Baryogenesis from Helical Magnetic Fields Through the EW Phase - - PowerPoint PPT Presentation

SLIDE 1

Baryogenesis from Helical Magnetic Fields Through the EW Phase Transition

Andrew Long

EWPT Workshop at U Mass Amherst April 7, 2017

based on 1606.08891 (PRD) & 1610.03074 (PRD) in collab. w/ Kohei Kamada

SLIDE 2

Among the outstanding problems in modern cosmology (dark matter, dark energy, inflation, baryogenesis) … the matter / anti-matter asymmetry is uniquely challenging, because we only know one number (nB/s = 10-10)! Therefore it is compelling to study models with “secondary predictions” that we can test in the lab (e.g., EWBG tested by collider observables & EDMs). However, the physics of baryogenesis may not within reach of terrestrial

• experiments. In this case, we may still probe the origin of the matter / anti-

matter asymmetry through observations of baryogenesis “by-products”. Baryogenesis requires a departure from thermal equilibrium (Sakharov), and such conditions may create additional cosmological relics (e.g., gravity waves and topological defects) or the OOE conditions may be provided by other relics (e.g., primordial black holes and primordial magnetic fields). If we could observe these other relics, we would gain a new handle on the

• rigin of the matter / anti-matter asymmetry (more numbers) .

Baryogenesis “by-products”

April 7, 2017 Andrew Long

SLIDE 3

April 7, 2017 Andrew Long

Primordial Magnetic Fields

The creation of long-range, coherent magnetic fields in the early universe has been studied extensively (e.g., Turner & Widrow 1987). The evolution of such fields is studied with sophisticated magnetohydrodynamics simulations. There is a natural connection between magnetic helicity and baryogenesis (SM anomalies). However, the mapping from B-field to BAU depends sensitively on the nature of the EW phase transition. The PMF will persist in the universe today as an intergalactic magnetic field (IGMF). Currently there is no evidence for an IGMF, but it is being probed by observations of the CMB and TeV blazars.

generation evolution this work detection

SLIDE 4

April 7, 2017

Helical Primordial Hyper-magnetic Field

(axion inHlation, etc)

Baryon Asymmetry

• f the Universe

Standard Model Quantum Anomalies, d.jB = YYdual ηB = nB/s ' 10−10 Intergalactic Magnetic Field

(baryogenesis by-product)

Magneto- hydrodynamics B0 , λ0

Andrew Long

EW Phase Transition Final BAU depends sensitively on how BY converts into Bem! B0 ηB

SLIDE 5

April 7, 2017

E.g., field generation via axion inflation

For example, a helical magnetic field may be generated during inflation from a pseudo-scalar inflaton (or spectator field).

−Lint = ϕ 4f Fµν e F µν = dϕ/dt 2f A · B + · · ·

Garretson, Field, & Carroll (1992); Anber & Sorbo (2006) Durrer, Hollenstein, Jain (2010) Barnaby, Moxon, Namba, Peloso, Shiu, & Zhou (2012) Fujita, Namba, Tada, Takeda, Tashiro (2015) Anber & Sabancilar (2015)

ξ ≡ dϕ/dt fH

✓ ∂2 ∂η2 + k2 ± k ξ η ◆ A±(η, k) = 0

• ()
• λ (-)

Lattice simulation

• f B-field growth

during preheating after axion inflation

Adshead, Gilpin, Scully, Sfakianakis (2016)

axion coupled to EM … rolling sources helicity ...

• pens kinetic instability

Btoday ∼ 10−13 Gauss λtoday ∼ 10 pc

Andrew Long

SLIDE 6

What is a Helical Magnetic Field?

April 7, 2017 Andrew Long

SLIDE 7

Statistically isotropic, stochastic magnetic field: (1) Helicity means more power in L- or R-circular pol: (2) Helicity means parity violation

What is a helical magnetic field?

hB · r ⇥ Bi = Z d3k (2π)3 2k PH(t, k) eik·(x−x0) hBRB⇤

Ri hBLB⇤ Li = PH(t, k) (2π)3 δ(3)(k k0)

Pij(t, k) = ⇣ ij − ˆ kiˆ kj ⌘ PE(t, k) − i✏ijmˆ km PH(t, k) hBi(t, k)Bj(t, k0)⇤i = Pij(t, k) (2π)3 δ(3)(k k0)

energy spectrum helicity spectrum

April 7, 2017 Andrew Long

SLIDE 8

(3) Helicity measures “topology” of linked flux tubes (Gauss linking number)

What is a helical magnetic field?

Moffatt (1969); Berger & Field (1984)

H > 0 H < 0

H = Z A · B d3x H = Φ1 I A · dl1 + Φ2 I A · dl2 = ±2Φ1Φ2

April 7, 2017 Andrew Long

SLIDE 9

The pseudoscalar product describes helicity changes

Changing Helicity

H = Z A · B d3x

April 7, 2017 Andrew Long

Fµν e F µν = −4E · B = 2 h ∂ ∂t

• A · B
• + r ·
• φB + E × A

i Z d3x Fµν e F µν = 2∂H ∂t

with

SLIDE 10

Axial Fermion-Number Generation in QED in the Presence of a Helical Magnetic Field

April 7, 2017 Andrew Long

SLIDE 11

Massless Electrodynamics

Let’s think about massless electrodynamics. There are four kinds of particles, classified by their quantum numbers under two charges. Interactions between these particles and the photons leave the two charges conserved. electric charge chiral charge == helicity (h=S.p)

April 7, 2017 Andrew Long

SLIDE 12

We are interested in how the various particle densities evolve. (Analogous to baryon number in the Standard Model.) We describe the evolution with a system of Boltzmann equations. (schematic!)

Bring System to Finite Temperature and Density

These terms account for particle- changing processes like annihilations: These equations encode the electric & chiral charge conservation:

April 7, 2017 Andrew Long

SLIDE 13

When quantum effects are taken into account, the chiral charge is not conserved. This is the well-known chiral (or axial) anomaly of QED [Adler, Bell, Jackiw, ’69] How does this affect our Boltzmann equations? In the presence of a mag. field…

Including Quantum Effects

where the source term is The anomaly violates the conservation of chiral charge

April 7, 2017 Andrew Long

SLIDE 14

Semi-Classical Understanding

B E

E-field wants p align with qE B-field wants µ∼qS align with B good for both E & B good for both E & B (“quantum effects”) p p S

April 7, 2017 Andrew Long

SLIDE 15

Semi-Classical Understanding

B E

E-field wants p align with qE B-field wants µ∼qS align with B good for both E & B good for both E & B (“quantum effects”) p S p

April 7, 2017 Andrew Long

SLIDE 16

Diagrammatic Representation

E · B< 0 E · B> 0

April 7, 2017 Andrew Long

SLIDE 17

The Chiral Magnetic Effect

In a medium with a chiral asymmetry (nonzero net chiral charge) a magnetic field induces a current in electric charge. Also well-known, B-field wants µ∼qS align with B electric current

B

Ohm’s law chiral mag. effect

[Vilenkin, ’80 … Fukushima, Kharzeev, & Warringa, ’08]. April 7, 2017 Andrew Long

SLIDE 18

The Chiral Magnetic Effect

In a medium with a chiral asymmetry (nonzero net chiral charge) a magnetic field induces a current in electric charge. Also well-known, B-field wants µ∼qS align with B electric current

B

Ohm’s law chiral mag. effect

[Vilenkin, ’80 … Fukushima, Kharzeev, & Warringa, ’08]. April 7, 2017 Andrew Long

SLIDE 19

QED at Finite Density in a Magnetic Field

spin-flip reactions that violate chiral charge conservation, induced by the electron mass electron-positron annihilation via interactions with photons Source term is a pseudo-scalar. Arises in presence of a helical magnetic field. chiral magnetic effect tends to erase any chiral asymmetry.

Recent applications to early universe: Frohlich & Pedrini, ‘00; Boyarsky, Frohlich, & Ruchaiskiy, ‘12; Pavlovic, Leite, & Sigl, ‘16 April 7, 2017 Andrew Long

SLIDE 20

QED at Finite Density in a Magnetic Field

source washout

changing magnetic helicity wants to grow the chiral asymmetry spin-flip and CME want to washout the asymmetry

April 7, 2017 Andrew Long

SLIDE 21

Generation of Baryon- and Lepton-Number from Helical Hypermagnetic Field

April 7, 2017 Andrew Long

SLIDE 22

Quantum anomalies in the Standard Model relate topology of gauge fields to global charge non-conservation. The SU(2)L term arises from thermal fluctuations of the SU(2)L gauge fields (EW sphaleron), and it plays a key role in many models of baryogenesis. The EW sphaleron (along with the Yukawa interactions) tend to wash out the baryon-number.

Kuzmin, Rubakov, Shaposhnikov (1985)

SU(2)L gauge field U(1)Y gauge field baryon & lepton number

˙ nB = ˙ nL = −Γw.o.

• nB + nL
• April 7, 2017

Andrew Long

W f W > 0 SM Global Anomalies - Sphaleron

‘t Hooft (1976)

¯ bR ¯ cR ¯ tR ¯ dR ¯ sR ¯ uR eL µLτL uL cL tL

SLIDE 23

Quantum anomalies in the Standard Model relate topology of gauge fields to global charge non-conservation. The U(1)Y source term arises from changing magnetic helicity Helicity decays because of ohmic losses SU(2)L gauge field U(1)Y gauge field baryon & lepton number

SM Global Anomalies – Helicity

April 7, 2017

hYµν ˜ Y µνi = 4hBY · r ⇥ BY i/σY

b/c EY = jY /σY ≈ r × BY /σY

• σY ∼ 100T
• Andrew Long

‘t Hooft (1976)

Y e Y > 0

eL , µL , τL × y2

L

uL , cL , tL × y2

Q

dL , sL , bL × y2

Q

eR , µR , τR × y2

eR

uR , cR , tR × y2

uR

dR , sR , bR × y2

dR

νeL , νµL , ντL × y2

L

SLIDE 24

B-generation from decaying hyper-magnetic helicity

April 7, 2017

Seminal work connecting hyper-PMF & BAU: Joyce & Shaposhnikov (1997), Giovannini & Shaposhnikov (1997), Giovannini (1999) Applications to Baryogenesis: Semikoz, Sokoloff, Dvornikov, Valle, Smirnov (2003…); Bamba (2004); Bamba, Geng, & Ho (2009); AL, Sabancilar, & Vachaspati (2014); Zadeh & Gousheh (2016); Fujita & Kamada (2016) Focus on EW crossover: Kamada & AL (2016a, 2016b)

Andrew Long

SLIDE 25

What do we calculate?

(1) Derive a system of kinetic equations, which govern the evolution of the various SM particle-number asymmetries (including baryon-number). (2) Assume a helical B-field as initial condition. (E.g., arises in axion inflation) (3) MHD evolution of B-field leads to inverse cascade scaling behavior. (4) Solve kinetic equations and read off relic baryon asymmetry.

Garretson, Field, & Carroll (1992)

schematically:

hB · r ⇥ Bi ⇡ ±Bp(t)2/λB(t) Bp(t) =

• a/a0

−2 τ/τrec −1/3B0 λB(t) =

• a/a0
• τ/τrec

2/3λ0

schematically:

˙ nB = Γw.o.nB + αY hB · r ⇥ Bi/σY nB(t) ≈ α2

Y Bp(t)2 /

• λB(t)σY (t)Γw.o.(t)
• Frisch, Pouquet, Leorat, Mazure, 75,76

Banerjee & Jedamzik, 2004 Campenelli, 2007 Kahniashvilli et. al. 2013

April 7, 2017 Andrew Long

SLIDE 26

dηui

L

dx = −Si

udw − Ng

X

j=1

⇣ Sij

uhu + Sij uu + Sij uhd

⌘ − Ss,sph − Nc 2 Sw,sph + ⇣ Ncy2

QLSbkg y

+ Nc 2 Sbkg

w

+ Nc yQL 2 Sbkg

yw

⌘ dηdi

L

dx = Si

udw − Ng

X

j=1

⇣ Sij

dhd + Sij dd + Sij dhu

⌘ − Ss,sph − Nc 2 Sw,sph + ⇣ Ncy2

QLSbkg y

+ Nc 2 Sbkg

w

− Nc yQL 2 Sbkg

yw

⌘ dηνi

L

dx = −Si

νew − Ng

X

j=1

Sij

νhe − 1

2Sw,sph + ⇣ y2

LLSbkg y

+ 1 2Sbkg

w

+ yLL 2 Sbkg

yw

⌘ dηei

L

dx = Si

νew − Ng

X

j=1

⇣ Sij

ehe + Sij ee

⌘ − 1 2Sw,sph + ⇣ y2

LLSbkg y

+ 1 2Sbkg

w

− yLL 2 Sbkg

yw

⌘ dηui

R

dx =

Ng

X

j=1

⇣ Sji

uhu + Sji uu + Sji dhu

⌘ + Ss,sph − Ncy2

uRSbkg y

dηdi

R

dx =

Ng

X

j=1

⇣ Sji

dhd + Sji dd + Sji uhd

⌘ + Ss,sph − Ncy2

dRSbkg y

dηei

R

dx =

Ng

X

j=1

⇣ Sji

ehe + Sji ee + Sji νhe

⌘ − y2

eRSbkg y

dηφ+ dx = − ⇣ Shhw + Shw ⌘ +

Ng

X

i,j=1

⇣ −Sij

dhu + Sij uhd + Sij νhe

⌘ dηφ0 dx = Shhw − Sh +

Ng

X

i,j=1

⇣ −Sij

uhu + Sij dhd + Sij ehe

⌘ dηW + dx = ⇣ Shhw + Shw ⌘ +

Ng

X

i=1

⇣ Si

udw + Si νew

⌘ .

Standard Model Boltzmann Equations w/ Anomalous Sources

Si

udw ≡ γi udw

ηui

L

kui

L

− ηdi

L

kdi

L

− ηW + kW + ! Si

νew ≡ γi νew

ηνi

L

kνi

L

− ηei

L

kei

L

− ηW + kW + ! Shhw ≡ γhhw ✓ηφ+ kφ+ − ηφ0 kφ0 − ηW + kW + ◆ Ss,sph ≡ γs,sph

Ng

X

i=1

ηui

L

kui

L

+ ηdi

L

kdi

L

− ηui

R

kui

R

− ηdi

R

kdi

R

! , Sw,sph ≡ γw,sph

Ng

X

i=1

Nc 2 ηui

L

kui

L

+ Nc 2 ηdi

L

kdi

L

+ 1 2 ηνi

L

kνi

L

+ 1 2 ηei

L

kei

L

! Sij

uu ≡ γij uu

⇣ηui

L

kui

L

− ηuj

R

kuj

R

⌘ , Sij

dd ≡ γij dd

⇣ηdi

L

kdi

L

− ηdj

R

kdj

R

⌘ , Sij

ee ≡ γij ee

⇣ηei

L

kei

L

− ηej

R

kej

R

⌘ , Shw ≡ γhw ✓ηφ+ kφ+ − ηW + kW + ◆ Sh ≡ γh ηφ0 kφ0 .

Sij

dhu ≡ γij dhu

2 ⇣ηdi

L

kdi

L

+ ηφ+ kφ+ − ηuj

R

kuj

R

⌘ , Sij

uhu ≡ γij uhu

2 ⇣ηui

L

kui

L

+ ηφ0 kφ0 − ηuj

R

kuj

R

⌘ , Sij

uhd ≡ γij uhd

2 ⇣ηui

L

kui

L

− ηφ+ kφ+ − ηdj

R

kdj

R

⌘ , Sij

dhd ≡ γij dhd

2 ⇣ηdi

L

kdi

L

− ηφ0 kφ0 − ηdj

R

kdj

R

⌘ , Sij

νhe ≡ γij νhe

2 ⇣ηνi

L

kνi

L

− ηφ+ kφ+ − ηej

R

kej

R

⌘ , Sij

ehe ≡ γij ehe

2 ⇣ηei

L

kei

L

− ηφ0 kφ0 − ηej

R

kej

R

⌘ ,

Sbkg

y

= 1 sT ↵y 4⇡ 1 2✏µνρσhYµνihYρσi Sbkg

w

= 1 sT 1 2 ↵w 4⇡ 1 2✏µνρσhW a

µνihW a ρσi

Sbkg

yw = 1

sT gg0/4⇡ 4⇡ ✏µνρσhYµνihW 3

ρσi .

Related work: Giovannini & Shaposhnikov; Fujita & Kamada; AL, Sabancilar, & Vachaspati; Semikoz, Dvornikov, Smirnov, Sokoloff, Valle April 7, 2017 Andrew Long

SLIDE 27

The source term appears in the kinetic equations as and it is equal to Now using Ohm’s law and the chiral magnetic effect current, The source takes the form

April 7, 2017

U(1)Y source term

Sbkg

y

= 1 sT αy 4π

• −4EY · BY
• jY = σY EY + 2

π αy µ5,Y BY Sbkg

y

= ⇣ − 1 sT αy π BY · r × BY σY ⌘ + ⇣ 12 T 3 α2

y

π2 |BY |2 σY ⌘ η5,Y dηa dx ⊃ χa ga y2

a Sbkg y

changing U(1)Y helicity sources a chiral asymmetry

ηa = asymmetry = (na − n¯

a)/s

χa = chirality = ±1 ga = color factor = 1, 3 ya = hypercharge

Vilenkin (1980); see also Boyarsky, Frohlich, & Ruchaiskiy (2015)

U(1)Y B-Hield tends to wash out a chiral asymmetry via CME

Andrew Long

SLIDE 28

η(eq)

B

⇡ # αy

sT

• BY · r ⇥ BY
• /σY

#|ye|2m2

h(T)/T 2 + # α2

y

T 3 |BY |2/σY

'

• 4 ⇥ 10−12B2

14

λ1

• T/Tw

4/3 0.08 m2

h(T)/T 2 + B2 14

• T/Tw

2/3

Evolution before EW crossover

• = /
• η = /

()

= - λ = - ↔ = = field strength & coherence length today April 7, 2017 equilibrium baryon asymmetry: nB / s source from decaying magnetic helicity washout due to sphaleron + Yukawa interactions + chiral magnetic effect we’ll discuss evolution through the EW crossover next

• B14 ≡ B0/(10−14 G) , λ1 ≡ λ0/(1 pc) , Tw ≡ 162 GeV
• Andrew Long

SLIDE 29

Let’s play with the parameters until we get ηB ~ 10-10 to match observed BAU

• = /
• η = /

()

= × - λ = × -

• = /
• η = /

()

= × - λ = × -

• = /
• η = /

()

= × - λ = × -

• = /
• η = /

()

= × - λ = × -

• = /
• η = /

()

= × - λ = ×

• = /
• η = /

()

= × - λ = ×

… while keeping

• - - - - - -
• ( )

η = / λ ( )

η ≃ (/) / ( γ↔ + γ + γ

)

↔ = = ↔ = = ↔ = = ↔ = =

Washout induced by chiral magnetic effect … prevents ηB from reaching 10-10 for large B0. This behavior was overlooked in some previous studies. The CME cannot be neglected!

April 7, 2017

η(eq)

B

⇡ # αy

sT

• BY · r ⇥ BY
• /σY

#|ye|2m2

h(T)/T 2 + # α2

y

T 3 |BY |2/σY

'

• 4 ⇥ 10−12B2

14

λ1

• T/Tw

4/3 0.08 m2

h(T)/T 2 + B2 14

• T/Tw

2/3

Andrew Long

SLIDE 30

April 7, 2017

How do the B-number and helical magnetic field evolve through the electroweak crossover?

based on 1606.08891 & 1610.03074 (PRD) with Kohei Kamada

Andrew Long

SLIDE 31

Evolution through EW Crossover

April 7, 2017

At this time… … the source shuts off, because the U(1)Y field is converted into a U(1)em field, which does not source B-number. … the washout shuts off, because the W-boson mass grows, suppressing EW sphaleron transitions.

Γsph. ∝ exp h −# MW (T)/αW i ∂jB ⇠ W ˜ W Y ˜ Y 6= F ˜ F

Andrew Long

SLIDE 32

Evolution through EW Crossover

increasing time, decreasing temperature baryon asymmetry turn on helical B-Hield washout processes come into equilibrium, & suppress the baryon asymmetry at the EW crossover, both the source & washout processes go out of equilibrium

Source & washout shut

• ff simultaneously

(Fujita & Kamada, 2016) Source remains active after washout shuts off (Kamada & Long, 2016b) Washout remains active after source has shut off (Kamada & Long, 2016a)

April 7, 2017 Andrew Long

SLIDE 33

April 7, 2017 Andrew Long

Sphaleron at EW Crossover

130 140 150 160 170 T / GeV

• 45
• 40
• 35
• 30
• 25
• 20
• 15
• 10

log Γ/Τ

4

standard multicanonical fit perturbative pure gauge log[αH(T)/T]

D’Onofrio, Rummukainen, & Tranberg (2014) Both numerical lattice calculations and perturbative analytic calculations agree that the EW sphaleron “shuts

• ff” (goes out of equilibrium) at

T~(130-135) GeV.

SLIDE 34

We use the Z-gamma mixing as a proxy for BY à Bem conversion.

U(1)Y to U(1)em conversion

θW(t)

BY Bem BZ

BW 3

BA

April 7, 2017 Andrew Long

V = 1 2 W 3 Y ✓ m2

W (T)

m2

Y W (T)

m2

Y W (T)

m2

Y (T)

◆ ✓ W 3 Y ◆ m2

W (T) = #g4T 2 + 1

4g2v(T)2 m2

Y (T) = 1

4g02v(T)2 m2

Y W (T) = −1

4gg0v(T)2

magnetic mass

tan 2θW (T) = − 2m2

Y W (T)

m2

W (T) − m2 Y (T)

This approach assumes adiabatic evolution. Better to solve for B-field evolution directly.

SLIDE 35

SM Mixing Angle through Crossover

• [ ]

θ

= Δ = = Δ = = Δ = = Δ = = Δ =

• April 7, 2017

dots & error bars = lattice simulation from D’Onofrio & Rummukainen (2015). black dashed = analytic approx. from Kajantie, Laine, Rummukainen, & Shaposhnikov (1996) … see below colored curves = we use tanh functions to model the crossover

Andrew Long

Evolution of the weak mixing angle at the SM crossover is poorly understood! The analytic calculation evaluates 1-loop residue of 1/k2 pole in <BiBj>

cos2 θW (high T) = 1 − z 48π√y

• z = g02

3 /g2 3 , y = m2 3/g4 3

• cos2 θW (low T) = cos2 θW

⇣ 1 + 11 12 g2

3 sin2 θW

πmW ⌘

SLIDE 36

Model the U(1)Y to U(1)em conversion

April 7, 2017

hW 1

µ(x)i = hW 2 µ(x)i = 0

hW 3

µ(x)i = sin ✓W(t) Aµ(x)

hYµ(x)i = cos ✓W(t) Aµ(x)

Andrew Long

Sbkg

w

= 1 2 ⇣ 1 sT 1 16π2 ⌘ g2 hW a

µνihf

W aµνi Sbkg

y

= ⇣ 1 sT 1 16π2 ⌘ g02 hYµνihe Y µνi Sbkg

yw = 2

⇣ 1 sT 1 16π2 ⌘ gg0 hYµνihf W 3µνi

Sbkg

w

= 1 2 ⇣ 1 sT 1 16π2 ⌘ g2⇣ sin2 θW(t)Aµν ˜ Aµν + 2dθW dt sin 2θW(t)δ0

µAν ˜

Aµν ⌘ Sbkg

y

= ⇣ 1 sT 1 16π2 ⌘ g02⇣ cos2 θW(t)Aµν ˜ Aµν − 2dθW dt sin 2θW(t)δ0

µAν ˜

Aµν ⌘ Sbkg

yw = 2

⇣ 1 sT 1 16π2 ⌘ gg0⇣ sin θW(t) cos θW(t)Aµν ˜ Aµν + 2dθW dt cos 2θW(t)δ0

µAν ˜

Aµν ⌘

AA · BA −4EA · BA

SLIDE 37

BAU Evolution through EW Crossover

E D C B A

• /

η = / ()

= - λ = -

pessimistic regime … washout active after source shuts off realistic regime … source active after washout shuts off April 7, 2017

ηeq

B ≈ 11

37 g02 cos2 θw SBdB +

dθw d ln x sin 2θw SAB

• 1

2

• γ11

ehe + γ11 νhe

• + γ11

ee + g04 cos4 θwγCME

B · r ⇥ B A · B

Andrew Long

SLIDE 38

Relic Baryon-Number

E C D B A

• ( )

η = / λ ( )

η ≃ - = Δ = = Δ = = Δ = = Δ = = Δ =

April 7, 2017

The conversion of U(1)Y B-field into U(1)em B-field at the EW crossover is not well-understood. However, the relic baryon asymmetry depends sensitively

• n these details.

Consequently, the predicted baryon asymmetry is very uncertain. Need to understand the crossover better!

Andrew Long

SLIDE 39

April 7, 2017 Andrew Long

Recall that (B-L) = 0 at all times! But, Kuzmin, Rubakov, & Shaposhnikov (‘85) taught us that B à 0 and L à 0 in equilibrium. How is washout avoided? The helical U(1)Y field sources B-number and shifts the equilibrium point away from B=L=0. The helical U(1)em field does not source B-number, but it does source axial fermion-

• number. (This is just the ABJ anomaly of QED, extended to the full SM fermion

content.) This source shifts the equilibrium point away from BL = BR = 0.

(toy model)

Baryogenesis without (B-L)?

∂jB ∼ W ˜ W − Y ˜ Y ⇒ ˙ nB ∼ −Γsph.nB + SY ⇒ n(eq)

B

∼ SY /Γsph. n(eq)

BL = 0

n(eq)

BR = Sem/Γflip

˙ nBL = Γflip

• nBR − nBL
• − Sem − Γsph.nBL

˙ nBR = Γflip

• nBR − nBL
• + Sem

SLIDE 40

Probes of IGMF

• - - -
• λ ( )

( )

• η=

halo morphology measurements could inform IGMF helicity CMB

• bservations

cannot push much farther Primordial B- field lives on dashed line This is for the “pessimistic” case … BAU much larger for “realistic” model Predicted by axion inflation magnetogenesis

April 7, 2017 Andrew Long

SLIDE 41

April 7, 2017 Andrew Long

Lots of directions for future work!

(1) How can we improve the calculation of θW(T) and thereby reduce the uncertainty in the BAU prediction for the SM crossover? (2) How good is the adiabatic approximation? That is, can we model the BY to Bem conversion using θW( T ) ? ( 3 ) How does the BAU prediction change if the EWPT is first order? (4) How can we extend the calculation to a general B-field spectrum, rather than reducing to just Bp and λB? (5) How can we include back-reaction of BAU growth on B-field evolution? Important if BAU grows to O(1).

SLIDE 42

“Ordinary Matter” also matters

I have discussed how the matter / anti-matter asymmetry may have arisen from a primordial (hyper-)magnetic field at temperatures T > 100 GeV in the early universe. A few interesting features to emphasize: ① No (B-L)-violation is required even though T > 100 GeV. ② No BSM physics is required (except for generating the initial B-field). ③ Thus, some amount of helical-PMFàBAU conversion is inevitable! Predicted BAU depends sensitively on the conversion of U(1)Y to U(1)em field at the EW crossover. Needs to be studied (analytically & lattice) more carefully. How can we search for the relic, helical IGMF? ① CMB observations access B0 > nG, but struggle to probe weaker fields. ② Blazar observations probe weak fields (>10-16 G), but helicity information is likely

• nly accessible for large coherence length (>100 Mpc). Not expected for PMF.

③ Something new?

April 7, 2017 Andrew Long