Lauren Pearce (UIUC) 9 / 23

Higgs Relaxation Leptogenesis

Higgs Relaxation Leptogenesis

Consider instead the operator: L ⊇ ϕ2 Λ2

n

W ˜ W , ϕ : Higgs field Following same steps as above gives: L ⊇ ∂µϕ2 Λ2

n

jµ

B+L

Lauren Pearce (UIUC) 9 / 23

Higgs Relaxation Leptogenesis

Higgs Relaxation Leptogenesis

Consider instead the operator: L ⊇ ϕ2 Λ2

n

W ˜ W , ϕ : Higgs field Following same steps as above gives: L ⊇ ∂µϕ2 Λ2

n

jµ

B+L

Higgs VEV φ =

• ϕ2 gives:

L ⊇ ∂tφ2 Λ2

n

nB+L

Lauren Pearce (UIUC) 9 / 23

Higgs Relaxation Leptogenesis

Higgs Relaxation Leptogenesis

Consider instead the operator: L ⊇ ϕ2 Λ2

n

W ˜ W , ϕ : Higgs field Following same steps as above gives: L ⊇ ∂µϕ2 Λ2

n

jµ

B+L

Higgs VEV φ =

• ϕ2 gives:

L ⊇ ∂tφ2 Λ2

n

nB+L If have B- or L-violating processes, produces a matter/antimatter asymmetry

Lauren Pearce (UIUC) 9 / 23

Higgs Relaxation Leptogenesis

Advantages

The Higgs field exists & naturally acquires a large VEV during inflation

Lauren Pearce (UIUC) 10 / 23

Higgs Relaxation Leptogenesis

Advantages

The Higgs field exists & naturally acquires a large VEV during inflation ∂tφ2 decreases during relaxation in every Hubble patch

Lauren Pearce (UIUC) 10 / 23

Higgs Relaxation Leptogenesis

Advantages

The Higgs field exists & naturally acquires a large VEV during inflation ∂tφ2 decreases during relaxation in every Hubble patch Therefore same sign asymmetry in each Hubble patch

Lauren Pearce (UIUC) 10 / 23

Higgs Relaxation Leptogenesis

Advantages

The Higgs field exists & naturally acquires a large VEV during inflation ∂tφ2 decreases during relaxation in every Hubble patch Therefore same sign asymmetry in each Hubble patch (Unlike ∂t a)

Lauren Pearce (UIUC) 10 / 23

CP Violation & Higgs Relaxation Leptogenesis

CPT & CP

Note that (∂tφ2/Λn)nB+L breaks CPT

Lauren Pearce (UIUC) 11 / 23

CP Violation & Higgs Relaxation Leptogenesis

CPT & CP

Note that (∂tφ2/Λn)nB+L breaks CPT (as does (∂t a /f )nB+L)

Lauren Pearce (UIUC) 11 / 23

CP Violation & Higgs Relaxation Leptogenesis

CPT & CP

Note that (∂tφ2/Λn)nB+L breaks CPT (as does (∂t a /f )nB+L) However, this is dynamical CPT breaking, due to the evolving VEV

Lauren Pearce (UIUC) 11 / 23

CP Violation & Higgs Relaxation Leptogenesis

CPT & CP

Note that (∂tφ2/Λn)nB+L breaks CPT (as does (∂t a /f )nB+L) However, this is dynamical CPT breaking, due to the evolving VEV Both aW ˜ W /f and ϕ2W ˜ W /Λ2

n conserve CPT:

C P T Psuedoscalar (a) 1 −1 −1 Scalar (ϕ) 1 1 1 Gauge fields (F ˜ F) 1 −1 −1

Lauren Pearce (UIUC) 11 / 23

CP Violation & Higgs Relaxation Leptogenesis

CPT & CP

Note that (∂tφ2/Λn)nB+L breaks CPT (as does (∂t a /f )nB+L) However, this is dynamical CPT breaking, due to the evolving VEV Both aW ˜ W /f and ϕ2W ˜ W /Λ2

n conserve CPT:

C P T Psuedoscalar (a) 1 −1 −1 Scalar (ϕ) 1 1 1 Gauge fields (F ˜ F) 1 −1 −1

However, the effective operator ϕ2W ˜ W /Λ2

n does break CP...

Lauren Pearce (UIUC) 11 / 23

CP Violation & Higgs Relaxation Leptogenesis

CPT & CP

Note that (∂tφ2/Λn)nB+L breaks CPT (as does (∂t a /f )nB+L) However, this is dynamical CPT breaking, due to the evolving VEV Both aW ˜ W /f and ϕ2W ˜ W /Λ2

n conserve CPT:

C P T Psuedoscalar (a) 1 −1 −1 Scalar (ϕ) 1 1 1 Gauge fields (F ˜ F) 1 −1 −1

However, the effective operator ϕ2W ˜ W /Λ2

n does break CP...

→ Λn involves both the scale of new physics and the CP violation in this new sector

Lauren Pearce (UIUC) 11 / 23

CP Violation & Higgs Relaxation Leptogenesis

Building the ϕ2W ˜ W /Λ2

n Operator

I generally don’t discuss model building much:

Lauren Pearce (UIUC) 12 / 23

CP Violation & Higgs Relaxation Leptogenesis

Building the ϕ2W ˜ W /Λ2

n Operator

I generally don’t discuss model building much:

◮ All of our constraints & parameter space results depend only on Λn Lauren Pearce (UIUC) 12 / 23

CP Violation & Higgs Relaxation Leptogenesis

Building the ϕ2W ˜ W /Λ2

n Operator

I generally don’t discuss model building much:

◮ All of our constraints & parameter space results depend only on Λn

But since this is a workshop on CP violation, I will discuss model building...

Lauren Pearce (UIUC) 12 / 23

CP Violation & Model Building

• M. E. Shaposhnikov (1987)
• M. E. Shaposhnikov (1988)

Standard Model

As Shaposhnikov pointed out, this operator exists in the Standard Model:

Lauren Pearce (UIUC) 13 / 23

CP Violation & Model Building

• M. E. Shaposhnikov (1987)
• M. E. Shaposhnikov (1988)

Standard Model

As Shaposhnikov pointed out, this operator exists in the Standard Model: (Works in basis in which diagonalizes SU(2) eigenstates, so Higgs couplings are not diagonal)

Lauren Pearce (UIUC) 13 / 23

CP Violation & Model Building

• M. E. Shaposhnikov (1987)
• M. E. Shaposhnikov (1988)

Standard Model

As Shaposhnikov pointed out, this operator exists in the Standard Model: (Works in basis in which diagonalizes SU(2) eigenstates, so Higgs couplings are not diagonal) To pick up the CP-violating CKM phase, need to use all three generations of quarks:

Lauren Pearce (UIUC) 13 / 23

CP Violation & Model Building

• M. E. Shaposhnikov (1987)
• M. E. Shaposhnikov (1988)

Standard Model

As Shaposhnikov pointed out, this operator exists in the Standard Model: (Works in basis in which diagonalizes SU(2) eigenstates, so Higgs couplings are not diagonal) To pick up the CP-violating CKM phase, need to use all three generations of quarks:

L R L

Lauren Pearce (UIUC) 13 / 23

CP Violation & Model Building

• M. E. Shaposhnikov (1987)
• M. E. Shaposhnikov (1988)

Standard Model

As Shaposhnikov pointed out, this operator exists in the Standard Model: (Works in basis in which diagonalizes SU(2) eigenstates, so Higgs couplings are not diagonal) To pick up the CP-violating CKM phase, need to use all three generations of quarks:

L R L

But this operator is extremely tiny:

Lauren Pearce (UIUC) 13 / 23

CP Violation & Model Building

• M. E. Shaposhnikov (1987)
• M. E. Shaposhnikov (1988)

Standard Model

As Shaposhnikov pointed out, this operator exists in the Standard Model: (Works in basis in which diagonalizes SU(2) eigenstates, so Higgs couplings are not diagonal) To pick up the CP-violating CKM phase, need to use all three generations of quarks:

L R L

But this operator is extremely tiny:

◮ Small CP-violating phase Lauren Pearce (UIUC) 13 / 23

CP Violation & Model Building

• M. E. Shaposhnikov (1987)
• M. E. Shaposhnikov (1988)

Standard Model

As Shaposhnikov pointed out, this operator exists in the Standard Model: (Works in basis in which diagonalizes SU(2) eigenstates, so Higgs couplings are not diagonal) To pick up the CP-violating CKM phase, need to use all three generations of quarks:

L R L

But this operator is extremely tiny:

◮ Small CP-violating phase ◮ Small quark Yukawa couplings Lauren Pearce (UIUC) 13 / 23

CP Violation & Model Building

L R L

Model Building

But there’s a more serious problem as well:

Lauren Pearce (UIUC) 14 / 23

CP Violation & Model Building

L R L

Model Building

But there’s a more serious problem as well: Quark masses ∝ Higgs VEV φ

Lauren Pearce (UIUC) 14 / 23

CP Violation & Model Building

L R L

Model Building

But there’s a more serious problem as well: Quark masses ∝ Higgs VEV φ So Λn ∝ φ

Lauren Pearce (UIUC) 14 / 23

CP Violation & Model Building

L R L

Model Building

But there’s a more serious problem as well: Quark masses ∝ Higgs VEV φ So Λn ∝ φ So the coefficient of the jµ

B+L term is:

∂µ φ2 Λ2

n

• ∝ ∂µ

φ2 φ2

• = 0

Lauren Pearce (UIUC) 14 / 23

CP Violation & Model Building

L R L

Model Building

A similar operator can be constructed using leptons:

Lauren Pearce (UIUC) 14 / 23

CP Violation & Model Building

L R L

Model Building

A similar operator can be constructed using leptons: (Even smaller Yukawas)

Lauren Pearce (UIUC) 14 / 23

CP Violation & Model Building

L R L

Model Building

A similar operator can be constructed using leptons: (Even smaller Yukawas) But scale Λn ∝ MRH if RH neutrinos have a Majorana mass

Lauren Pearce (UIUC) 14 / 23

CP Violation & Model Building

L R L

Model Building

A similar operator can be constructed using leptons: (Even smaller Yukawas) But scale Λn ∝ MRH if RH neutrinos have a Majorana mass Easiest solution: Copy the lepton sector, with larger Yukawa couplings and smaller Majorana masses

Lauren Pearce (UIUC) 14 / 23

CP Violation & Model Building

L R L

Model Building

A similar operator can be constructed using leptons: (Even smaller Yukawas) But scale Λn ∝ MRH if RH neutrinos have a Majorana mass Easiest solution: Copy the lepton sector, with larger Yukawa couplings and smaller Majorana masses (Make sure Yukawa couplings are large enough that you don’t disturb Higgs decays)

Lauren Pearce (UIUC) 14 / 23

CP Violation & Model Building

Basic Conditions

Need to involve states that:

Lauren Pearce (UIUC) 15 / 23

CP Violation & Model Building

Basic Conditions

Need to involve states that: Couple to the Higgs

Lauren Pearce (UIUC) 15 / 23

CP Violation & Model Building

Basic Conditions

Need to involve states that: Couple to the Higgs Couple to the SU(2) gauge bosons

Lauren Pearce (UIUC) 15 / 23

CP Violation & Model Building

Basic Conditions

Need to involve states that: Couple to the Higgs Couple to the SU(2) gauge bosons Do not (all) get their masses from the Higgs mechanism

Lauren Pearce (UIUC) 15 / 23

CP Violation & Model Building

Basic Conditions

Need to involve states that: Couple to the Higgs Couple to the SU(2) gauge bosons Do not (all) get their masses from the Higgs mechanism Allow for additional CP violation

Lauren Pearce (UIUC) 15 / 23

CP Violation & Model Building

Basic Conditions

Need to involve states that: Couple to the Higgs Couple to the SU(2) gauge bosons Do not (all) get their masses from the Higgs mechanism Allow for additional CP violation Several other options as well

Lauren Pearce (UIUC) 15 / 23

CP Violation & Model Building

Basic Conditions

Need to involve states that: Couple to the Higgs Couple to the SU(2) gauge bosons Do not (all) get their masses from the Higgs mechanism Allow for additional CP violation Several other options as well

Main Point

We don’t particularly care about the source of CP violation in the UV-complete theory, once the effective operator is constructed and the “effective scale” Λn is known

Lauren Pearce (UIUC) 15 / 23

Having Said That...

In the Standard Model, the relevant parameter space is in the regime in which the use of effective field theory is questionable:

Γ Λ Λ ϕ Λ

Lauren Pearce (UIUC) 16 / 23

Having Said That...

In the Standard Model, the relevant parameter space is in the regime in which the use of effective field theory is questionable:

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5 6 7 8 9 8 10 12 14 16 log(ΓI [GeV]) log(Λn [GeV]) Λn < ϕ0 Λn < TMax

Inflaton scale: ΛI = 1015 GeV x-axis: Inflaton decay scale ΓI, controls reheating → creation of plasma in which / L interactions

• ccur

(Used RH neutrino for / L violation, masses set high enough to suppress thermal leptogenesis)

Lauren Pearce (UIUC) 16 / 23

Having Said That...

In the Standard Model, the relevant parameter space is in the regime in which the use of effective field theory is questionable:

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• 14
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• 10
• 8
• 6
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5 6 7 8 9 8 10 12 14 16 log(ΓI [GeV]) log(Λn [GeV]) Λn < ϕ0 Λn < TMax

Models with extended Higgs sector:

◮ Can protect flat direction ◮ Regime in which EFT is

valid

• H. Gertov et. al., Phys.Rev. D93

(2016) no.11, 115042

Lauren Pearce (UIUC) 16 / 23

Having Said That...

In the Standard Model, the relevant parameter space is in the regime in which the use of effective field theory is questionable:

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• 6
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5 6 7 8 9 8 10 12 14 16 log(ΓI [GeV]) log(Λn [GeV]) Λn < ϕ0 Λn < TMax

Relevant scales: Λn ∼ 108 to 1010 GeV

Lauren Pearce (UIUC) 16 / 23

Having Said That...

In the Standard Model, the relevant parameter space is in the regime in which the use of effective field theory is questionable:

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• 24
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• 20
• 18
• 16
• 14
• 12
• 10
• 8
• 6
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5 6 7 8 9 8 10 12 14 16 log(ΓI [GeV]) log(Λn [GeV]) Λn < ϕ0 Λn < TMax

Relevant scales: Λn ∼ 108 to 1010 GeV (Not likely to be probed any time soon)

Lauren Pearce (UIUC) 16 / 23

Having Said That...

In the Standard Model, the relevant parameter space is in the regime in which the use of effective field theory is questionable:

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• 24
• 22
• 20
• 18
• 16
• 14
• 12
• 10
• 8
• 6
• 4

5 6 7 8 9 8 10 12 14 16 log(ΓI [GeV]) log(Λn [GeV]) Λn < ϕ0 Λn < TMax

Relevant scales: Λn ∼ 108 to 1010 GeV (Not likely to be probed any time soon) Other observational consequences?

Lauren Pearce (UIUC) 16 / 23

Isocurvature Perturbations

VEV Variation

The Fokker-Planck equation gives us the Higgs VEV averaged

• ver many Hubble

volumes

Lauren Pearce (UIUC) 17 / 23

Isocurvature Perturbations

VEV Variation

The Fokker-Planck equation gives us the Higgs VEV averaged

• ver many Hubble

volumes

Lauren Pearce (UIUC) 17 / 23

Isocurvature Perturbations

φ′ φ0 φ′′

VEV Variation

The Fokker-Planck equation gives us the Higgs VEV averaged

• ver many Hubble

volumes The VEVs in individual Hubble volumes will vary

Lauren Pearce (UIUC) 17 / 23

Isocurvature Perturbations

φ′ φ0 φ′′

VEV Variation

The Fokker-Planck equation gives us the Higgs VEV averaged

• ver many Hubble

volumes The VEVs in individual Hubble volumes will vary Therefore, the final partial-antiparticle asymmetry also varies

Lauren Pearce (UIUC) 17 / 23

Isocurvature Perturbations

VEV Variation

The Fokker-Planck equation gives us the Higgs VEV averaged

• ver many Hubble

volumes The VEVs in individual Hubble volumes will vary Therefore, the final partial-antiparticle asymmetry also varies

Lauren Pearce (UIUC) 17 / 23

Isocurvature Perturbations

Isocurvature Perturbations

Because the Higgs VEV does not dominate the energy density of the universe, these are isocurvature perturbations

Lauren Pearce (UIUC) 18 / 23

Isocurvature Perturbations

• S. Weinberg

Phys.Rev. D70 (2004) 083522 astro-ph/0405397

Isocurvature Perturbations

Because the Higgs VEV does not dominate the energy density of the universe, these are isocurvature perturbations Weinberg has a famous theorem that isocurvature perturbations must decay when as the universe thermalizes...

Lauren Pearce (UIUC) 18 / 23

Isocurvature Perturbations

• S. Weinberg

Phys.Rev. D70 (2004) 083522 astro-ph/0405397

Isocurvature Perturbations

Because the Higgs VEV does not dominate the energy density of the universe, these are isocurvature perturbations Weinberg has a famous theorem that isocurvature perturbations must decay when as the universe thermalizes... ...“become adiabatic if the universe after inflation enters an era of local thermal equilibrium, with no non-zero conserved quantities”

Lauren Pearce (UIUC) 18 / 23

Isocurvature Perturbations

Isocurvature Perturbations

Because the Higgs VEV does not dominate the energy density of the universe, these are isocurvature perturbations Weinberg has a famous theorem that isocurvature perturbations must decay when as the universe thermalizes... ...“become adiabatic if the universe after inflation enters an era of local thermal equilibrium, with no non-zero conserved quantities” In our scenario: isocurvature perturbations survive because they are carried along with nonzero lepton/baryon number

Lauren Pearce (UIUC) 18 / 23

Isocurvature Perturbations

Isocurvature Perturbations

Because the Higgs VEV does not dominate the energy density of the universe, these are isocurvature perturbations Weinberg has a famous theorem that isocurvature perturbations must decay when as the universe thermalizes... ...“become adiabatic if the universe after inflation enters an era of local thermal equilibrium, with no non-zero conserved quantities” In our scenario: isocurvature perturbations survive because they are carried along with nonzero lepton/baryon number

Why Isocurvature?

Few theories produce isocurvature perturbations

Lauren Pearce (UIUC) 18 / 23

Isocurvature Perturbations

Isocurvature Perturbations

Because the Higgs VEV does not dominate the energy density of the universe, these are isocurvature perturbations Weinberg has a famous theorem that isocurvature perturbations must decay when as the universe thermalizes... ...“become adiabatic if the universe after inflation enters an era of local thermal equilibrium, with no non-zero conserved quantities” In our scenario: isocurvature perturbations survive because they are carried along with nonzero lepton/baryon number

Why Isocurvature?

Few theories produce isocurvature perturbations Stringently constrained by CMB & Lyman α data

Lauren Pearce (UIUC) 18 / 23

Isocurvature

In fact, too strong...

In fact, isocurvature constraints already rule out the naive version I’ve introduced here (details below)!

Lauren Pearce (UIUC) 19 / 23

Isocurvature

In fact, too strong...

In fact, isocurvature constraints already rule out the naive version I’ve introduced here (details below)! Decrease amplitude of perturbations → suppresses asymmetry

Lauren Pearce (UIUC) 19 / 23

Isocurvature

In fact, too strong...

In fact, isocurvature constraints already rule out the naive version I’ve introduced here (details below)! Decrease amplitude of perturbations → suppresses asymmetry Cannot eliminate isocurvature perturbations!

Lauren Pearce (UIUC) 19 / 23

Isocurvature

In fact, too strong...

In fact, isocurvature constraints already rule out the naive version I’ve introduced here (details below)! Decrease amplitude of perturbations → suppresses asymmetry Cannot eliminate isocurvature perturbations! But can shift to smaller scales via a Higgs-inflaton coupling:

V (φ) φ

Couplings ∼ I nφm lead to I n φm terms in the potential

Lauren Pearce (UIUC) 19 / 23

Isocurvature

In fact, too strong...

In fact, isocurvature constraints already rule out the naive version I’ve introduced here (details below)! Decrease amplitude of perturbations → suppresses asymmetry Cannot eliminate isocurvature perturbations! But can shift to smaller scales via a Higgs-inflaton coupling:

V (φ) φ

Couplings ∼ I nφm lead to I n φm terms in the potential Can destroy flatness

Lauren Pearce (UIUC) 19 / 23

Isocurvature

In fact, too strong...

In fact, isocurvature constraints already rule out the naive version I’ve introduced here (details below)! Decrease amplitude of perturbations → suppresses asymmetry Cannot eliminate isocurvature perturbations! But can shift to smaller scales via a Higgs-inflaton coupling:

V (φ) φ

Couplings ∼ I nφm lead to I n φm terms in the potential Can destroy flatness These terms → 0 at the end of inflation

Lauren Pearce (UIUC) 19 / 23

Isocurvature

In fact, too strong...

In fact, isocurvature constraints already rule out the naive version I’ve introduced here (details below)! Decrease amplitude of perturbations → suppresses asymmetry Cannot eliminate isocurvature perturbations! But can shift to smaller scales via a Higgs-inflaton coupling:

V (φ) φ

Couplings ∼ I nφm lead to I n φm terms in the potential Can destroy flatness These terms → 0 at the end of inflation VEV grows only at end of inflation

Lauren Pearce (UIUC) 19 / 23

Isocurvature

In fact, too strong...

In fact, isocurvature constraints already rule out the naive version I’ve introduced here (details below)! Decrease amplitude of perturbations → suppresses asymmetry Cannot eliminate isocurvature perturbations! But can shift to smaller scales via a Higgs-inflaton coupling:

V (φ) φ

Couplings ∼ I nφm lead to I n φm terms in the potential Can destroy flatness These terms → 0 at the end of inflation VEV grows only at end of inflation Isocurvature only on small scales

Lauren Pearce (UIUC) 19 / 23

Isocurvature

Isocurvature & Small Structures

Parameterize by Nlast, number of e-folds VEV grows through

35 40 45 50 55 10-4 0.01 1 100 104 106 Nlast of e-folds ks [Mpc-1] CMB constraint Lyman-α Forest constraint ΛI = 1016 GeV ΛI = 1014 GeV ΛI = 1012 GeV TRH = 1010 GeV

ks: Largest scale of isocurvature perturbations

Lauren Pearce (UIUC) 20 / 23

Isocurvature

Isocurvature & Small Structures

Parameterize by Nlast, number of e-folds VEV grows through

35 40 45 50 55 10-4 0.01 1 100 104 106 Nlast of e-folds ks [Mpc-1] CMB constraint Lyman-α Forest constraint ΛI = 1016 GeV ΛI = 1014 GeV ΛI = 1012 GeV TRH = 1010 GeV

ks: Largest scale of isocurvature perturbations

Decreases predictive power, obviously

Lauren Pearce (UIUC) 20 / 23

Isocurvature

Isocurvature & Small Structures

Parameterize by Nlast, number of e-folds VEV grows through

35 40 45 50 55 10-4 0.01 1 100 104 106 Nlast of e-folds ks [Mpc-1] CMB constraint Lyman-α Forest constraint ΛI = 1016 GeV ΛI = 1014 GeV ΛI = 1012 GeV TRH = 1010 GeV

ks: Largest scale of isocurvature perturbations

Decreases predictive power, obviously But perhaps has interesting consequences...

Lauren Pearce (UIUC) 20 / 23

Isocurvature

Isocurvature & Small Structures

Power spectrum enhanced at small scales:

• 2
• 1

1 2

• 8
• 6
• 4
• 2

2 4 log(k [h/Mpc]) log(P(k) [h-3Mpc3]) Silk dampling Lyman-α Forest

• Ad. z = 0
• Ad. z = 10
• Ad. z = 20
• Iso. z = 0
• Iso. z = 10
• Iso. z = 20

Lauren Pearce (UIUC) 20 / 23

Isocurvature

Isocurvature & Small Structures

Power spectrum enhanced at small scales:

• 2
• 1

1 2

• 8
• 6
• 4
• 2

2 4 log(k [h/Mpc]) log(P(k) [h-3Mpc3]) Silk dampling Lyman-α Forest

• Ad. z = 0
• Ad. z = 10
• Ad. z = 20
• Iso. z = 0
• Iso. z = 10
• Iso. z = 20

Leads to small structures collapsing early

Lauren Pearce (UIUC) 20 / 23

Isocurvature

Kashlinsky et. al. Astrophys.J. 804 (2015) no.2, 99 arXiv:1412.5566

Cosmic Infrared Background

Spitzer and Akari space telescopes have observed (source-subtracted) anisotropies in the cosmic infrared background (5 arcminutes, 2 − 5 µm, 0.09 nW m−2 sr−1).

Lauren Pearce (UIUC) 21 / 23

Isocurvature

Kashlinsky et. al. Astrophys.J. 804 (2015) no.2, 99 arXiv:1412.5566

Cosmic Infrared Background

Spitzer and Akari space telescopes have observed (source-subtracted) anisotropies in the cosmic infrared background (5 arcminutes, 2 − 5 µm, 0.09 nW m−2 sr−1). From the anisotropy, can infer a large isotropic CIB flux

Lauren Pearce (UIUC) 21 / 23

Isocurvature

Kashlinsky et. al. Astrophys.J. 804 (2015) no.2, 99 arXiv:1412.5566

Cosmic Infrared Background

Spitzer and Akari space telescopes have observed (source-subtracted) anisotropies in the cosmic infrared background (5 arcminutes, 2 − 5 µm, 0.09 nW m−2 sr−1). From the anisotropy, can infer a large isotropic CIB flux Can explain with early stars (z = 10) if mass fraction of baryons in star-forming collapsed halos, fhalo, ∼ 0.2

Lauren Pearce (UIUC) 21 / 23

Isocurvature

Kashlinsky et. al. Astrophys.J. 804 (2015) no.2, 99 arXiv:1412.5566

Cosmic Infrared Background

Spitzer and Akari space telescopes have observed (source-subtracted) anisotropies in the cosmic infrared background (5 arcminutes, 2 − 5 µm, 0.09 nW m−2 sr−1). From the anisotropy, can infer a large isotropic CIB flux Can explain with early stars (z = 10) if mass fraction of baryons in star-forming collapsed halos, fhalo, ∼ 0.2 But this is too large a value to accomodate in the usual cosmological picture

Lauren Pearce (UIUC) 21 / 23

Isocurvature

Early Stars

However, we can nicely collapse the requisite small halos early without disturbing dwarf galaxy halos:

10 20 30 40 10-5 10-4 0.001 0.010 0.100 1 z fhalo

• Iso. with

ks = 30 Mpc-1

• Iso. with

ks = 65 Mpc-1

• Iso. with

ks = 100 Mpc-1 Ad.

Lauren Pearce (UIUC) 22 / 23

Isocurvature

Early Stars

However, we can nicely collapse the requisite small halos early without disturbing dwarf galaxy halos:

10 20 30 40 10-5 10-4 0.001 0.010 0.100 1 z fhalo

• Iso. with

ks = 30 Mpc-1

• Iso. with

ks = 65 Mpc-1

• Iso. with

ks = 100 Mpc-1 Ad.

Solid: Mass fraction of baryons in collapsed halos 106M⊙ (star forming)

Lauren Pearce (UIUC) 22 / 23

Isocurvature

Early Stars

However, we can nicely collapse the requisite small halos early without disturbing dwarf galaxy halos:

10 20 30 40 10-5 10-4 0.001 0.010 0.100 1 z fhalo

• Iso. with

ks = 30 Mpc-1

• Iso. with

ks = 65 Mpc-1

• Iso. with

ks = 100 Mpc-1 Ad.

Solid: Mass fraction of baryons in collapsed halos 106M⊙ (star forming) Dashed: Mass fraction of baryons in collapsed halos 108M⊙ (dwarf galaxy)

Lauren Pearce (UIUC) 22 / 23

Isocurvature

Early Stars

However, we can nicely collapse the requisite small halos early without disturbing dwarf galaxy halos:

10 20 30 40 10-5 10-4 0.001 0.010 0.100 1 z fhalo

• Iso. with

ks = 30 Mpc-1

• Iso. with

ks = 65 Mpc-1

• Iso. with

ks = 100 Mpc-1 Ad.

By choosing Nlast, we can explain infrared excess in most of parameter space where also generate a large enough baryon asymmetry

Lauren Pearce (UIUC) 22 / 23

Conclusions

In Higgs Relaxation Leptogenesis

Lauren Pearce (UIUC) 23 / 23

Conclusions

In Higgs Relaxation Leptogenesis

CP violation is required in the construction of the O6 operator used in Higgs relaxation leptogenesis

Lauren Pearce (UIUC) 23 / 23

Conclusions

In Higgs Relaxation Leptogenesis

CP violation is required in the construction of the O6 operator used in Higgs relaxation leptogenesis However the relevant parameter, Λn, depends both on the CP violation parameter and the scale of new physics

Lauren Pearce (UIUC) 23 / 23

Conclusions

In Higgs Relaxation Leptogenesis

CP violation is required in the construction of the O6 operator used in Higgs relaxation leptogenesis However the relevant parameter, Λn, depends both on the CP violation parameter and the scale of new physics Isocurvature perturbations are necessarily produced...

Lauren Pearce (UIUC) 23 / 23

Conclusions

In Higgs Relaxation Leptogenesis

CP violation is required in the construction of the O6 operator used in Higgs relaxation leptogenesis However the relevant parameter, Λn, depends both on the CP violation parameter and the scale of new physics Isocurvature perturbations are necessarily produced... ...which constrains the models (but can be used to explain the cosmic infrared excess)

Lauren Pearce (UIUC) 23 / 23

Conclusions

In Higgs Relaxation Leptogenesis

CP violation is required in the construction of the O6 operator used in Higgs relaxation leptogenesis However the relevant parameter, Λn, depends both on the CP violation parameter and the scale of new physics Isocurvature perturbations are necessarily produced... ...which constrains the models (but can be used to explain the cosmic infrared excess)

Thank you! Questions?

Lauren Pearce (UIUC) 23 / 23

Back-Up Slides

Back-Up Slides

More model building Details of asymmetry calculation

Lauren Pearce (UIUC) 1 / 6

Model Building

Unusual Proposal

We don’t actually know why left-handed fermions couple to SU(2) and right-handed ones don’t...

Lauren Pearce (UIUC) 2 / 6

Model Building

Unusual Proposal

We don’t actually know why left-handed fermions couple to SU(2) and right-handed ones don’t... Introduce the following fields (YW = Q − T3):

Lauren Pearce (UIUC) 2 / 6

Model Building

Unusual Proposal

We don’t actually know why left-handed fermions couple to SU(2) and right-handed ones don’t... Introduce the following fields (YW = Q − T3):

◮ ψDi (both left and right): SU(2) doublet, hypercharge −1/2 Lauren Pearce (UIUC) 2 / 6

Model Building

Unusual Proposal

We don’t actually know why left-handed fermions couple to SU(2) and right-handed ones don’t... Introduce the following fields (YW = Q − T3):

◮ ψDi (both left and right): SU(2) doublet, hypercharge −1/2 ⋆ Can construct mass term Mij( ¯

ψDLiψDRj + ¯ ψDRjψDLi) + h.c.

Lauren Pearce (UIUC) 2 / 6

Model Building

Unusual Proposal

We don’t actually know why left-handed fermions couple to SU(2) and right-handed ones don’t... Introduce the following fields (YW = Q − T3):

◮ ψDi (both left and right): SU(2) doublet, hypercharge −1/2 ⋆ Can construct mass term Mij( ¯

ψDLiψDRj + ¯ ψDRjψDLi) + h.c.

◮ ψS (both left and right): SU(2) singlet, hypercharge −1 Lauren Pearce (UIUC) 2 / 6

Model Building

Unusual Proposal

We don’t actually know why left-handed fermions couple to SU(2) and right-handed ones don’t... Introduce the following fields (YW = Q − T3):

◮ ψDi (both left and right): SU(2) doublet, hypercharge −1/2 ⋆ Can construct mass term Mij( ¯

ψDLiψDRj + ¯ ψDRjψDLi) + h.c.

◮ ψS (both left and right): SU(2) singlet, hypercharge −1 ⋆ Can construct mass term m( ¯

ψSLψSR + ¯ ψSRψSL)

Lauren Pearce (UIUC) 2 / 6

Model Building

Unusual Proposal

We don’t actually know why left-handed fermions couple to SU(2) and right-handed ones don’t... Introduce the following fields (YW = Q − T3):

◮ ψDi (both left and right): SU(2) doublet, hypercharge −1/2 ⋆ Can construct mass term Mij( ¯

ψDLiψDRj + ¯ ψDRjψDLi) + h.c.

◮ ψS (both left and right): SU(2) singlet, hypercharge −1 ⋆ Can construct mass term m( ¯

ψSLψSR + ¯ ψSRψSL)

◮ Can couple to SM Higgs ϕ: SU(2) doublet, hypercharge 1/2 via: Lauren Pearce (UIUC) 2 / 6

Model Building

Unusual Proposal

We don’t actually know why left-handed fermions couple to SU(2) and right-handed ones don’t... Introduce the following fields (YW = Q − T3):

◮ ψDi (both left and right): SU(2) doublet, hypercharge −1/2 ⋆ Can construct mass term Mij( ¯

ψDLiψDRj + ¯ ψDRjψDLi) + h.c.

◮ ψS (both left and right): SU(2) singlet, hypercharge −1 ⋆ Can construct mass term m( ¯

ψSLψSR + ¯ ψSRψSL)

◮ Can couple to SM Higgs ϕ: SU(2) doublet, hypercharge 1/2 via: ⋆ yieiδi Φ( ¯

ψDLiψSR + ¯ ψDRiψSL) + h.c.

Lauren Pearce (UIUC) 2 / 6

Chemical Potential

Higgs VEV Evolution

To find the chemical potential as a function of time we need to know the evolution of the Higgs VEV in time.

Lauren Pearce (UIUC) 3 / 6

Chemical Potential

Higgs VEV Evolution

To find the chemical potential as a function of time we need to know the evolution of the Higgs VEV in time. Equation of motion: ¨ φ + 3H(t) ˙ φ + V ′

φ(φ, T(t)) = 0

Lauren Pearce (UIUC) 3 / 6

Chemical Potential

Higgs VEV Evolution

To find the chemical potential as a function of time we need to know the evolution of the Higgs VEV in time. Equation of motion: ¨ φ + 3H(t) ˙ φ + V ′

φ(φ, T(t)) = 0

Include running couplings, one-loop correction, and finite temperature corrections in potential.

Lauren Pearce (UIUC) 3 / 6

Chemical Potential

Higgs VEV Evolution

To find the chemical potential as a function of time we need to know the evolution of the Higgs VEV in time. Equation of motion: ¨ φ + 3H(t) ˙ φ + V ′

φ(φ, T(t)) = 0

Include running couplings, one-loop correction, and finite temperature corrections in potential. Also include condensate decay; not an important effect.

Lauren Pearce (UIUC) 3 / 6

Lepton Number Violation

Lepton Number Violation

µeff = 0 implies the energy of the system is minimized at nL = 0.

Lauren Pearce (UIUC) 4 / 6

Lepton Number Violation

Lepton Number Violation

µeff = 0 implies the energy of the system is minimized at nL = 0. However, we still need a lepton-number-violating process to allow the system to relax to its minimum energy.

Lauren Pearce (UIUC) 4 / 6

Lepton Number Violation

Lepton Number Violation

µeff = 0 implies the energy of the system is minimized at nL = 0. However, we still need a lepton-number-violating process to allow the system to relax to its minimum energy. Use right-handed neutrinos to generate lepton-number-violating processes...

νL NR Nc

R

νc

ℓ

h0 h0 νL NR Nc

R

νc

ℓ

h0 h0 νL νℓ h0 h0 NR NR νc

L

νc

ℓ

h0 h0 Nc

R

Nc

R

Lauren Pearce (UIUC) 4 / 6

Lepton Number Violation

Lepton Number Violation

µeff = 0 implies the energy of the system is minimized at nL = 0. However, we still need a lepton-number-violating process to allow the system to relax to its minimum energy. Use right-handed neutrinos to generate lepton-number-violating processes... ...but ensure T ≪ MR to suppress thermal leptogenesis!

νL NR Nc

R

νc

ℓ

h0 h0 νL NR Nc

R

νc

ℓ

h0 h0 νL νℓ h0 h0 NR NR νc

L

νc

ℓ

h0 h0 Nc

R

Nc

R

Lauren Pearce (UIUC) 4 / 6

Washout

Washout

µeff ∝ ∂tφ2 changes sign as VEV oscilates.

Lauren Pearce (UIUC) 5 / 6

Washout

Washout

µeff ∝ ∂tφ2 changes sign as VEV oscilates. Drives production with opposite sign.

Lauren Pearce (UIUC) 5 / 6

Washout

Washout

µeff ∝ ∂tφ2 changes sign as VEV oscilates. Drives production with opposite sign. Options to suppress this washout:

Lauren Pearce (UIUC) 5 / 6

Washout

Washout

µeff ∝ ∂tφ2 changes sign as VEV oscilates. Drives production with opposite sign. Options to suppress this washout:

◮ Choose parameters such that the Higgs oscillation is significantly

damped.

Lauren Pearce (UIUC) 5 / 6

Washout

Washout

µeff ∝ ∂tφ2 changes sign as VEV oscilates. Drives production with opposite sign. Options to suppress this washout:

◮ Choose parameters such that the Higgs oscillation is significantly

damped.

◮ Choose parameters such that the asymmetry generation freezes out

during the first swing (if it is even in equilibrium).

Lauren Pearce (UIUC) 5 / 6

Washout

Washout

µeff ∝ ∂tφ2 changes sign as VEV oscilates. Drives production with opposite sign. Options to suppress this washout:

◮ Choose parameters such that the Higgs oscillation is significantly

damped.

◮ Choose parameters such that the asymmetry generation freezes out

during the first swing (if it is even in equilibrium).

T ≪ MR suppresses lepton-number-violating cross section.

Lauren Pearce (UIUC) 5 / 6

Washout

Washout

µeff ∝ ∂tφ2 changes sign as VEV oscilates. Drives production with opposite sign. Options to suppress this washout:

◮ Choose parameters such that the Higgs oscillation is significantly

damped.

◮ Choose parameters such that the asymmetry generation freezes out

during the first swing (if it is even in equilibrium).

T ≪ MR suppresses lepton-number-violating cross section. Regime where thermal leptogenesis is inefficient automatically is regime where washout is suppressed!

Lauren Pearce (UIUC) 5 / 6

Washout

Small Cross Section Effects

The small cross section is counteracted by large chemical potential µeff (because the Higgs VEV relaxes (relatively) quickly compared to Hubble parameter).

Lauren Pearce (UIUC) 6 / 6

Washout

Small Cross Section Effects

The small cross section is counteracted by large chemical potential µeff (because the Higgs VEV relaxes (relatively) quickly compared to Hubble parameter). The system won’t reach the equilibrium asymmetry, but approaches it.

Lauren Pearce (UIUC) 6 / 6

Washout

Small Cross Section Effects

The small cross section is counteracted by large chemical potential µeff (because the Higgs VEV relaxes (relatively) quickly compared to Hubble parameter). The system won’t reach the equilibrium asymmetry, but approaches it. Production of asymmetry described by Boltzmann-style equation: d dt nL + 3HnL ∼ = − 2 π2 T 3σR

• nL − 2

π2 µeff T 2

• .

Lauren Pearce (UIUC) 6 / 6