Baryo/Leptogenesis from Axion In fm ation Kyohei Mukaida Desy, - - PowerPoint PPT Presentation

baryo leptogenesis from axion in fm ation
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Baryo/Leptogenesis from Axion In fm ation Kyohei Mukaida Desy, - - PowerPoint PPT Presentation

Baryo/Leptogenesis from Axion In fm ation Kyohei Mukaida Desy, Hamburg CERN Based on 1905.13318 , 20xx.xxxxx , 1806.08769, 1812.08021, 1910.01205 Collaboration with Y. Ema, V. Domcke, B. von Harling, K.Kamada, E. Morgante, R. Sato, K.


slide-1
SLIDE 1

Baryo/Leptogenesis from Axion Infmation

Kyohei Mukaida

Kyohei Mukaida

Desy, Hamburg → CERN Based on 1905.13318, 20xx.xxxxx, 1806.08769, 1812.08021, 1910.01205 Collaboration with

  • Y. Ema,
  • V. Domcke, B. von Harling, K.Kamada, E. Morgante,
  • R. Sato, K. Schmitz, M.Yamada
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SLIDE 2

Introduction

1.

slide-3
SLIDE 3

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Introduction

3

Cosmic Inflation v.s. Baryon Asymmetry

  • Inflation: accelerated expansion of Universe
  • Solve horizon/flatness problems + Provide density perturbations.
  • Dilute unwanted relics, but also SM particles such as baryons.
  • Baryogenesis: production of baryon asymmetry after inflation.
  • Baryon to photon ratio (BBN) →

➡ Baryogenesis from Inflation?

Inflaton SM particles

  • Reheating requires couplings btw inflaton and the SM particles.

Baryogenesis ?

φ

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η = nB nγ ' 6£10°10

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slide-4
SLIDE 4

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

  • Flat potential protected by the shift sym.

Introduction

Inflaton w/ Chern-Simons coupling

4

  • Flat potential v.s. Coupling to radiation

φ 7! φ+c

  • Reheating via the Chern-Simons coupling

S = Z d4x Ωp°g ∑g µν 2 ∂µφ∂νφ°V (φ) ∏ ° 1 4FµνF µν + φ 4ΛFµν ˜ F µν æ

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slide-5
SLIDE 5

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Introduction

5

  • Flat potential v.s. Coupling to radiation

❖ Helical-gauge field production during inflation: .

  • Reheating via the Chern-Simons coupling

Inflaton w/ Chern-Simons coupling

  • Flat potential protected by the shift sym. φ 7! φ+c

where

Horizon

0 = h ∂2

η +k(k ±2ξaH)

i A±(η,k)

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0 6= ≠ Fµν ˜ F µνÆ = °4hE ·Bi

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˙ φ 6= 0

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E

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➡ (Pre)Reheating, chiral GWs, baryogenesis, magnetogenesis,…

W.Garretson+ 9209238, M.Anber, L.Sorbo 0606534,…

B

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S = Z d4x Ωp°g ∑g µν 2 ∂µφ∂νφ°V (φ) ∏ ° 1 4FµνF µν + φ 4ΛFµν ˜ F µν æ

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ξ ≡ ˙ φ 2ΛH

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slide-6
SLIDE 6

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Inflaton w/ Chern-Simons coupling to U(1)Y

6

0 = h ∂2

η +k(k ±2ξaH)

i AY,±(η,k)

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where

0 6= ≠ Yµν ˜ Y µνÆ = °4hEY ·BY i

<latexit sha1_base64="QFMCTWXkm8+mAdwI3WlRn6ECKDc=">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</latexit>

❖ Helical-gauge field production during inflation.

Helical gauge & Chiral fermion

U(1)Y SM particles charged under U(1)Y

Horizon

EY

<latexit sha1_base64="Zx5WHFh9Xt0peEMa6zK0rn5a8=">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</latexit>

BY

<latexit sha1_base64="eNORLH9Xx93TsL6LPSPgfBklGH0=">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</latexit>

ξ ≡ ˙ φ 2ΛH

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S = Z d4x Ωp°g ∑g µν 2 ∂µφ∂νφ°V (φ) ∏ ° 1 4YµνY µν + φ 4ΛYµν ˜ Y µν + X

α

ψ†

ασ·(i∂° gY QαAY )ψα +···

æ

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slide-7
SLIDE 7

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 7

6= 0

0 = h ∂2

η +k(k ±2ξaH)

i AY,±(η,k)

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Horizon

0 6= ≠ Yµν ˜ Y µνÆ = °4hEY ·BY i

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∂µJµ

B+L =

3 16π2 ≥ g 2

2W a µν ˜

W aµν − g 2

Y Yµν ˜

Y µν¥

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❖ Helical-gauge field production during inflation.

Helical gauge & Chiral fermion

EY

<latexit sha1_base64="Zx5WHFh9Xt0peEMa6zK0rn5a8=">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</latexit>

BY

<latexit sha1_base64="eNORLH9Xx93TsL6LPSPgfBklGH0=">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</latexit>

∆qB+L > 0

<latexit sha1_base64="vxk9N9nQRgtpNLQwFShQC/iRw=">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</latexit>

Inflaton w/ Chern-Simons coupling to U(1)Y

❖ B+L generation during inflation!

U(1)Y SM particles charged under U(1)Y

S = Z d4x Ωp°g ∑g µν 2 ∂µφ∂νφ°V (φ) ∏ ° 1 4YµνY µν + φ 4ΛYµν ˜ Y µν + X

α

ψ†

ασ·(i∂° gY QαAY )ψα +···

æ

<latexit sha1_base64="+wh2/hy8CZqwoJ8a+aIeL7W4als=">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</latexit>

where

ξ ≡ ˙ φ 2ΛH

<latexit sha1_base64="qk2cqJqkmA7x4lG/v2za9Ji/k0M=">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</latexit>
slide-8
SLIDE 8

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Our Idea

8

Baryogenesis from B+L asymmetry?

Time

TYe ∼ 105 GeV

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Inflation

∂µJµ

B = ∂µJµ L =

3 32π2 ≥ g 2

2W a µν ˜

W aµν − g 2

Y Yµν ˜

Y µν¥

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TEW ∼ 102 GeV

<latexit sha1_base64="S7MiOKh0XeG9yh5MkPJXT2zCIFg=">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</latexit>
slide-9
SLIDE 9

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Our Idea

9

Baryogenesis from B+L asymmetry?

Time

TYe ∼ 105 GeV

<latexit sha1_base64="5LMXV2chYjtMysacNlnYZYo6EaI=">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</latexit>

Inflation

−3 4 αY π ∆hY

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∂µJµ

B = ∂µJµ L =

3 32π2 ≥ g 2

2W a µν ˜

W aµν − g 2

Y Yµν ˜

Y µν¥

<latexit sha1_base64="hvQxPJXzW71SoY8QSfx0ZAEjkGM=">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</latexit>

3∂µK µ

CS

<latexit sha1_base64="G+6n8j4DEgMjzfy3Hr1cHEO19Is=">AE3ichVNaxNRFL2po9b40VQ3gpvRENFNeJNGmrqQjdCEdrGtIWmDjOTl2bofDEzia3DrAsuxJ1IVwouRNzqD3DjXlz0J4jLCm5ceN7LhFowkxcyc9+5957rvzMCxo5ixo8LUGeXsufPTF4oXL12+MlOavboe+f3Q4i3Ld/xw0zQi7tgeb8V27PDNIOSGazp8w9xdEv6NAQ8j2/cex/sB3aNHc/u2pYRA9JLN+fagRHGtuHoSdvtp+qy3o75XpwsNdMnANSiXiqzqta4x+oNFcZCbY7VYNTmaxoMrcrkKlO2VvzZwjdqU4d8sqhPLnHyKIbtkERflukEaMA2DYlwEJYtvRzSqmI2D5YHAwD6C6eO9htZaiHvcgZyWgLVRz8Q0SqVGHf2Xt2zL6yD+wH+zM2VyJzC37eJvDWB7oM8+vN39PjHLxjql3EpUTYKd31NMXWrIXmz0FkhEdGkN8w+evTpu3l+rJLfZW/YT/b1hR+wLOvQGv6x3q3ztENkrufl9oDYQUWOkvSNP0AbLy9GXQJsPTwgml2c8nhl8+1h18mYHuynckaurOzBkwAfAB+AI74EoUoFJqbfhba2zOMhq0BUeMtgpZITSsU9yQpPsfLrPYJaB5wEli4RcZ7eCa0Ij3phAwB6n/KD7Re2esxrsTchr4OqL/5hyekLgX4/sfMfJrdOQshDWafAgrkWiKmz26vup4Y71W1erVhdV6efFBdsen6QbdQucazdMiPcQZtlD7gD7SJ/qsGMqB8kJ5OaROFbKYa3RqKa/ApQiDbU=</latexit>

Inefficient

TEW ∼ 102 GeV

<latexit sha1_base64="S7MiOKh0XeG9yh5MkPJXT2zCIFg=">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</latexit>

−3αY 4π ∂µhµ

Y

<latexit sha1_base64="L+nv2yrXd/n+yB6YVvRThKtpBqE=">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</latexit>

−3 4 αY π ∆hY

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slide-10
SLIDE 10

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Our Idea

10

Baryogenesis from B+L asymmetry?

Time

TYe ∼ 105 GeV

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Inflation

−3 4 αY π ∆hY

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−3 4 αY π ∆hY

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Inefficient diffusion No CPI (chiral plasma instability) Inefficient

TEW ∼ 102 GeV

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via Sphaleron + Yukawa

∂µJµ

B = ∂µJµ L =

3 32π2 ≥ g 2

2W a µν ˜

W aµν − g 2

Y Yµν ˜

Y µν¥

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3∂µK µ

CS

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−3αY 4π ∂µhµ

Y

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−3 4 αY π ∆hY

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3 4 αY π ∆hY

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slide-11
SLIDE 11

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Our Idea

11

Baryogenesis from B+L asymmetry?

Time

TYe ∼ 105 GeV

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TEW ∼ 102 GeV

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Inflation

−3 4 αY π ∆hY

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−3 4 αY π ∆hY

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Inefficient via Sphaleron + Yukawa ⊿ hY is converted to U(1)em

∂µJµ

B = ∂µJµ L =

3 32π2 ≥ g 2

2W a µν ˜

W aµν − g 2

Y Yµν ˜

Y µν¥

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3∂µK µ

CS

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−3αY 4π ∂µhµ

Y

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−3 4 αY π ∆hY

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3 4 αY π ∆hY

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3 4 αY π ∆hY

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3 4 αY π ∆hY

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Inefficient diffusion No CPI (chiral plasma instability)

slide-12
SLIDE 12

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Our Idea

12

Baryogenesis from B+L asymmetry?

Time

TYe ∼ 105 GeV

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TEW ∼ 102 GeV

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Inflation

−3 4 αY π ∆hY

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3 4 αY π ∆hY

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−3 4 αY π ∆hY

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≤× 3 4 ÆY º ∆hY

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Inefficient Sphaleron freezes out via Sphaleron + Yukawa ⊿ hY is converted to U(1)em

∂µJµ

B = ∂µJµ L =

3 32π2 ≥ g 2

2W a µν ˜

W aµν − g 2

Y Yµν ˜

Y µν¥

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3∂µK µ

CS

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−3αY 4π ∂µhµ

Y

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−3 4 αY π ∆hY

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≤× 3 4 ÆY º ∆hY

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Inefficient diffusion No CPI (chiral plasma instability)

slide-13
SLIDE 13

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

4. 3. 2.

13

Baryogenesis from B+L asymmetry?

Time

TYe ∼ 105 GeV

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TEW ∼ 102 GeV

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Inflation

−3 4 αY π ∆hY

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3 4 αY π ∆hY

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−3 4 αY π ∆hY

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Inefficient diffusion No CPI (chiral plasma instability)

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≤× 3 4 ÆY º ∆hY

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Inefficient via Sphaleron + Yukawa ⊿ hY is converted to U(1)em Sphaleron freezes out

Outline of this Talk

∂µJµ

B = ∂µJµ L =

3 32π2 ≥ g 2

2W a µν ˜

W aµν − g 2

Y Yµν ˜

Y µν¥

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3∂µK µ

CS

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−3αY 4π ∂µhµ

Y

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−3 4 αY π ∆hY

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≤× 3 4 ÆY º ∆hY

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K.Kamada’s talk @ PPP2019

slide-14
SLIDE 14

Production of

Helical gauge & Chiral fermion

2.

slide-15
SLIDE 15

Kyohei Mukaida / 1905.13318, 20xx.xxxxx Right-handed

Fermion Production

Landau Levels

15 Energy Pz Left-handed

  • Turn off EY; BY field modifies the dispersion relation.

Horizon

v ×BY

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BY

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  • Landau level n : transverse motion
  • Pz : parallel motion
slide-16
SLIDE 16

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Fermion Production

Lowest Landau Level (n=0) & Chiral Anomaly

16

  • Turn on EY and see what happens.

Nielsen, Ninomiya, Phys.Lett.130B (1983)

Right-handed Energy Pz Left-handed

slide-17
SLIDE 17

Kyohei Mukaida / 1905.13318, 20xx.xxxxx Right-handed Energy Pz Left-handed

Fermion Production

Lowest Landau Level (n=0) & Chiral Anomaly

17

Nielsen, Ninomiya, Phys.Lett.130B (1983)

  • Turn on EY and see what happens.

EY

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EY

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slide-18
SLIDE 18

Kyohei Mukaida / 1905.13318, 20xx.xxxxx Anti-particle production Particle production Right-handed Energy Pz Left-handed

Fermion Production

Lowest Landau Level (n=0) & Chiral Anomaly

18

Nielsen, Ninomiya, Phys.Lett.130B (1983)

  • Turn on EY and see what happens.

EY

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EY

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➡ Reproduce chiral anomaly!

˙ qα = ˙ nα − ˙ ¯ nα = εαNα g 2

Y Q 2 α

4π2 EY BY = −εαNα g 2

Y Q 2 α

16π2 Y µν ˜ Yµν

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w/ εα = ± for R/L, Nα = dof

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slide-19
SLIDE 19

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

  • Turn on EY and see what happens.

Right-handed Energy Pz Left-handed

Fermion Production

19

Higher Landau Levels (n≧1) & Pair Production

e.g., V.Domcke and KM 1806.08769

slide-20
SLIDE 20

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

  • Turn on EY and see what happens.

Right-handed Energy Pz Left-handed

Fermion Production

20

Higher Landau Levels (n≧1) & Pair Production

Tunneling Tunneling

➡ Pair-production via Schwinger effect

˙ n(n)

α = ˙

¯ n(n)

α = Nα

g 2

Y Q 2 α

4π2 EY BY e −

2πnBY EY <latexit sha1_base64="irhQGJ9iZjHsfp/3zfGLwfr08yc=">AEaXichVPLbtNAFL1uA5TwaEI3FQ9pRFTULojGJqgpUqUKhMQKNS3pQ3Vi+TFJrDpjy3aCyshrJH6ABSuQWCA+gw0/wKfgCpWRWLDgjsTRxWIpBM5vnPuefOmRk7UeAnKaXH2sxs4cLFS3OXi1euXrs+Xyrf2EnCQeyphsGYbzn2AkLfM6aqZ8GbC+Kmd13ArbrHD6R+d0hixM/5C/So4i1+naX+x3ftVOErNJr0wtTwi1h2kHUs7O2WOYrGVknEhemY8eEZ/9mSXG9+NwaYcTsxLYrutZ+2yCNHGwbmagRM/IxIE+tfIYH9YW93O2IXOESzgTmM8yq1ShVb3+kNbqBIM14wE1MDBWDR0DvUrVqEA+NsOyxsAED0JwYQB9YMAhxTgAGxL8HYAOFCLEWiAQizHyVZ5BkWsHSCLIcNG9BD/uzg7yFGOc6mZqGoXuwT4xFhJYIl+o5/oKf1KP9Pv9PdELaE05FqO8O2Malkzb9Z3P51blUf3yn0zqmVDjInu4phQ7UlRcfvUKkS7dkf7w1dvT7UdbS+Ie/UBP0N97eky/oEM+/Ol+bLCtd+eoh4j6iMgO45V7av98ZPEpqxOIjc6shzNPMSWX4+yl2vm+UuSYE4hHeApST5vSyHyRDvYcRmdCKgLj2ZyJO9e5hZyftP0rRxB5P/apowxEjenUnaZ4zpPTzlTUbj/YkxEgqVt398xcnkYMeo6rXqWqNW2ajn38Ec3IK76FyHVdiAZ7AJTez9Q1vQbmt3Zk8K5cJi4eaIOqPlNQvw1yhU/gCs0QI7</latexit>
  • Never contribute to asymmetries!

e.g., V.Domcke and KM 1806.08769

slide-21
SLIDE 21

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

  • Turn on EY and see what happens.

Right-handed Energy Pz Left-handed

Fermion Production

21

Higher Landau Levels (n≧1) & Pair Production

Tunneling Tunneling

➡ Pair-production via Schwinger effect

˙ n(n)

α = ˙

¯ n(n)

α = Nα

g 2

Y Q 2 α

4π2 EY BY e −

2πnBY EY <latexit sha1_base64="irhQGJ9iZjHsfp/3zfGLwfr08yc=">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</latexit>
  • Never contribute to asymmetries!

X

n=1

˙ n(n)

α = Nα

g 2

Y Q 2 α

4π2 EY BY 1 e

2πBY EY

− 1

<latexit sha1_base64="cqETesQ+bV+y5pw13xQH2VK8a8=">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</latexit>

e.g., V.Domcke and KM 1806.08769

slide-22
SLIDE 22

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

  • Turn on EY and see what happens.

Fermion Production in BY ∥ EY

Right-handed Energy Pz Left-handed

Fermion Production

22

EY

<latexit sha1_base64="4DBiH7hxvwLGrsjvFkELNv1iYDI=">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</latexit>

EY

<latexit sha1_base64="4DBiH7hxvwLGrsjvFkELNv1iYDI=">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</latexit>
  • Chiral anomaly from the lowest Landau level (n=0).
  • Pair production from higher Landau levels (n=1,2,…).

e.g., V.Domcke and KM 1806.08769

slide-23
SLIDE 23

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

  • Primordial generation of B+L asym.

23

  • Backreaction suppresses gauge field

Implications on Axion Inflation

  • /

w/o backreaction w/ backreaction

∆hrh

Y

a 3

rh

= − 2 3Hrh ⌦ ˆ

EY · ˆ BY

rh

<latexit sha1_base64="QpZXrWgCQZikUQd0FHTo4Gzvuek=">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</latexit>

where

∆q rh

B+L = −3

2 αY π ∆hrh

Y

<latexit sha1_base64="paiYZsFw8NHpx8WIdE1oL1Z91cE=">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</latexit>

0 = −∂t EY +r ×BY + a g 2

Y

4π2 ˙ φ fa

BY − gY JY

<latexit sha1_base64="B+dKtLgCeaR/LsO/cx8r0NUJ9ls=">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</latexit>

gY JY = a X

α

Nα g 3

Y |Qα|3

12π2 coth ✓ π ˆ BY ˆ EY ◆ ˆ BY H

  • EY
<latexit sha1_base64="1gMYi8f5wNTXIjPLvGCLXysFho4=">AEjXichVPLbtNAFL0uBkp5tIUNEpsRUVG7icZOqwYEqIAqKhaoaelLndQaO5PYql+ynaBi+Qf4ARasQGKB+hls+AEW/QTEskhsWHBnYlMhkXQsx2fOPfcuTMTO/a9NKP0RJu4oF+8dHnytTVa9dvTM/M3txOo37iC0n8qNk1+ap8L1QbGVe5ovdOBE8sH2xYx8+k/GdgUhSLwpfZUexaAe8F3pdz+EZUtbMc/aI8wO8hcFgkeE+aLbrZPWNoPLMb92OXkZQVYN+FOjikHDcK4neatMlIcNIrcMAmLvQOzIMyJMnfoNF8mYQwl2fkqbVX5AqtIiIs8XputlCp/irWqlBbLW8Vl2fN1GjdaC7RxSZBcN9sUBOBuWwaCIw6VaMG5ViPZjUBDoQgQN9CEBACBliHzik+OyDARi5NqQI5cg8lRcQAFTmNtHlUAFR/YQf3s42y/ZEOfSM1XZDlbx8U0wk8Ac/UY/01P6lR7T7/T3SK9ceci1HOHXHuaK2Jp+e3vz17lZAX4zcM+yxmTYqB7fUwZdaKpePOwtVozs0hn6D968O918sDGX36Mf6Q/s7wM9oV+w3Dw0/nUEhvz3GPkPWQkRWqlXfU/nmoCsesLkdueGYuzjpKbUhzl6rnQ+UY4ixHPkYT0H6yfNtK0aeaBcrzmMnOdSQlz0x1MnaLkYWyvqjPDnuYPpfTwYDRPLujPI+U4yv0VG9SVTtT4IoV2yBt7+64mQ02DbrRqNuthZrK4vl/2AS7sBd7NyAZViBNViHLXC0W1ZW9Ge6NP6kv5QfzyUTmhlzi34Z+jP/wDbw/+</latexit>

Helical gauge & Chiral fermion

ˆ E 2

Y

<latexit sha1_base64="t71bpowAQiwKpSRzeAXoHRuJQro=">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</latexit> ˆ

EY ˆ BY

<latexit sha1_base64="FMi/LV7x4oi8JpMwHv7hpO4Iy6E=">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</latexit>

ˆ B 2

Y

<latexit sha1_base64="75TyzQ14AzE7AJ8atIOa908dnhc=">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</latexit>

V.Domcke and KM 1806.08769

µrh

B+L

Trh ∼ 10−3 Å Hrh 1014 GeV ã 3

2 ✓〈 ˆ

EY · ˆ BY 〉rh/H 4

rh

105 ◆

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Horizon

EY

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BY

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∆qB+L > 0

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slide-24
SLIDE 24

3.

Survival of

Helical Gauge Field

slide-25
SLIDE 25

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

4. 3. 2.

25

Baryogenesis from B+L asymmetry?

Time

TYe ∼ 105 GeV

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TEW ∼ 102 GeV

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Inflation

−3 4 αY π ∆hY

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3 4 αY π ∆hY

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−3 4 αY π ∆hY

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Inefficient diffusion No CPI (chiral plasma instability)

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≤× 3 4 ÆY º ∆hY

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Inefficient via Sphaleron + Yukawa ⊿ hY is converted to U(1)em Sphaleron freezes out

Outline of this Talk

∂µJµ

B = ∂µJµ L =

3 32π2 ≥ g 2

2W a µν ˜

W aµν − g 2

Y Yµν ˜

Y µν¥

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3∂µK µ

CS

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−3αY 4π ∂µhµ

Y

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−3 4 αY π ∆hY

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≤× 3 4 ÆY º ∆hY

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K.Kamada’s talk @ PPP2019

slide-26
SLIDE 26

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 26

Avoid Chiral Plasma Instability

  • Survival of qe from Sphaleron +

Yukawa washout

Survival of Helical Gauge Field

V.Domcke, B.Harling, E.Morgante, KM 1905.13318

Sphaleron washout Electron Yukawa

qe

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qLe

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Electron Yukawa is NOT equilibrated till

T < TYe ∼ 105 GeV

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slide-27
SLIDE 27

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 27

Avoid Chiral Plasma Instability

  • Survival of qe from Sphaleron +

Yukawa washout

Survival of Helical Gauge Field

V.Domcke, B.Harling, E.Morgante, KM 1905.13318

Sphaleron washout Electron Yukawa

qe

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qLe

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˙ φ = 0

<latexit sha1_base64="nWUKo8U9046QKHvGQoTHhihTt8=">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</latexit>
  • Chiral Plasma Instability (CPI) as an inverse process

∂· Je = − g 2

Y

16π2 Yµν ˜ Y µν +(Yukawa)

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Inflation

˙ φhY

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Electron Yukawa is NOT equilibrated till

T < TYe ∼ 105 GeV

<latexit sha1_base64="uZVaeDMCrQfCzM2VvdXf8axixc=">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</latexit>
slide-28
SLIDE 28

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 28

Avoid Chiral Plasma Instability

  • Survival of qe from Sphaleron +

Yukawa washout

Survival of Helical Gauge Field

V.Domcke, B.Harling, E.Morgante, KM 1905.13318

Sphaleron washout Electron Yukawa

qe

<latexit sha1_base64="sWgkaJRaPQ/UQ1WCvtJuDJbQI=">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</latexit>

qLe

<latexit sha1_base64="0q5onRuGClWvSOhvIDoDA2y0TtA=">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</latexit>

˙ φ = 0

<latexit sha1_base64="nWUKo8U9046QKHvGQoTHhihTt8=">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</latexit>
  • Chiral Plasma Instability (CPI) as an inverse process

Inflation

−αY 2π ∆hY

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−αY 2π ∆hY

<latexit sha1_base64="CSRENEh+jdBD0mpVtwi/Z1TfFMU=">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</latexit>

˙ φhY

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∂· Je = − g 2

Y

16π2 Yµν ˜ Y µν +(Yukawa)

<latexit sha1_base64="4mJCdgFX8IwcRhKvA1IBhFdCrzA=">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</latexit>

−αY 2π ∂·hY

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Electron Yukawa is NOT equilibrated till

T < TYe ∼ 105 GeV

<latexit sha1_base64="uZVaeDMCrQfCzM2VvdXf8axixc=">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</latexit>
slide-29
SLIDE 29

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 29

Avoid Chiral Plasma Instability

  • Survival of qe from Sphaleron +

Yukawa washout

Survival of Helical Gauge Field

V.Domcke, B.Harling, E.Morgante, KM 1905.13318

Sphaleron washout Electron Yukawa Electron Yukawa is NOT equilibrated till

qe

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qLe

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˙ φ = 0

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Chiral Plasma Instability

TCPI ∼ 105GeV µ Hrh 1014GeV ∂3 √≠ ˆ

EY · ˆ BY

Æ

rh /H4 rh

105 !2

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  • Chiral Plasma Instability (CPI) as an inverse process

Inflation

−αY 2π ∆hY

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−αY 2π ∆hY

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˙ φhY

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T < TYe ∼ 105 GeV

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∂· Je = − g 2

Y

16π2 Yµν ˜ Y µν +(Yukawa)

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−αY 2π ∂·hY

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∂ηhY,k(η) = 2k σY µ kCPI rk(η) −k ∂ hY,k(η)

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kCPI = 2αY π 95 18µe, rk(η) = khY,k(η)/2 ρB,k(η)

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w/

Joyce, Shaposhnikov 9703005, Akamatsu, Yamamoto 1302.2125,…

slide-30
SLIDE 30

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 30

Avoid Chiral Plasma Instability

  • Survival of qe from Sphaleron +

Yukawa washout

Survival of Helical Gauge Field

V.Domcke, B.Harling, E.Morgante, KM 1905.13318

Sphaleron washout Electron Yukawa

qe

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qLe

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  • Chiral Plasma Instability (CPI) as an inverse process

∂· Je = − g 2

Y

16π2 Yµν ˜ Y µν +(Yukawa)

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Inflation

−αY 2π ∂·hY

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−αY 2π ∆hY

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−αY 2π ∆hY

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˙ φhY

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˙ φ = 0

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−αY 2π ∆hY

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Sphaleron + Yukawa

TCPI < TYe ∼ 105 GeV

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Chiral Plasma Instability

TCPI ∼ 105GeV µ Hrh 1014GeV ∂3 √≠ ˆ

EY · ˆ BY

Æ

rh /H4 rh

105 !2

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˙ qe = −αY 2π ˙ hY − 711 481ΓYe qe

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Electron Yukawa is NOT equilibrated till

T < TYe ∼ 105 GeV

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slide-31
SLIDE 31

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 31

  • Chiral Magneto Hydro Dynamics (ChMHD)

Avoid Magnetic Diffusion

∂BY ∂η = r2 σY

BY +r×(v ×BY )+ 2αY

π µY,5 σY

r×BY

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∂ ∂ηv +v ·rv = vr2v + 1 ρ +P µ −1 2rB2

Y +(BY ·r)BY

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µY,5 = X

Æ

≤ÆNÆQ2

Y,ƵÆ

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w/

Survival of Helical Gauge Field

V.Domcke, B.Harling, E.Morgante, KM 1905.13318

slide-32
SLIDE 32

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 32

  • Chiral Magneto Hydro Dynamics (ChMHD)

Avoid Magnetic Diffusion

∂BY ∂η = r2 σY

BY +r×(v ×BY )+ 2αY

π µY,5 σY

r×BY

<latexit sha1_base64="tZdOgrXM+0/obyMVm3cmoGsO4=">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</latexit>

∂ ∂ηv +v ·rv = vr2v + 1 ρ +P µ −1 2rB2

Y +(BY ·r)BY

<latexit sha1_base64="bm8pO8dyTRNJncXOq9jcjzvDRQ8=">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</latexit>

µY,5 = X

Æ

≤ÆNÆQ2

Y,ƵÆ

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w/ Chiral Plasma Instability Magnetic Diffusion

Survival of Helical Gauge Field

V.Domcke, B.Harling, E.Morgante, KM 1905.13318

Magnetic diffusion

Tdiff ∼ αY lnα−1

Y

5 Hrh

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−αY 2π ∆hY

<latexit sha1_base64="CSRENEh+jdBD0mpVtwi/Z1TfFMU=">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</latexit>
slide-33
SLIDE 33

Kyohei Mukaida / 1905.13318, 20xx.xxxxx Inverse cascade 33

  • Chiral Magneto Hydro Dynamics (ChMHD)

Avoid Magnetic Diffusion

∂BY ∂η = r2 σY

BY +r×(v ×BY )+ 2αY

π µY,5 σY

r×BY

<latexit sha1_base64="tZdOgrXM+0/obyMVm3cmoGsO4=">AFonichVNaxNBGH5Tjdb60VQvgpfFWGmphMm2pVEQil6kIPTDfki3htnNJBm6X+xuou2yf8A/4MGTgfxZ3jxLh569yIeK3jx4DOTDU2hSdk951nud53dmxw5dGSeMHRXGLlwsXro8fmXi6rXrNyZLUze34qATOWLTCdwg2rF5LFzpi81EJq7YCSPBPdsV2/b+U7W+3RVRLAP/RXIQij2Pt3zZlA5PANVLP61mxJ3UCnmUSO4alu2lT7J6+jLBkCR8OxzgTB8rnt8uxVaipWLFse14oB9dwAz7AS6YnYckUzmVF4tw8NCKxItrJ7Fwvi2lY3A3bvF+IhKX3usAe2AsnpH5dLoB73qpzCrV2iJbqBkIHprzERgLplVBNUK06NM+VgNpgrfyaIGBeRQhzwS5FOC2CVOMX67VCVGIbA9SoFiKReF5TRBLQdsAQYHOg+ni3MdnPUx1x5xlrtIuLfwSlQdPsB/vMjtk39oX9Yv+GeqXaQ9VygLfd04qwPvn29sbfc1Ue3gm1T1QjFDbYo3tKqEk13YtEb6FGVJdOz797+O549H6dHqfWS/0d8HdsS+okO/+8f5tCbW38N9eqR/AFQCUTn6tTf0Dkqw/BH1pagtwEoEptB7PJwZ5+fbxqyRM3Er/UZeTqzj5UeBd4Fxz1JaiqDGDq9JuozdI+PlwVYmC1DFamOZGuK1Z0SnW6HzPUa0LToqorhG1x2/wTGlVr2TnOITI5w9UfFLvzNAaZ8/x5Pg64jM9ezuk7sXw/vuM0Tka+ixU1D/5CFGqUXWz+9fXGB5smZXqfMVcWygv1/I7Pk536C46r9ISLdMz7OEmOYWVQlg4KBwW7xVXimvFjR51rJBrbtGpUbT+A0j0WRM=</latexit>

∂ ∂ηv +v ·rv = vr2v + 1 ρ +P µ −1 2rB2

Y +(BY ·r)BY

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µY,5 = X

Æ

≤ÆNÆQ2

Y,ƵÆ

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w/ Chiral Plasma Instability Magnetic Diffusion

Survival of Helical Gauge Field

V.Domcke, B.Harling, E.Morgante, KM 1905.13318

Magnetic diffusion

Tdiff ∼ αY lnα−1

Y

5 Hrh

<latexit sha1_base64="7cX27k0WPTM70+1TKzlLK1jrbD8=">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</latexit>
  • Inverse cascade: transfer from short to long wave length.
<latexit sha1_base64="sSLpsWgb2yduiAvzc09o/ORsNw=">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</latexit>

−αY 2π ∆hY

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Tic ∼ vrhTrh

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−αY 2π ∆hY

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Inverse cascade

  • Approximate conservation of hY.

Tic > Tdiff ↔ Rm ≡ σY Lrhvrh > 1

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i.e., Large magnetic Reynolds #

See e.g., R.Durrer, A.Neronov 1303.7121

slide-34
SLIDE 34

4.

Regeneration of

Baryon Asymmetry

slide-35
SLIDE 35

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

4. 3. 2.

35

Baryogenesis from B+L asymmetry?

Time

TYe ∼ 105 GeV

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TEW ∼ 102 GeV

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Inflation

−3 4 αY π ∆hY

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3 4 αY π ∆hY

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−3 4 αY π ∆hY

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Inefficient diffusion No CPI (chiral plasma instability)

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≤× 3 4 ÆY º ∆hY

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Inefficient via Sphaleron + Yukawa ⊿ hY is converted to U(1)em Sphaleron freezes out

Outline of this Talk

∂µJµ

B = ∂µJµ L =

3 32π2 ≥ g 2

2W a µν ˜

W aµν − g 2

Y Yµν ˜

Y µν¥

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3∂µK µ

CS

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−3αY 4π ∂µhµ

Y

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−3 4 αY π ∆hY

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≤× 3 4 ÆY º ∆hY

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K.Kamada’s talk @ PPP2019

✔ ✔

slide-36
SLIDE 36

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 36

  • Transport equation @ EW Crossover

Baryogenesis from Decaying Helicity

Regeneration of Baryon Asym.

  • Slowest processes: EW sphaleron & Decaying helicity

ΓW,sph ∝ e−

Msph(T ) T

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Msph(T ) ∝ v(T )

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{

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∂ηqB = −111 34 ΓW,sphqB + 3 2 ° g 2

2 + g 2 Y

¢ sin(2θ) ° ∂ηθ ¢ ∆hrh

Y

8π2

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  • T. Fujita, K.Kamada 1602.02109

K.Kamada, A.Long 1610.03074

slide-37
SLIDE 37

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 37

Baryogenesis from Decaying Helicity

Regeneration of Baryon Asym.

∝ ∂ηhY

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ΓW,sph ∝ e−

Msph(T ) T

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Msph(T ) ∝ v(T )

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{

<latexit sha1_base64="q/FeIm4a7rB9d+YbuTkWMi3dxUM=">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</latexit>

∂ηqB = −111 34 ΓW,sphqB + 3 2 ° g 2

2 + g 2 Y

¢ sin(2θ) ° ∂ηθ ¢ ∆hrh

Y

8π2

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hem

<latexit sha1_base64="DbCaQ5jEUuqGM6oM5QR84fLeyYg=">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</latexit>

hY

<latexit sha1_base64="/ZOKmpnBgBMYZa1PzQ+w5tNlEBI=">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</latexit>

E W c r

  • s

s

  • v

e r

  • T. Fujita, K.Kamada 1602.02109

K.Kamada, A.Long 1610.03074

∆hrh

Y

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  • Transport equation @ EW Crossover
  • Slowest processes: EW sphaleron & Decaying helicity
slide-38
SLIDE 38

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 38

Baryogenesis from Decaying Helicity

Regeneration of Baryon Asym.

∝ ∂ηhY

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  • EW sphaleron washout v.s. Decaying helicity

ΓW,sph ∝ e−

Msph(T ) T

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Msph(T ) ∝ v(T )

<latexit sha1_base64="HjE5lfwPmQ4IcC8FZnOIw48gAJo=">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</latexit>

{

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∂ηqB = −111 34 ΓW,sphqB + 3 2 ° g 2

2 + g 2 Y

¢ sin(2θ) ° ∂ηθ ¢ ∆hrh

Y

8π2

<latexit sha1_base64="p+JZ+Qh8JSQe1vBJQbzLSwxTXWs=">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</latexit>

hem

<latexit sha1_base64="DbCaQ5jEUuqGM6oM5QR84fLeyYg=">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</latexit>

hY

<latexit sha1_base64="/ZOKmpnBgBMYZa1PzQ+w5tNlEBI=">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</latexit>
  • T. Fujita, K.Kamada 1602.02109

K.Kamada, A.Long 1610.03074

∆hrh

Y

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Sphaleron washout factor

f (θ,T ) = −T dθ dT sin(2θ)

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w/

≤ ≡ ∑ 34 111 µ 1+ Æ2 ÆY ∂ H ΓW,sph f (µ,T ) ∏

TEW

<latexit sha1_base64="SK/YIquFN5IpDte2hZKFCJE52g=">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</latexit>
  • Huge uncertainties…

∆hrh

Y = −

2 3Hrh ⌦ ˆ

EY · ˆ BY

rh

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¥B = qB s ' ≤£ 3ÆY 4º ∆hY s Ø Ø Ø Ø

rh

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E W c r

  • s

s

  • v

e r

  • Transport equation @ EW Crossover
  • Slowest processes: EW sphaleron & Decaying helicity
slide-39
SLIDE 39

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 39

Viable parameters for Baryogenesis

Rm < 1 Rm

max < 1

B < 10-10 T

  • CPI > 105 GeV

no MHD

3 4 5 10 20 30 40 50 108 109 1010 1011 1012 1013 1014

  • Hrh [GeV]

equilibrium EYBY

Magnetic diffusion Chiral Plasma Instability

Hinf

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Observed Baryon #

  • Successful baryogenesis
  • nly with SM + inflaton
  • ChMHD puts lower/upper

bounds.

  • Mild dependence on the

Chern-Simons coupling

Baryogenesis from axion infmation

V.Domcke, B.Harling, E.Morgante, KM 1905.13318

ª ≡ Ø Ø ˙ ¡ Ø Ø 2ΛH ∼ ≤1/2 MP Λ

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slide-40
SLIDE 40

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 40

Viable parameters for Baryogenesis

Rm < 1 Rm

max < 1

B < 10-10 T

  • CPI > 105 GeV

no MHD

3 4 5 10 20 30 40 50 108 109 1010 1011 1012 1013 1014

  • Hrh [GeV]

equilibrium EYBY

Magnetic diffusion Chiral Plasma Instability

Hinf

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Observed Baryon # Viable?

Competition btw

  • verprod. and CPI.
  • Successful baryogenesis
  • nly with SM + inflaton
  • ChMHD puts lower/upper

bounds.

  • Mild dependence on the

Chern-Simons coupling

Baryogenesis from axion infmation

V.Domcke, B.Harling, E.Morgante, KM 1905.13318

ª ≡ Ø Ø ˙ ¡ Ø Ø 2ΛH ∼ ≤1/2 MP Λ

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slide-41
SLIDE 41

5.

Leptogenesis from axion infmation

slide-42
SLIDE 42

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 42 Time Inefficient

−3 4 αY π ∆hY

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−3 4 αY π ∆hY

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−3 4 αY π ∆hY

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Inflation

Leptogenesis?

What we have discussed so far…

  • Setup: inflaton + SM

∂µJµ

B

= ∂µJµ

L =

3 32π2 ≥ g 2

2W a µν ˜

W aµν − g 2

Y Yµν ˜

Y µν¥

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V.Domcke, B.Harling, E.Morgante, KM 1905.13318

slide-43
SLIDE 43

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 43

Leptogenesis from B+L asymmetry?

Time Inefficient

−3 4 αY π ∆hY

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−3 4 αY π ∆hY

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−3 4 αY π ∆hY

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−3 4 αY π ∆hY

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Washout via Majorana νR

−(1−κ)3 4 αY π ∆hY

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κ3 4 αY π ∆hY

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−3 4 αY π ∆hY

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Inflation

NR

<latexit sha1_base64="hBrybQgrsA9bV7132WqDiqyRLQE=">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</latexit>

lL

<latexit sha1_base64="zgWMW8fqYqz/y2vFjq/mPSLrI7c=">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</latexit>

H

<latexit sha1_base64="DqKMwFJAH7MF0g3z8UlVeNMtluU=">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</latexit>

NR

<latexit sha1_base64="hBrybQgrsA9bV7132WqDiqyRLQE=">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</latexit>

lL

<latexit sha1_base64="zgWMW8fqYqz/y2vFjq/mPSLrI7c=">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</latexit>

H

<latexit sha1_base64="DqKMwFJAH7MF0g3z8UlVeNMtluU=">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</latexit>

lL

<latexit sha1_base64="zgWMW8fqYqz/y2vFjq/mPSLrI7c=">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</latexit>

H

<latexit sha1_base64="DqKMwFJAH7MF0g3z8UlVeNMtluU=">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</latexit>

κ ⇠ O (1)

<latexit sha1_base64="U4GFY6uHghf01SquH3DuOCMi4E=">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</latexit>

Leptogenesis?

∂µJµ

L =

3 32π2 ≥ g 2

2W a µν ˜

W aµν − g 2

Y Yµν ˜

Y µν¥ +(ihNL · H +H.c.)

<latexit sha1_base64="CXYcqSBcydc1MV7euEMFStYBr5Y=">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</latexit>

∂µJµ

B

= 3 32π2 ≥ g 2

2W a µν ˜

W aµν − g 2

Y Yµν ˜

Y µν¥

<latexit sha1_base64="c/5zyRE03OtFnN+KXHNjDTv8byk=">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</latexit>

3∂µK µ

CS

<latexit sha1_base64="5TFVKfatWXxHfceVtTSw+sNOmzU=">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</latexit>

−3αY 4π ∂µhµ

Y

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  • Setup: inflaton + SM + Majorana NR

3∂µK µ

CS

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−3αY 4π ∂µhµ

Y

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V.Domcke, K.Kamada, KM, K.Schmitz, M.Yamada 20xx.xxxxx

slide-44
SLIDE 44

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 44 Time Inefficient via Sphaleron + Yukawa

−3 4 αY π ∆hY

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−3 4 αY π ∆hY

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−3 4 αY π ∆hY

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−3 4 αY π ∆hY

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Washout via Majorana νR

−(1−κ)3 4 αY π ∆hY

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κ3 4 αY π ∆hY

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−3 4 αY π ∆hY

<latexit sha1_base64="Ce2ARJCr8uRCxmDLxJKsG/MK+aM=">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</latexit>

−28κ 79 × 3 4 αY π ∆hY

<latexit sha1_base64="5QSed0yR5sRmj8Mh1dHkTKeQSek=">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</latexit>

51κ 79 × 3 4 αY π ∆hY

<latexit sha1_base64="bpcrbz3rRiol3oEGHyKTUQUtXk=">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</latexit>

µ 1− 28κ 79 ∂ × 3 4 αY π ∆hY

<latexit sha1_base64="YvfNn8UmT4q1/RFG2IbrHGp1PE=">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</latexit>

Inflation

NR

<latexit sha1_base64="hBrybQgrsA9bV7132WqDiqyRLQE=">AEv3ichVNb9NAEJ0UA6V8tIULEheLKAgu0boNOFU1AsXUJuQtlJbRbazSaza8t2DMHKH0DiSg89gcQB8TO4cEc+hMQxyJx4cDbjaNSCTsbxZ5982bmzazXClwnihk7Kc1d0C5eujx/ZeHqtes3FpeWb25H/jC0edv2XT/ctcyIu47g7diJXb4bhNz0LJfvWIcb0r+T8DByfPEiHgX8wDP7wuk5thkDaj3vNDtLZVY1amurjbrOqg8No7bCYNRXHzVqDd2oMrXKlK1Nf7n0jfapSz7ZNCSPOAmKYbtkUoTfHhnEKAB2QCmwEJaj/JzGtIDYIVgcDBPoIZ597PYyVGAvc0Yq2kYVF/8QkTpV2Hf2iZ2yr+wz+8H+5OZKVQ6pZYS3NYnlQWfxze3W75lRHt4xDc6iCiIsIt7iqlHdWLg94Chcgu7Un+5PXRaetxs5LeYx/YT/T3np2wL+hQJL/sj1u8eYzslcL8PlAHiKwx1d5VE3TAEgX6Umjz4QnB5GrG+cwoO98Bdt2MKWC/VGfkqcoCnhR4AjwBR34JUpUOTJ5+D9r2VR6BrBLR4S2DNVacUCkeKFZ4jlVc7xnUuCksDoKkTN+hWdKm8oznpEhQD3xj+IzvfdzNT6YkdPE1xH9N+dkQvJe5Pc/ZRTX6KqzkNb05ENYqULHuNnT6vnG9sruP3VxlatvF7P7vg83aG76NygNVqnp5hG7X79Jbe0ZH2ROtrQgsm1LlSFnOLzi1t9BeGSQEc</latexit>

lL

<latexit sha1_base64="zgWMW8fqYqz/y2vFjq/mPSLrI7c=">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</latexit>

H

<latexit sha1_base64="DqKMwFJAH7MF0g3z8UlVeNMtluU=">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</latexit>

NR

<latexit sha1_base64="hBrybQgrsA9bV7132WqDiqyRLQE=">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</latexit>

lL

<latexit sha1_base64="zgWMW8fqYqz/y2vFjq/mPSLrI7c=">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</latexit>

H

<latexit sha1_base64="DqKMwFJAH7MF0g3z8UlVeNMtluU=">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</latexit>

lL

<latexit sha1_base64="zgWMW8fqYqz/y2vFjq/mPSLrI7c=">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</latexit>

H

<latexit sha1_base64="DqKMwFJAH7MF0g3z8UlVeNMtluU=">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</latexit>

κ ⇠ O (1)

<latexit sha1_base64="U4GFY6uHghf01SquH3DuOCMi4E=">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</latexit>

Leptogenesis?

∂µJµ

L =

3 32π2 ≥ g 2

2W a µν ˜

W aµν − g 2

Y Yµν ˜

Y µν¥ +(ihNL · H +H.c.)

<latexit sha1_base64="CXYcqSBcydc1MV7euEMFStYBr5Y=">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</latexit>

3∂µK µ

CS

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−3αY 4π ∂µhµ

Y

<latexit sha1_base64="7FODgOW4mJ5lD8G+mVoCjZLzb5A=">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</latexit>

Leptogenesis from B+L asymmetry?

∂µJµ

B

= 3 32π2 ≥ g 2

2W a µν ˜

W aµν − g 2

Y Yµν ˜

Y µν¥

<latexit sha1_base64="c/5zyRE03OtFnN+KXHNjDTv8byk=">AGCnicjVS/b9NAGL0AgRJ+tIUFicUiCmoFRBcnpQkCqYIFAZX6gzat6tZynEti6tiu7YSWk/kDEDsDE0gMiK0bYoSBHSHRETbEWCQWBt6dE0IFSXEU+7t373v+58rni2FYSU7iQOHDyUPHxk6Gjq2PETJ4dHRk8tBm7LN9mC6dquv1QxAmZbDlsIrdBmS57PjGbFZuXK+g0xX24zP7Bc52645bHVplF3rJplGiEgfTRxW/MP7QMW+dasxUpt3R+PVqLY21jo2VUew/cUxmuyawrfr2ymk2V5jMl4oXaXYilyuoFExf7lUKEFts1o4pjlsQ/k7x53fOXyr3gjHIyV1Tav5hsnzEc+rUFhrXI2i2ESp6xgIQClLD0VzWhgb0IeWXW8LEZKd0a5JBTLsWK5p+iyl+PsEusU8P+NXVDGtJBthnzauOf6hmNED+Gjz41H+kgauIELRQVBCU1T1UE6qSaQ5DLUnmlSeacUcTH4hGqsQlJmRJmHEISFimxgkwG+F5AglHrBVwoH5iCw5z0hEUtC2wGJgGEDXca9jtNJBHYyFZyDVJrLY+PtQKiRDP9KXdJe+p6/oV/qzrxeXHqKWLTwrsZ5+vCjM/M/9lU18QxJo6caoKiAPbinkNRIUfZioTdPIqJLM/ZvP3iyO39lLsP0+f0G/p7RnfoW3TotL+bL2bZ3FO4Zwb6u0AtICJHt/aqXELGdAfRy1uZjxwWRyjfszg87+NjCqdpgO4vtyj5oys4MZDrwNvA2OeBNEVQowsfs1KZJHweuAlEwmwYrkhxfVtyQLH8Pa3C+aVRrg8MR6RIRa7yJOyczcibax8FDPuePinv1jvWtcXwfTwNvR/BPz3iFxLno3+XMThHVe6FiLo7yPiEhUnu3t8lf7BoqvRrY0W0hPXe2c8SFylpxD5zkySabITazhAjET24lPic+JL8nHye3k6+SbmHog0dGcJnu5LtfIHp1g=</latexit>
  • Setup: inflaton + SM + Majorana NR

3∂µK µ

CS

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−3αY 4π ∂µhµ

Y

<latexit sha1_base64="7FODgOW4mJ5lD8G+mVoCjZLzb5A=">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</latexit>

T ∼ 105GeV

<latexit sha1_base64="mXBnEREoPvyvA0a1SWmgFxBuG9s=">AE1nichVM9bxNBEB2HA0L4iANJoTlhE01t7hKA5VJApokPJlx1IcrLvzOl7lvnR3NoST0yEkKjoKhAUCMGfoKFHFPkJiDJINBS8XZ8VIuHzWr6bfNm5s3OrR26Ik4YOyrMnNHOnjs/e2Hu4qXLV+aLC1cbcdCPHF53AjeImrYVc1f4vJ6IxOXNMOKWZ7t8296/J/3bAx7FIvC3koOQ73rWni+6wrESQO3i4pbeioWnG+zRkt7yrKQXel93hi2iyVWMWpLrFrTYayYd5gJw1w2DRhGhalVomytBQuFb9SiDgXkUJ84uRTAtsli2L8dsgRiGwXUqBRbCE8nMa0hxi+2BxMCyg+3juYbeToT72Mmesoh1UcfGPEKlTmX1nH9gx+8o+sh/sz8RcqcohtRzgbY9iedief7G4+XtqlId3Qr2TqJwIG+z8nhLqUk31ItBbqBDZpTPKP3j6njz7kY5vcnesp/o7w07Yl/QoT/45bxf5xuvkb2cmz8AKoDIGmPtHXWCAiw/R18KbQE8EZhcnfFkZpzNt4dJ2P6sB+rGXmqsg9PCnwAfACO/BKkKh2YnH4X2loqj4+sEtHhLYE1VJxIKe4pVnSKlV/vIdS64KSw2gqRZ/wEz5TWlGc4JUOIev4/ik/03pqo8faUnBa+jvi/OUcnJO/F5P7HjPwaHTULaY0nH8FKFSpv9vj6pONhlkxqpWV9WptZbd8Vm6TjfQuUHLtEoPcIZ1D6kd/SJPmtN7VB7pj0fUWcKWcw1OrW0l38Bsl8JMQ=</latexit>

V.Domcke, K.Kamada, KM, K.Schmitz, M.Yamada 20xx.xxxxx

T ∼ TNR

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slide-45
SLIDE 45

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 45 Time Inefficient via Sphaleron + Yukawa

−3 4 αY π ∆hY −3 4 αY π ∆hY −3 4 αY π ∆hY −3 4 αY π ∆hY

Washout via Majorana νR

−(1−κ)3 4 αY π ∆hY

κ3 4 αY π ∆hY −3 4 αY π ∆hY

−28κ 79 × 3 4 αY π ∆hY 51κ 79 × 3 4 αY π ∆hY

µ 1− 28κ 79 ∂ × 3 4 αY π ∆hY

Inflation

T ∼ MR

NR lL H NR lL H lL H

κ ⇠ O (1)

Leptogenesis?

∂µJµ

L =

3 32π2 ≥ g 2

2W a µν ˜

W aµν − g 2

Y Yµν ˜

Y µν¥ +(ihNL · H +H.c.)

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3∂µK µ

CS

<latexit sha1_base64="5TFVKfatWXxHfceVtTSw+sNOmzU=">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</latexit>

−3αY 4π ∂µhµ

Y

<latexit sha1_base64="7FODgOW4mJ5lD8G+mVoCjZLzb5A=">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</latexit>

Leptogenesis from B+L asymmetry?

∂µJµ

B

= 3 32π2 ≥ g 2

2W a µν ˜

W aµν − g 2

Y Yµν ˜

Y µν¥

<latexit sha1_base64="c/5zyRE03OtFnN+KXHNjDTv8byk=">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</latexit>
  • Setup: inflaton + SM + Majorana NR

3∂µK µ

CS

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−3αY 4π ∂µhµ

Y

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T ∼ 105GeV

  • Resultant baryon asymmetry

qB s ∼ 10−9κ Å Hrh 1010 GeV ã 3

2 ✓〈 ˆ

EY · ˆ BY 〉rh/H 4

rh

105 ◆

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Majorana NR washout factor

  • Depends on when NR decouples.

κ ⇠ O (0.1)

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  • NR has to decouple before B+L is

completely washed out.

V.Domcke, K.Kamada, KM, K.Schmitz, M.Yamada 20xx.xxxxx

TNR > TYe ∼ 105 GeV

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slide-46
SLIDE 46

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 46

Summary

Inflaton w/ CS coupling to U(1)Y

  • Baryogenesis only with SM + inflaton
  • Leptogenesis with SM + inflaton + Majorana NR
  • Washout via NR generates B-L asym. from B+L asym.
Rm < 1 Rm max < 1 B < 10-10 T
  • CPI > 105 GeV
no MHD 3 4 5 10 20 30 40 50 108 109 1010 1011 1012 1013 1014
  • Hrh [GeV]
equilibrium EYBY

Magnetic diffusion Chiral Plasma Instability

Hinf

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Observed ηB

ξ ≡ Ø Ø ˙ φ Ø Ø 2ΛH

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  • BAU connected to Hinf
  • Mild dependence on the CS coupling
  • Upper/Lower bounds from ChMHD
  • Uncertainties: SM physics & backreaction

qB s ∼ 10−9κ Å Hrh 1010 GeV ã 3

2 ✓〈 ˆ

EY · ˆ BY 〉rh/H 4

rh

105 ◆

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  • Dual production of B+L asymmetry & helical U(1)Y

qL

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qB

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NR washout

slide-47
SLIDE 47

Back up

slide-48
SLIDE 48

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Decoupling Temperature

48

Summary plot of decoupling temperatures

  • Assume radiation dominated Universe.
  • During inflation, equilibration is more difficult because .

H2 > ρrad 3M2

P

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slide-49
SLIDE 49

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Field Rotation Invariance

49

Redundancies in inflaton-SM coupling

  • Warm up: coupling to CS term in massless QED

g 2φ 16π2 f Fµν ˜ F µν

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− φ 2f ∂µJµ

5

<latexit sha1_base64="vA5JLP3yHYZhBJ+/vcTcZAZu6s=">AE43ichVO/b9NAFH4pBkr50RQWJBaLKAgGorObqilTJRaEhNQfpK1UF8t2Lo1V/9LZCRTL/wDdEBIDYgCJATGxwsjCjhj6JyDGIrEw8PniqFQizln2vfve973p3Pjw3Thg7rEydUk6fOTt9bub8hYuXZqtzlzfisC8c3nZCLxRbthVzw14O3ETj29Fglu+7fFNe+9u7t8cBG7YfAw2Y/4jm/tBm7XdawEkFmt3za6wnJSI+q5Wap3M9WILJG4lmcafl+9by48wmxWa6yhtRZYs6XCWNLnmQ5DX9Q1GFqDyVGjYqyEc5VvZFCHQnKoTz5xCiB7ZFMZ5t0ohRBGyHUmACliv9nDKaQWwfLA6GBXQP312stgs0wDrPGctoB1U8vAKRKtXZd/aeHbGv7AP7wf6MzZXKHLmWfcz2MJZH5uyzq+u/J0b5mBPqHUeVRNhgl/eUJdashcXvUSybt0hvkHT18erd9Zq6c32Fv2E/29YfsCzoMBr+cd6t87RWy10vzh0BdIHmNkfaO3EXrKBEXwptITwCTC73eDwzLs63h1WnYAawH8sz8mXlAJ4U+AD4AJz8T8hVqcDy0+9CmyHzBMiaIyq8NbAyRFScU+yxAlWeb0HUOuBk8IyJZLv8RN8U1qRnmxChgj1gn8UH+u9OVbjrQk5Lfwd8X9zDncovxfj+x8xymt05Fnk1ujkBaxUohlu9uj6quONDb2hNRtLq83acqu49N0ja6jc40WaZnuYQ/bqH1AH+kTfVa4cqA8V14MqVOVIuYKnRjK679a0w9x</latexit>

Chiral rot.

  • Coupling to CS term of U(1)Y

0 = ∂µF µν − g Jν

<latexit sha1_base64="cLbz/YWQhGZKhrkWcbg3uhueB4c=">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</latexit>

ν

<latexit sha1_base64="xYd2PL+LxVKV9j5x1gPAliOdhY=">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</latexit>

φ

<latexit sha1_base64="tXDO9uaKht8Bi29AKG69Fv6q1A=">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</latexit>

<latexit sha1_base64="XfNI0fmI0yc/c7YEtyBisf6unMQ=">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</latexit>

A

<latexit sha1_base64="JBv62rnrQU2Jv0umyBb+nG2JyZk=">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</latexit>

= g 2∂µφ 4π2 f ˜ F µν

<latexit sha1_base64="KC2W2asZYUjOlTLMeJ2LX1uik=">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</latexit>

0 = ∂µF µν − g 2∂µφ 4π2 f ˜ F µν − g Jν

<latexit sha1_base64="Nq+jmhcbxNHFdCr4rft/iKjDqYE=">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</latexit>

g 2

Y φ

16π2 f Yµν ˜ Y µν

B+L rot.

ψ 7! e°iγ5

φ 2f ψ <latexit sha1_base64="iyCt937HcuJKSjSC6nxmgyCnKpg=">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</latexit>

φ f √ −1 3∂µJµ

B+L +

g 2

2

16π2 W a

µν ˜

W aµν ! 0 = DµW aµν − g 2

2∂µφ

4π2 f ˜ W aµν − g2J aν + g 2

2∂µφ

4π2 f ˜ W aµν

0 = DµW aµν − g2J aν

Equivalent! Equivalent! ➡ Field rotation never changes physics! (see also KM+ 2006.03148)

slide-50
SLIDE 50

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Field Rotation Invariance

50

Redundancies in inflaton-SM coupling

  • Warm up: coupling to CS term in massless QED

g 2φ 16π2 f Fµν ˜ F µν

<latexit sha1_base64="+fn65dMLW5C57fcBMHNtrZlLv4=">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</latexit>

− φ 2f ∂µJµ

5

<latexit sha1_base64="vA5JLP3yHYZhBJ+/vcTcZAZu6s=">AE43ichVO/b9NAFH4pBkr50RQWJBaLKAgGorObqilTJRaEhNQfpK1UF8t2Lo1V/9LZCRTL/wDdEBIDYgCJATGxwsjCjhj6JyDGIrEw8PniqFQizln2vfve973p3Pjw3Thg7rEydUk6fOTt9bub8hYuXZqtzlzfisC8c3nZCLxRbthVzw14O3ETj29Fglu+7fFNe+9u7t8cBG7YfAw2Y/4jm/tBm7XdawEkFmt3za6wnJSI+q5Wap3M9WILJG4lmcafl+9by48wmxWa6yhtRZYs6XCWNLnmQ5DX9Q1GFqDyVGjYqyEc5VvZFCHQnKoTz5xCiB7ZFMZ5t0ohRBGyHUmACliv9nDKaQWwfLA6GBXQP312stgs0wDrPGctoB1U8vAKRKtXZd/aeHbGv7AP7wf6MzZXKHLmWfcz2MJZH5uyzq+u/J0b5mBPqHUeVRNhgl/eUJdashcXvUSybt0hvkHT18erd9Zq6c32Fv2E/29YfsCzoMBr+cd6t87RWy10vzh0BdIHmNkfaO3EXrKBEXwptITwCTC73eDwzLs63h1WnYAawH8sz8mXlAJ4U+AD4AJz8T8hVqcDy0+9CmyHzBMiaIyq8NbAyRFScU+yxAlWeb0HUOuBk8IyJZLv8RN8U1qRnmxChgj1gn8UH+u9OVbjrQk5Lfwd8X9zDncovxfj+x8xymt05Fnk1ujkBaxUohlu9uj6quONDb2hNRtLq83acqu49N0ja6jc40WaZnuYQ/bqH1AH+kTfVa4cqA8V14MqVOVIuYKnRjK679a0w9x</latexit>

Chiral rot.

  • Coupling to CS term of U(1)Y

0 = ∂µF µν − g Jν

<latexit sha1_base64="cLbz/YWQhGZKhrkWcbg3uhueB4c=">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</latexit>

ν

<latexit sha1_base64="xYd2PL+LxVKV9j5x1gPAliOdhY=">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</latexit>

φ

<latexit sha1_base64="tXDO9uaKht8Bi29AKG69Fv6q1A=">AEwHichVNb9NAEJ0UA6V8tIULEpeIKAgu0doNasqpgsXpH6QtlJTRbazqVe18Z2DK2VP8CBa5E4gcQB8TO4cEc+hMQxyJx4cDbjaNSiTgbxZ5982bmzY7XiXyRpIydVGYuGBcvXZ69Mnf12vUb8wuLN7eScBC7vO2GfhjvOHbCfSF5OxWpz3eimNuB4/Nt5+CJ8m9nPE5EKJ+nhxHfC+x9KfrCtVMFdSJPdBdqrG2HrJmqwpjxVpiFgxr2TJhmA2mV42KtRYuVr5Rh3oUksDCoiTpBS2TzYl+O2SYwiYHuUA4thCe3nNKQ5xA7A4mDYQA/w3Mdut0Al9ipnoqNdVPHxjxFZpTr7zj6xU/aVfWY/2J+JuXKdQ2k5xNsZxfKoO/69ubvqVEB3il5Z1ElEQ7Y5T2l1KeW7kWgt0gjqkt3lD87Oj7dfLRz+xD+wn+nvPTtgXdCizX+7Hdb7xDtnrpflDoAKIqjHW3tMnKMCSJfpyaAvhicHk+ownM5Nivh52vYIpYb/UMwp0ZQlPDjwDnoGjvgSlqgpMTb8PbR2dRyKrQqrw1sAak6sFXuaFZ9jld7BrU+ODmsrkbUGb/CM6c17RlOyRChnvxH8Zne+xM1PpiS08bXkfw35+iE1L2Y3P+YUV6jp2ehrPHkY1i5Roe42ePrW51sbFkNs9lYW/WVlvFHZ+lO3QXnZu0TKv0FGfYRm2P3tAxvTUeG54RGi9G1JlKEXOLzi3j6C/rswGp</latexit>

<latexit sha1_base64="XfNI0fmI0yc/c7YEtyBisf6unMQ=">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</latexit>

A

<latexit sha1_base64="JBv62rnrQU2Jv0umyBb+nG2JyZk=">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</latexit>

= g 2∂µφ 4π2 f ˜ F µν

<latexit sha1_base64="KC2W2asZYUjOlTLMeJ2LX1uik=">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</latexit>

0 = ∂µF µν − g 2∂µφ 4π2 f ˜ F µν − g Jν

<latexit sha1_base64="Nq+jmhcbxNHFdCr4rft/iKjDqYE=">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</latexit>

g 2

Y φ

16π2 f Yµν ˜ Y µν

<latexit sha1_base64="hxosLFV7OBjTczNMleQZBJQ9xXM=">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</latexit>

B+L rot.

ψ 7! e°iγ5

φ 2f ψ <latexit sha1_base64="iyCt937HcuJKSjSC6nxmgyCnKpg=">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</latexit>

φ f √ −1 3∂µJµ

B+L +

g 2

2

16π2 W a

µν ˜

W aµν !

<latexit sha1_base64="1gKePT6cE68dzgA9yePNQ4c367c=">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</latexit>

0 = DµW aµν − g 2

2∂µφ

4π2 f ˜ W aµν − g2J aν

<latexit sha1_base64="jDsW6uYHwdpG5yFVaLKqIp/0xgQ=">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</latexit>

+ g 2

2∂µφ

4π2 f ˜ W aµν

<latexit sha1_base64="6TcfChd7YWdfiQLpYV6Bp+EzAaA=">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</latexit>

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0 = DµW aµν − g2J aν

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Equivalent! Equivalent! ➡ Field rotation never changes physics! (see also KM+ 2006.03148)

slide-51
SLIDE 51

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Chiral Vortical Effect

51

Chiral vortical effect as NLO in μ/T

  • Generalized Ohm’ law w/ velocity & its vortex
  • Assump: weak hyper gauge field & thermalized plasma.

ˆ

JY = σY

° ˆ

EY +v × ˆ BY

¢ + 2αY π µY,5 ˆ

BY +cCVE r

a ×v

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w/

X

Æ

≤ÆNÆQY,Æ = 0

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* A

° U(1)Y – grav. – grav. ¢ = 0

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  • Small chemical potential in the early Universe: μ/T ≪ 1.

cCVE = gY µX

Æ

≤ÆNÆQY,Æ µ2

Æ

4º2 + T 2 12 X

Æ

≤ÆNÆQY,Æ ∂ = gY 4º2 X

Æ

≤ÆNÆQY,Ƶ2

Æ

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ˆ

JY = æY

° ˆ

EY +v × ˆ BY

¢ + 2ÆY º µY,5 ˆ

BY + gY

4º2 µX

Æ

≤ÆNÆQY,Ƶ2

Æ

∂ r a ×v

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¿

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@ equipartition: ˆ

B2

Y ∼ T 4v2

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∼ gY µ2 v L ∼ µ2 T 2 ˆ BY g −1

Y L

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∼ µ T ˆ BY α−1

Y T −1

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e+

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v

<latexit sha1_base64="mPFK4v4+bOrmIQRprIvwegvIviY=">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</latexit>

Right-handed Left-handed where

A. Vilenkin, Phys. Rev. D 21, 2260 (1980)

Nα = d.o.f.

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εα = ± for R/L

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slide-52
SLIDE 52

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Induced Current

52

How does Induced Current look like?

  • Weak electromagnetic field in thermalized plasma
  • No magnetic mass for transverse mode of Abelian gauge field.
  • This expression holds if energy by acceleration ≪ temperature
  • Strong electromagnetic field ?
  • Estimate the current operator for the accelerated energy ≫ temperature

ˆ

JY = ˆ

σY ˆ

EY + 2αY

π ˆ µY,5 ˆ

BY

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→ ˆ J z

Y =

X

α

(g|Qα|)3 6π3 ˆ E2

Y

H

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BY → 0

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for

gY |Q| ˆ EY ˆ τint ø ˆ T

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Reproduce e.g., Kobayashi, Afshordi 1408.4141

ˆ

EY

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e +

i.e., Generalized Ohm’s law (neglecting velocity field)

  • E. Fradkin, Proc. of the Lebedev

Institute 29, 6 (1965).

ˆ J z

Y =

X

α

(g|Qα|)3 12π2 coth µπ ˆ BY ˆ EY ∂ ˆ EY ˆ BY 1 H

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slide-53
SLIDE 53

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Massive Fermion Production

53

Schwinger effect for massive fermion

  • Anomalous current equation w/ mass term
  • Induced current

Ambjorn, Olesen, Phys.Lett.B 218 (1989) 67; Kajantie+, Nucl.Phys.B 544 (1999) 357-373 See e.g., K.Fukushima+ 1807.04416

∂µJµ

5 = − g 2Q2

8π2 Fµv ˜ F µv +2im ¯ ψγ5ψ

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˙ q5 ' g 2Q2 2π2 EB exp µ ° πm2 g|QE| ∂

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g 2Q2 2π2 EB

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2m ≠ ¯ ψiγ5ψ Æ ' g 2Q2 2π2 EB ∑ exp µ ° πm2 g|QE| ∂ °1 ∏

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  • Production of W bosons is more violent.

➡Backreact to Higgs potential

0 = −∂t E +r ×B + a g 2 4π2 ˙ φ fa

B − g J

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gQ 〈J 〉ind = a 3 (g |Q|)3 6π2 ˆ

E| ˆ

B|coth ✓ π| ˆ B| ˆ E ◆ e

− πm2

g |Q| ˆ E 1

H

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Involves gauge coupling running finite terms, i.e., Euler-Heisenberg

Vacuum cont.

V.Domcke, Y.Ema, KM 1910.01205

E

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B

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slide-54
SLIDE 54

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Massive Fermion Production

54

Schwinger effect for massive fermion

  • Anomalous current equation w/ mass term
  • Induced current

Ambjorn, Olesen, Phys.Lett.B 218 (1989) 67; Kajantie+, Nucl.Phys.B 544 (1999) 357-373 See e.g., K.Fukushima+ 1807.04416

∂µJµ

5 = − g 2Q2

8π2 Fµv ˜ F µv +2im ¯ ψγ5ψ

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˙ q5 ' g 2Q2 2π2 EB exp µ ° πm2 g|QE| ∂

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g 2Q2 2π2 EB

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2m ≠ ¯ ψiγ5ψ Æ ' g 2Q2 2π2 EB ∑ exp µ ° πm2 g|QE| ∂ °1 ∏

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  • Production of W bosons is more violent.

➡Backreact to Higgs potential

0 = −∂t E +r ×B + a g 2 4π2 ˙ φ fa

B − g J

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gQ 〈J 〉ind = a 3 (g |Q|)3 6π2 ˆ

E| ˆ

B|coth ✓ π| ˆ B| ˆ E ◆ e

− πm2

g |Q| ˆ E 1

H

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Involves gauge coupling running finite terms, i.e., Euler-Heisenberg

Vacuum cont.

V.Domcke, Y.Ema, KM 1910.01205

PBH overproduction CMB

10 20 30 40 50 10-9 10-7 10-5 10-3

N [e-folds] s

2

equilibrium solution for E B

  • Heavy

m/H = 0

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10

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30

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100

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E

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B

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slide-55
SLIDE 55

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Massive Fermion Production

55

Schwinger effect for massive fermion

  • Anomalous current equation w/ mass term
  • Induced current

Ambjorn, Olesen, Phys.Lett.B 218 (1989) 67; Kajantie+, Nucl.Phys.B 544 (1999) 357-373 See e.g., K.Fukushima+ 1807.04416

∂µJµ

5 = − g 2Q2

8π2 Fµv ˜ F µv +2im ¯ ψγ5ψ

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˙ q5 ' g 2Q2 2π2 EB exp µ ° πm2 g|QE| ∂

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g 2Q2 2π2 EB

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2m ≠ ¯ ψiγ5ψ Æ ' g 2Q2 2π2 EB ∑ exp µ ° πm2 g|QE| ∂ °1 ∏

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  • Production of W bosons is more violent.

➡Backreact to Higgs potential

0 = −∂t E +r ×B + a g 2 4π2 ˙ φ fa

B − g J

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gQ 〈J 〉ind = a 3 (g |Q|)3 6π2 ˆ

E| ˆ

B|coth ✓ π| ˆ B| ˆ E ◆ e

− πm2

g |Q| ˆ E 1

H

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Involves gauge coupling running finite terms, i.e., Euler-Heisenberg

Vacuum cont.

V.Domcke, Y.Ema, KM 1910.01205

Heavy

30

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100

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E

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B

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LISA ET LIGO

10-15 10-10 10-5 1 105 10-14 10-11 10-8

f [Hz] GWh2 equilibrium solution for E B

  • m/H = 0
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10

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slide-56
SLIDE 56

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Rm < 1 B < 10-10 Rm

max < 1

10-11 10-12 T

  • CPI > 105 GeV

no MHD

3 4 5 10 20 108 109 1010 1011 1012 1013 1014

  • Hrh [GeV]

maximal EYBY

Result

56

Viable parameters for Baryogenesis

Magnetic diffusion Chiral Plasma Instability

Hinf

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V.Domcke, B.Harling, E.Morgante, KM 1905.13318

ª ≡ Ø Ø ˙ ¡ Ø Ø 2ΛH ∼ ≤1/2 MP Λ

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Observed Baryon # Viable?

slide-57
SLIDE 57

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Magnetic fjeld

Implications to intergalactic B-field?

57

  • Current lower limits to explain the intergalactic B-field.

Fermi-LAT 1804.08035

  • Our baryogenesis model yields

too small…

B . 10−17G for λ ∼ 0.1pc

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slide-58
SLIDE 58

Kyohei Mukaida / 1905.13318, 20xx.xxxxx P

Vacuum Contribution

Chiral anomaly in finite volume

58

  • Consider (1+1) QED on S1:

Left-handed Right-handed Energy P

E

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E

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∂· J5 = g 2πeµνFµν = gE π

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slide-59
SLIDE 59

Kyohei Mukaida / 1905.13318, 20xx.xxxxx P

Vacuum Contribution

Chiral anomaly in finite volume

59

  • Consider (1+1) QED on S1:

Left-handed Right-handed Energy P

E

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E

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∂· J5 = g 2πeµνFµν = gE π

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slide-60
SLIDE 60

Kyohei Mukaida / 1905.13318, 20xx.xxxxx P

Vacuum Contribution

Chiral anomaly in finite volume

60

  • Consider (1+1) QED on S1:

Left-handed Right-handed Energy P

E

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E

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➡ Particles are not yet generated… How do we fulfill the anomaly eq? ➡ Vacuum contribution accounts for the anomaly eq!

QR/L = X

p

∑µ ˆ b† ˆ b − 1 2 ∂ − µ ˆ d† ˆ d − 1 2 ∂∏

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Q(vac)

R/L = lim Λ→∞

X

p

∑ −1 2 sgn(ωR/L)R µ|ωR/L| Λ ∂∏

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Q(vac)

R/L = gE

π T L

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∂· J5 = g 2πeµνFµν = gE π

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Z dtdx gE π = gE π T L

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:QR/L : = 0

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slide-61
SLIDE 61

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Introduction

61

  • “Lightness” protected by the shift symmetry (classically):
  • Efficient helical-gauge field production by .

˙ φ 6= 0

φ 7! φ+c

➡ axion inflation, relaxion, chiral GWs, baryogenesis, magnetogenesis,…

S = Z d4x Ωp°g ∑g µν 2 ∂µφ∂νφ°V (φ) ∏ ° 1 4FaµνF aµν + αφ 4πfa Faµν ˜ F aµν æ

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+ Homogeneous & isotropic gauge field may develop.

0 6= ≠ Faµν ˜ F aµνÆ = °4 ≠Ea ·BaÆ

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f 00(η)+2f 3(η)°2aHξf 2(η) = 0

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where

ξ ≡ α ˙ φ 2πfaH f

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V (f )

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aHξ

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non-Abelian

Aa

0 = 0,

Aa

i = −g −1 f (η)δa i ,

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Inflaton w/ CS-coupling

slide-62
SLIDE 62

Kyohei Mukaida / 1905.13318, 20xx.xxxxx

Fermion Production

62

Subtleties for

  • No Landau levels, but we can still play the same game…
  • The spectrum is different between the initial and final states.

➡ Need to include the contributions from vacuum not only particles. Energy Momentum

f %

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f %

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Qα = : Qα : + Q(vac)

α

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Q(vac)

α

≡ lim

ˆ Λ→∞

vol ° R3¢Z d3k (2π)3 2 4−1 2 X

λ

sgn ≥ ω(λ)

α

¥ R @ Ø Ø Øω(λ)

α

Ø Ø Ø a ˆ Λ 1 A 3 5

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w/

Fundamental repr: 1

6(Anomaly)

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5 6(Anomaly)

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Aa

0 = 0,

Aa

i = −g −1 f (η)δa i

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The eta-invariant; see Atiyah and Singer V.Domcke,Y.Ema, KM, R.Sato 1812.08021

slide-63
SLIDE 63

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 63

Chiral Plasma Instability

Chiral Plasma Instability

  • Equation for Magnetic Helicity

µY,5 = X

Æ

≤ÆNÆQ2

Y,ƵÆ

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w/

∂ ∂ ηhY ,k = −2k 2 σY hY ,k + 8αY π µY ,5 σY ρB,k = −2k 2 σY hY ,k + 4αY π µY ,5 σY rk khY ,k

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rk ≡ k hk(η)/2 ρB,k(η)

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w/

∂ hY ∂ η = Z d3x vol(R3) Yµν ˜ Y µν 2 = −2 Z d3x vol(R3)EY ·BY

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0 = r ×BY −JY ,

JY = σY (EY +v ×BY ) + 2αY

π µY ,5BY

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∂ ∂ ηhY = Z d3x vol(R3) ✓ 2BY · r2 σY

AY + 4αY

π µY ,5 σY

B2

Y

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  • Mode equation
slide-64
SLIDE 64

Kyohei Mukaida / 1905.13318, 20xx.xxxxx 64

Scaling in Turbulent & Viscous Regimes

Kinetic Reynolds #

∂ ∂ηv +v ·rv = vr2v + 1 ρ +P µ −1 2rB2

Y +(BY ·r)BY

<latexit sha1_base64="bm8pO8dyTRNJncXOq9jcjzvDRQ8=">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</latexit>
  • Velocity equation in ChMHD

?

<latexit sha1_base64="eZ0O6ASfVTmJ/bTmlmEj1aCQlY=">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</latexit>

Re = Lv ν ? 1 :

<latexit sha1_base64="qUDKlEJnDSZlGPRcs51dbRtW9vo=">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</latexit>

∼ v2 L

<latexit sha1_base64="wBlIeoTFir+nR+y1VvIpqQk8Chw=">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</latexit>

∼ νv L2

<latexit sha1_base64="Ud1KzVN6NlCkMW6XwfVm4DmPnM=">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</latexit>

∼ B2

Y

<latexit sha1_base64="tm+JVj2Hx3D6AjveCjLZiWwKMw=">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</latexit>

Kinetic Reynolds #

  • Turbulent regime: Rm > Re > 1

ρv2 ∼ B2

Y

<latexit sha1_base64="h3T+YUCqw26Ak79b4U7PdLzI1k=">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</latexit>
  • const. = hY ∼ LB2

Y

<latexit sha1_base64="jxI3tT/D2MvkCphNc/9Ec7wm+vM=">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</latexit>

&

∂ηBY ∼ vBY L ∝ B4

Y

<latexit sha1_base64="ApYgZwczJ3XWXH1RSiklVUIEBto=">AE83ichVNb9NAEJ0UQ0v5aAoXJC4WURBcorWbqoFTBRcOIPWDtEV1sRxn01j1l9ZOoFj+A/wBDjlRwQEhfgTiguCIOPQnI5F4sKBt5tEpRJxN4o9+bNzJsdbyv2vSRl7LA0dUY7e2565vzshYuXLs+V569sJFPuLzpRn4ktlpOwn0v5M3US32+FQvuBC2fb7b27kv/Zp+LxIvCx+l+zHcCZzf0Op7rpIDs8qIVOyL1HN+2eOro9+wnupV4gW51hONmfV0iefYw161YRHEayf3Tul2usJrRWGT1hg7jrnATBjmkmnAMGpMrQqN1ko0X/pGFrUpIpd6FBCnkFLYPjmU4LdNBjGKge1QBkzA8pSfU06ziO2BxcFwgO7huYvd9gNsZc5ExXtoqPv0CkTlX2nb1jR+wze89+sD8Tc2Uqh9Syj3drGMtje+7ltfXfp0YFeKfUPY4qiGiBXdxTSh1qF489BYrRHbpDvP3X7w6Wr+7Vs1usgP2E/29ZofsEzoM+7/ct6t8bYDs1cL8EVAPiKwx1t5WJ+iBFRboy6AtgkeAydUZT2Ymo/l2sWuPmCHsZ2pGgaocwpMB7wPvgyO/BKlKByan34E2S+UJkVUiOrwVsHLFEUpxV7HECVZxvUdQ64OTwbIVIs/4OZ4ZrShPfkqGPXCfxQf6701UePtU3I6+DqS/+YcnpC8F5P7HzOKa7TVLKQ1nryAlSk0x80eX19srFh1oyFmrlaryw3Rnd8hq7TDXRu0BIt0wOcYRO1B/SRvtBXracNtAPtzZA6VRrFXKUTS/vwF5/BFQw=</latexit>
  • Viscous regime: Rm > 1 > Re

ρ v2 ∼ ReB2

Y

<latexit sha1_base64="FnUPyqlOr4XmCmhMpwxB+EG3I=">AE2HichVM9b9NQFL0pBkr5aEoXBItFAQSip7doqZMFSwsSG1K2kLTWrbz0lj1l2zHUKxI3RCMLAxMIGEGOA/sLAjhv4ExFgkFgbOe3FUKhHnRbHvO/fce8918KXSdOGDsoTZxQTp46PXlm6uy58xemyzMX1+KgF9m8aQduEG1YZsxdx+fNxElcvhFG3PQsl69bu3eFfz3lUewE/oNkL+RbnrnjOx3HNhNARvlyK+oGaum7rait2PLVhcPWO8XBbN8oVtPqt9h8XYWxqM8xHYa+oGswtBqTq0L5Wg5mSt+oRW0KyKYecTJpwS2SybF+G2SRoxCYFuUAYtgOdLPqU9TiO2BxcEwge7iuYPdZo762IucsYy2UcXFP0KkSlX2nX1gh+wr+8h+sD8jc2Uyh9Cyh7c1iOWhMf3i0urvsVEe3gl1j6IKIiywi3tKqEN12YuD3kKJiC7tQf706avD1duNanaNvWU/0d8bdsC+oEM/W/W+GN18heLcwfAHWAiBpD7W15g5YfoG+DNoCeCIwuTzj0cw4n28Xu3bO9GE/ljPyZGUfngx4CjwFR3wJQpUKTEy/A20tmcdHVoGo8FbA6ktOJBV3JSs6xiqudx9qXAyWIZExBk/wTOjZenpj8kQop7/j+IjvdHarwxJqeJryP+b87BCYl7Mbr/IaO4RlvOQljDyUewMon2cbOH1cdbazpNW2upq/MV5bq+R2fpCt0FZ1rtEBLdA9n2ETtfXpPn+iz8kjZV54pzwfUiVIeM0vHlvLyL7obCSk=</latexit>

BY ∼ µηt η ∂ 1

3

BY,t, L ∼ µ η ηt ∂ 2

3

Lt

<latexit sha1_base64="5hDkLtpUrxMbYVwfHunwJB2b6bE=">AFTHichVNb9NAEJ2UtJTy0RQuC4rQqpWqK1U9TAqYILhyL1g36guliOs2msOrZlbwPF8h/gwJUDJ5A4IH4GF05cEIf+BMSxkTgAEm83iUpRk64T7+ybN29mdr21yPcSyflhbuRcfnTs/PiFiYuXLl+ZLExd3UjC/dgV627oh/FWzUmE7wViXrSF1tRLJxWzRebtb0Hyr/ZFnHihcFjeRCJnZazG3gNz3UkILvwirH7dvokY9NW4rWY5YuGnGFWI3bc1BLSsWm54xZsbfblLNPuz4jSyuZDp1jMptjlvqpZ4KxJXa6VtZX/E/L1FpLdiozu1DkZaN6h89XGYy7ZoWbMwF04BhlLkeReqN5XAq95UsqlNILu1TiwQFJGH75FCZ5sM4hQB26EUWAzL035BGU0gdh8sAYDdA/vXay2e2iAtdJMdLSLD7+MSIZlfg3/oEf8c/8I/Ofw/USrWGquUAc60bKyJ78uX1tZ9nRrUwS2oeRw2JqIE9vCdJDarqXjz0FmlEdel29dsvXh+t3VstpdP8Hf+B/t7yQ/4JHQbtjvt+Ray+gXpqH4I1AOicvRr+sd9MAKhtSXorYQnhMofd4MDPpnW8Tq3qPGcB+ps+opTMH8KTA28Db4KgvQVXFgKnTb6A2S+sEUFUIg7cIVqY5sa64qVnxCdbwfI9QrQ9OCsvWiNrj53intKw92RkKEfIF/1R8XO/MwBpnz9B08HUkp2p2d0jdi8H9xnDc9T1WSirf/IxrFSj6mb3ry8bGyYZaNSNlfmi4vV3h0fp5t0C50btECL9B7uI7cndyNXDF3O/8l38n/yv/pUkdyvZhrdGKMjv0F/jczMQ=</latexit>

& const. = hY ∼ LB2

Y

<latexit sha1_base64="jxI3tT/D2MvkCphNc/9Ec7wm+vM=">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</latexit>

∂ηBY ∼ vBY L ∝ B3

Y

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BY ∼ µηt η ∂ 1

2

BY,t, L ∼ µ η ηt ∂ Lt

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