1. Spontaneous Baryo/Leptogenesis 2. Schwinger Effect & Chiral Anomaly

1. Spontaneous Baryo/Leptogenesis 2. Schwinger eﬀect & Chiral anomaly Kyohei Mukaida

Desy, Hamburg → CERN

Based on 1806.08769, 1910.01205, 2006.03148 In collaboration with Y. Ema, V. Domcke, R.Sato, M.Yamada

Kyohei Mukaida

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V.Domcke, Y.Ema, KM, M.Yamada Spontaneous Baryo/Leptogensis 2006.03148 ‣ We can generate baryon asymmetry for almost any SM-ALP couplings. - Complementary to Keisuke and Raymond’s talk

°Y ˙ 1 WS Ye SS Yd u1 Yu 2 cB 24n 22n 21n 18n 18 n q c T = 158 S ° S ° S + S ° ° S B = B √ Yd1 ! f ˙ 24 WS 19 SS 15 Yt 115 W 2 cB L nS nS nS nS qB L = cB L T ° = 261 ° 174 + 58 ° 348 f

V.Domcke, Y.Ema, KM Chiral fermion & Helical gauge ﬁeld 1806.08769, 1910.01205 ‣ Helical gauge ﬁelds & chiral fermions are generated simultaneously. - Complementary to Benedict’s talk † eR µ 3 @ J g 2W a W˜ aµ∫ g 2 Y Y˜ µ∫ µ B L 2 2 µ∫ Y µ∫ EY 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 + = 16º ° 0 ≠ ≥ ¥6= eR Kyohei Mukaida 3 1. Spontaneous Baryo/Leptogenesis

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‣ Baryon asymmetry of Universe (BAU) - Baryon to photon ratio by CMB & BBN: η ~ 6 x10-10

➡ Production of BAU after inﬂation before BBN Baryogenesis

@ JB L W W˜ , @ JB L 0 · + æ · ° = - Sphaleron: ° Æ5T 4 WS ª 2 Leptogenesis

Kyohei Mukaida 5

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‣ Violation of Baryon or Lepton # ⇄ Q˙B [QB , H] 0 / 6= ‣ C and CP violation ⇄ Asymmetry between particle and anti-particle

ØH ØH 1 ‣ Departure from thermal equilibrium ⇄ Tr[e° QB ] Tr[e° (CPT)QB (CPT)° ] = ØH Tr[e° Q ] = ° B Examples ‣ Thermal Leptogenesis (out of equilibrium decay) ‣ Afﬂeck-Dine Baryogenesis (motion sourced by CPV) ‣ Decaying Helicity (out of equilibrium “decay") ‣ Spontaneous Baryo/Leptogenesis

Kyohei Mukaida 6

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Q. Do we have to couple to B or L current?

Short answer. No! e.g., Keisuke and Raymond’s Talk Kyohei Mukaida 7

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- B+L genesis via weak sphaleron

21 12 18 21 15 25 11 cB ± cg cW cq cu¯ c ¯ c` ce¯ = 158 ° ° 79 + 79 i ° 158 i ° 158 di + 237 i ° 237 i µ ∂ i µ ∂ X Keisuke and Raymond’s Talk

°Y 1 WS Ye SS Yd u1 Yu V.Domcke, Y.Ema, KM, M.Yamada cB 24n 22n 21n 18n 18 n = 158 S ° S ° S + S ° ° S 2006.03148 √ Yd1 !

- B-L genesis via dim.5 Weinberg operator

46 WS 19 SS 45 Yt 115 W V.Domcke, Y.Ema, KM, M.Yamada cB L n n n nS ° = 87 S ° 29 S + 29 S ° 58 2006.03148

Kyohei Mukaida 8

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‣ Current equations with two breaking operators: OX and OV.

@ J1 OX OV & @ J O · = ° + · 2 = X ‣ We would like to generate @ J @ (J J ) O · B = · 1 + 2 = V

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 2 - Conventional

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th-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 Kyohei Mukaida 9

‣ Current equations with two breaking operators: OX and OV.

@ J1 OX OV & @ J O · = ° + · 2 = X ‣ We would like to generate @ J @ (J J ) O · B = · 1 + 2 = V

‣ Current equations with two breaking operators: OX and OV.

@ J1 OX OV & @ J O · = ° + · 2 = X ‣ We would like to generate @ J @ (J J ) O · B = · 1 + 2 = V

‣ Current equations with two breaking operators: OX and OV.

@ J1 OX OV & @ J O · = ° + · 2 = X ‣ We would like to generate @ J @ (J J ) O · B = · 1 + 2 = V

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 B B ¡@ J ¡O =0 =0 QAAACZnichVHLSsNAFD2N7/qqiii4CRbFVblJlVpXohuXfVgVVEoSxxpMk5CkBS3+gODWLlwpiIif4cYfcNE/UFwquHHhbVoRF+odZubMmXvunJnRXcv0A6JGROro7Oru6e2L9g8MDg3HRkY3fKfiGaJgOJbjbemaLyzTFoXADCyx5XpCK+uW2NQPV5v7m1Xh+aZjrwdHrtgtayXb3DcNLWAqny2uFGNxSiiLC/PplMwgrarpJAM1pSqUlJUEhRFHOzJO7AY72IMDAxWUIWAjYGxBg89tGwoILnO7qDHnMTLDfYETRFlb4SzBGRqzhzyWeLXdZm1eN2v6odrgUyzuHitlzNAj3dIrPdAdPdPHr7VqYY2mlyOe9ZZWuMXh08n8+7+qMs8BDr5Vf3oOsI/F0KvJ3t2Qad7CaOmrx/XX/FJupjZLV/TC/i+pQfd8A7v6ZlxnRe4CUf6Ar1eWfwcbakJJJtTsfHx5vf0VvZjCNOb4vVNYxhoyKPC5JZzhHPXIkzQkjUsTrVQp0taM4UdI8ifOY4rn B B V 6 · $ - Unconventional ¡@ J ¡O · 2 $ X - No B-asymmetry ¡@ (J J ) · 2 ° 1 ¡(2OX OV ) 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 1 $ ° th-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 Kyohei Mukaida 12

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 AAADTHicjVK/b9NAFH5xIZTyoyksSCwnoqIgQXQ2QU07VWJhbBuSRmpKZDvn9lT7bNnniGL1H2BgZWACiQGxssLCwsTG0D8BMbYSAyDx2XGFGBo46+6999373r3vfE7ky0RzflgxZs6crZ6bPT934eKly/O1hSu9JExjV3Td0A/jvmMnwpdKdLXUvuhHsbADxxebzt79fH9zLOJEhuqh3o/EdmDvKOlJ19aAhrVGQw07j/q3WW56t9hAhXogFTMHWjzW2Z2RDFiSxt7BsFbnTbN9j7faDM6ydZdbcKwly4RjNnkx6lSOtXChUqUBjSgkl1IKSJAiDd8nmxJ8W2QSpwjYNmXAY Transport w/ ALP source Toy Model of two species

‣ Current equations with two breaking operators: OX and OV.

@ J1 OX OV & @ J O · = ° + · 2 = X ‣ We would like to generate @ J @ (J J ) O · B = · 1 + 2 = V

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 Q Q 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 X V B B ¡(nS OX nS OV )

=0 =0 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 6 B + ¡[nV @ J (nX nV )@ J ] = S · 1 + S + S · 2 ➡ Condition for Baryogenesis 0 nX 2nV 6= S + S nV (nX nV ) = S + S + S

✓ Should not be orthogonal to QB X V (nS ,nS ) 1-dim surf 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 1 62

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 AAADQ3icjVI9b9RAEJ0zEEL4yAUaJAosTkFUp7E5lEsKFImGjiTHJZFywbJ9e7lV1h+y1ycFKyUNf4CCCiQKlBZ+AULiD1DkJ6B0JBINSLyzHSGKHKy1uzNv583OW48XK5lq5sOace78hamL05dmLl+5em22Pnd9PY2yxBddP1JRsum5qVAyFF0ttRKbcSLcwFNiw9t9ND7fGIkklVH4VO/FYjtwd0I5kL6rATn12714KM1emgWONEOn86znqnjomk+c0nDqDW5a7QfcapswFu37bMOwF2wLhtXkYjSoGivRXG2KetSniHzKKCBBIWnYilxK8W2RRUwxsG3KgSWwZHEuaJ9mwM0QJRDhAt3FugNvq0JD+OOca Transport w/ ALP source Generalizing the statement

‣ Current equations with arbitrary breaking operators: Oα. Æ @ Ji ni OÆ for Æ 1, ,NÆ & i 1, ,N with NÆ N · = Æ = ··· = ··· ∑ X ‣ B B Æ We would like to generate Q B n i Q i w/ ni ni 0 for some Æ = i i 6= X X Æ 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 B - General coupling: ¡ nS OÆ i X ➡ Condition for Baryogenesis B Æ 0 vÆ nS 6= Æ X ✓ Should not be orthogonal to QB (nÆ) (N 1)-dim surf S 62 Æ °

Kyohei Mukaida 14

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 Transport w/ ALP source

V.Domcke, Y.Ema, KM, M.Yamada General ALP-SM coupling 2006.03148

‣ Baryogenesis if SM-ALP coupling is not orthogonal to QB E.g., axiogenesis (B+L genesis via GG~), Lepto-axiogenesis (B-L genesis via GG~) - B+L genesis via weak sphaleron WS ˜ nS W W 1 °Yu WS Ye SS Yd 1 Yu n SS G G˜ cB 24nS 22nS 21nS 18nS 18 nS S = 158 ° ° + ° ° Ye √ Yd1 ! † nS Ye eH¯ L Yu - B-L genesis via dim.5 Weinberg operator nS Yu uH¯ Q n Yd Y dH¯ †·Q 24 WS 19 SS 15 Yt 115 W S d cB L nS nS nS nS W 2 ° = 261 ° 174 + 58 ° 348 nS (L H ) · ➡ Even Random coupling typically leads to baryon asymmetry.

‣ If some processes involved in baryogenesis is not efﬁcient, multiply ∞ suppression factor: Æ . H

Kyohei Mukaida 15 2. Schwinger eﬀect & Chiral Anomaly

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 AAAD6nichVPLbtNAFL2peZQWaAsbJDYRURFsous20IRVJYTEsg/SFpoosp1JM6o9tmwnqFj5AZYICaEKJBAsEJ/Bhh/oop+AWBaJDQvOTBxVSCQdy/adM+eeO2cebuTLJGU+LkxZ585fuDh9aWb28pWrc/ML17aSsBd7ou6FfhjvuE4ifKlEPZWpL3aiWDiB64ttd/+hHt/uiziRoXqSHkSiGTh7Snak56SAnmUNN8geDQatp635EpftyspyrVrk8j3briwxgury/VqlVrTLbFqJ8rYWLhQENahNIXnUo4AEKUoR++RQgmeXbGKKgDUpAxYjkmZc0IBmkNsDS4DhAN3Hdw+93RxV6GvNxGR7qOLjjZFZpEU+4i98wt/5K//gP2O1MqOh53KAvzvMFVFr7uWNzd9nZgX4p9Q9zZqQ4YI92VNKHaoaLxLeIoNol95Qv//izcnmg43F7DZ/5J/w94GP+Rscqv4v7/O62Dg8Qz0EKoHoCqOZt836SbDUhNllwIZ71kWvbZiaq9B7blY+MIoKYxnwCLug9fT+Ng2id7SDinfgJKMScO2pAZ6u3cXI3bz+OE0HK5j8V7NBfUT67IzTPmVMrtE23nQ0Wp8YUWbQAU7/6IgXxwdbS7gh5dp6pbRaze/BNN2kW3Bu0wqt0mNaozpqK3pN7+i95VuvrLfW4ZA6VchzrtM/zfr0Fw3Y2Zw= Helical gauge & Chiral fermion

Inﬂaton w/ CS coupling to U(1)Y

µ∫ 4 g 1 µ∫ ÆY ¡ µ∫ S d x p g @µ¡@∫¡ V (¡) Yµ∫Y Yµ∫Y˜ = ° 2 ° ° 4 + 4ºf Z Ω ∑ ∏ a √† æ (i@ g Q A )√ + Æ · ° Y Æ Y Æ +··· Æ æ BY EY X ‣ Helical-gauge ﬁeld production during inﬂation.

2 0 @¥ k(k 2ªaH) AY , (¥,k) µ∫ AAAFHXichVPPaxNBFH6p0db6o6leBC+DIdJgCZNtpVEQKl56EfrDtJVsXHY3k2TIZnfZ3cTWJf+A/4AHD6LgQfwzpOBBvIhI/wTpsRUvHvx2klALJplld95873vvfW9mx/IdGUacH6amzqXPX5ieuTh76fKVq3OZ+WvbodcJbFG2PccLdi0zFI50RTmSkSN2/UCYbcsRO1brUeLf6YoglJ77JNr3RbVtNlxZl7YZATIyBmcPmO6IelRhum8GkTQdZrCY6SIyWY89g6lhvsNabAGv7rex1vckM9kayzM9kI1mVGUPjfjpovL2wFPBi6DnjUyWF4qlu3y5xGDc05a4BkNb0YowigWuRpYGY92bT30jnWrkkU0dapMglyLYDpkU4qlQkTj5wKoUAwtgSeUX1KNZxHbAEmCYQFv4NrCqDFAX6yRnqKJtVHHwBohklOPf+Qd+zD/zj/wn/zMyV6xyJFr2MVv9WOEbcy9vbP2eGNXGHFHzNGpMhAX2+J4iqlNJ9SLRm6+QpEu7n7/74tXx1v3NXHybv+NH6O8tP+Sf0KHbPbHfb4jN18ieG5vfAyqBJDWG2mtqByVY7hh9MbR58ARgCrXHo5nh4HybWNUGTBf2c3VGbVXZhScG3gXeBSf5ExJVDFhy+nVo01UeF1kThMGbBaunOIFS3FSs4AxrfL3HUOuAE8MyFJLs8R6+Ma0rT29CBh/13H8Un+pdGKkxPyGnib8j/G/O/g4l92J0/0PG+Bo1dRaJNTz5AFas0B5u9vD6stHGtlYoLhW0jeXsamlwx2foJt1C50VaoVVawx6WUfuAjuiEfqXfpA/SX9Jf+9Sp1CDmOp0Z6R9/AT49H14= = + ± ± 0 Y Y˜ 6= µ∫ h i Æ¡˙ ª 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 ≠ 4 EY BÆ Y where = ° h · i Horizon ¥ 2ºfa H

Kyohei Mukaida 17

Inﬂaton w/ CS coupling to U(1)Y

‣ How do we understand the chiral fermion production? - Asymmetry generation via the SM chiral anomaly 3 µ 2 a ˜ aµ∫ 2 ˜ µ∫ @µ JB L 2 g2Wµ∫W gY Yµ∫Y 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 + = 16º ° 0 ≥ ¥ - Pair production via the Schwinger effect 6=

Kyohei Mukaida 18 Fermion Production Landau Levels

‣ Turn off EY; B Y ﬁeld modiﬁes the dispersion relation. 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 Y

0 i @⌘ i gQ↵AY ,0 gQ↵AY ↵,R L 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 = /

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 B ± r · ± · Y ⇥ where AY , 0,0, B Y x ,0 (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 µ)=( ) Horizon

‣ Landau Level n: transverse motion; pz: parallel motion Left-handed Right-handed Energy

Pz Kyohei Mukaida 19 Fermion Production Lowest Landau Level (n=0) & Chiral Anomaly

Nielsen, Ninomiya, Phys.Lett.130B (1983) ‣ Turn on EY and see what happens. Left-handed Right-handed Energy

Kyohei Mukaida 20 Fermion Production Lowest Landau Level (n=0) & Chiral Anomaly

Nielsen, Ninomiya, Phys.Lett.130B (1983) ‣ Turn on EY and see what happens. Left-handed Right-handed

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 Y

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 Energy EY

Kyohei Mukaida 21

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 Fermion Production Lowest Landau Level (n=0) & Chiral Anomaly

Nielsen, Ninomiya, Phys.Lett.130B (1983) ‣ Turn on EY and see what happens. Left-handed Right-handed

Anti-particle prod: Pz Particle prod: g 2Q 2 g 2 Q 2 q˙ n˙ n˙ N ↵ E B q˙ n˙ n˙ N Y ↵ E B ↵,L = ↵,L ↵,L = ↵ 2 Y Y ↵,R = ↵,R ↵,R =+ ↵ 2 Y Y 4⇡ 4⇡

2 2 2 2 g Y Q↵ g Y Q↵ µ⌫ ➡ q˙ ✏ N E B ✏ N Y Y˜ w/ ✏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 ↵ = for R/L ABJ anomaly: ↵ = ↵ ↵ 2 Y Y = ↵ ↵ 2 µ⌫ 4⇡ 16⇡ ± Kyohei Mukaida 22 Fermion Production

Higher Landau Levels (n≧1) & Pair Production V.Domcke and KM 1806.08769 ‣ Turn on EY and see what happens. Left-handed Right-handed Energy

Kyohei Mukaida 23 Fermion Production

Higher Landau Levels (n≧1) & Pair Production V.Domcke and KM 1806.08769 ‣ Turn on EY and see what happens. Left-handed Right-handed

Tunneling Tunneling Energy

Pz ➡ Pair-production via Schwinger effect

Kyohei Mukaida 24 Fermion Production

Higher Landau Levels (n≧1) & Pair Production V.Domcke and KM 1806.08769 ‣ Turn on EY and see what happens. Left-handed Right-handed

Tunneling Tunneling Energy

Pz ➡ Pair-production via Schwinger effect 2 2 2 2 g Q 2⇡nBY g Q (n 1) (n 1) (n 1) (n 1) Y ↵ Y ↵ 1 n˙ n˙ n˙ n˙ N E B e EY N E B ↵,R = ↵,R = ↵,L = ↵,L = ↵ 2 Y Y = ↵ 2 Y Y 2⇡BY 4⇡ 4⇡ EY 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 n=1 e 1 X ˙ ˙ - Never contribute to asymmetries! q˙L n 1 =(n˙L n L )n 1 = 0, q˙R n 1 =(n˙R n R )n 1 = 0 | | Kyohei Mukaida 25

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 Fermion Production

Fermion Production in BY ∥ EY V.Domcke and KM 1806.08769 Left-handed Right-handed

Nielsen, Ninomiya, ‣ ABJ anomaly from Lowest Landau Level (n=0) Phys.Lett.130B (1983) 2 2 2 2 g Y Q↵ g Y Q↵ µ⌫ q˙ ✏ N E B ✏ N Y Y˜ w/ ✏↵ = for R/L N↵ = d.o.f. ↵ = ↵ ↵ 2 Y Y = ↵ ↵ 2 µ⌫ 4⇡ 16⇡ ± ‣ Schwinger pair-production from Higher ones (n=1,2,…) g 2 Q 2 (n 1) (n 1) (n 1) (n 1) Y ↵ 1 n˙ n˙ n˙ n˙ N E B ↵,R = ↵,R = ↵,L = ↵,L = ↵ 2 Y Y 2⇡BY 4⇡ EY 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 e 1 Kyohei Mukaida 26

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 AAAD6nichVPLbtNAFL2peZTyaAsbJDYRURFsrJs0VZKuKtiw7IO0hSaKbGfSjGqPLdtJVaz8AEuEhFAFEggWiM9gww+w6CcglkViw4Izk0QVEknHsufOmXPPnTMzdiNfJinzSW7GunDx0uXZK3NXr12/Mb+weHM7CXuxJ+pe6IfxruskwpdK1FOZ+mI3ioUTuL7YcQ8e6fmdvogTGaon6VEkmoGzr2RHek4K6FnWcIPs4WDQetpaKLBdK5dWapU828vV6nKJTVCprXC+aLNpBRq19XAxJ6hBbQrJox4FJEhRitgnhxI8e1QkpghYkzJgMSJp5gUNaA65PbAEGA7QA3z3MdoboQpjrZmYbA9VfLwxMvO0xN/5M5/yN/7CP/jPRK3MaOi1HKF3h7kias2/uL31+9ysAH1K3bOsKRku2NM9pdShqvEi4S0yiHbpDfX7z1+fbq1uLmX3+AP/hL/3fMJf4VD1f3mfNsTm8TnqIVAJRFcYr7xt9k+CpaasLgM2PLMuRm3D1FyF0aHZ+cAoKsxlwCOcgtbT59s0iD7RDireh5OMCsC1pwZ4unYXMw9G9SdpOtjB5L+aDeoj0ndnkvYZY3qNtvGmo/H+xIgygw5w+8dXPD852C7ZxbJd2ygX1qqj/2CW7tBdOC9ShdboMa1THbUVvaK39M7yrZfWG+t4SJ3JjXJu0T/N+vgXH0HZoQ== 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 Helical gauge & Chiral fermion

Implications on Axion Inﬂation V.Domcke and KM 1806.08769

‣ Backreaction suppresses gauge ﬁeld 2 2 Eˆ

˙ 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 g Y Y 0 @ E B a B g J BY EY t Y Y Y Y Y ˆ ˆ = + + /

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 B 4 2 f e + Y Y 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 r ⇡ ⇥ a Bˆ 2 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 Y 3 3 ˆ ˆ g Y Q↵ ⇡BY BY g Y JY = a N↵ | | coth EY 12⇡2 Eˆ H 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  ↵ ✓ Y ◆ X See also Warringa 1205.5679 e w/o backreaction w/ backreaction ‣ Primordial generation of B+L asym. h rh 2 rh 3 ↵Y rh Y ˆ ˆ q h where EY BY B+L = Y 3 = rh 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 2 ⇡ a 3Hrh 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 rh · ⌦ ↵

rh 3 ˆ ˆ 3 4 µ 6 H 2 EY BY H 2 Eˆ Bˆ /H B+L ↵Y rh rh 3 rh Y Y rh rh = · 10 T ⇡ M H 4 1014 GeV h · 105i rh ⌦ rh ↵ ⇠ Å ⇤ ã Å ã ✓ ◆ Kyohei Mukaida 27

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 AAAD6HichVPLbtNAFL2peZTy6IMNEpuIqAg20XUb2oRVJYTEsg/SRmqiynYmzbT22LKdoGLlB1ghNhUqGyqxQHwGG36ART8BsSwSGxacmTiqkEg6lu07Z849d8483MiXScp8Vpiyrly9dn36xszNW7fvzM7NL2wnYS/2RN0L/TBuuE4ifKlEPZWpLxpRLJzA9cWOe/hMj+/0RZzIUL1MjyLRCpx9JTvSc1JAjazpBtnzwWBvrsRlu7K6XKsWufzEtitLjKC6vFKr1Ip2mU0rUd7Ww/mCoCa1KSSPehSQIEUpYp8cSvDskk1MEbAWZcBiRNKMCxrQDHJ7YAkwHKCH+O6jt5ujCn2tmZhsD1V8vDEyi7TI3/kzn/M3/sI/+M9Yrcxo6Lkc4e8Oc0W0N/vm3tbvS7MC/FPqXmRNyHDBnuw Massive Fermion Production

V.Domcke, Y.Ema, KM Schwinger effect for massive fermion 1910.01205 ‣ Anomalous current equation w/ mass term B E 2 2 µ g Q µv @µ J Fµv F˜ 2im√∞¯ 5√ 5 = ° 8º2 +

See e.g., K.Fukushima+ 1807.04416 g 2Q2 ºm2 g 2Q2 g 2Q2 ºm2 q˙5 EBexp EB 2m √¯ i∞5√ EB exp 1 ' 2º2 ° g QE 2º2 ' 2º2 ° g QE ° µ | | ∂ ∑ µ ∂ ∏ ≠ Æ | | 1.0

L R 0.5

n 0.0

Energy -0.5

-1.0

-1.0 -0.5 0.0 0.5 1.0 kz Pz Kyohei Mukaida 28

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V.Domcke, Y.Ema, KM Schwinger effect for massive fermion 1910.01205 ‣ Anomalous current equation w/ mass term B E 2 2 µ g Q µv @µ J Fµv F˜ 2im√∞¯ 5√ 5 = ° 8º2 +

See e.g., K.Fukushima+ 1807.04416 g 2Q2 ºm2 g 2Q2 g 2Q2 ºm2 q˙5 EBexp EB 2m √¯ i∞5√ EB exp 1 ' 2º2 ° g QE 2º2 ' 2º2 ° g QE ° µ | | ∂ ∑ µ ∂ ∏ ≠ Æ | | - Production of W bosons is more violent. Ambjorn, Olesen, Phys.Lett.B 218 (1989) 67; Kajantie+, Nucl.Phys.B 544 (1999) 357-373 ➡ Backreact to Higgs potential

‣ Induced current 2 g ˙ Involves gauge coupling running 0 @ E B a B g J Vacuum cont. = t + + 2 ﬁnite terms, i.e., Euler-Heisenberg r ⇥ 4⇡ fa

3 g Q ⇡ Bˆ ⇡m2 1 3 ( ) ˆ ˆ g Q Eˆ gQ J ind = a E B coth e | | 6|⇡2| E|ˆ | H h i | | ✓ ◆ Kyohei Mukaida 29

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V.Domcke, Y.Ema, KM Schwinger effect for massive fermion 1910.01205 ‣ Anomalous current equation w/ mass term B E 2 2 µ g Q µv equilibrium solution for E B @ J F F˜ 2im√∞¯ √ -3 µ 5 2 µv 5 10 = ° + PBH overproduction 8º 100

10-See5 e.g., K.Fukushima+ 1807.0441630 2 2 2 2 2 2 2 2

g Q ºm g Q 2 s g Q ºm

10 q˙5 EBexp EB 2m √¯ i∞5√ EB exp Heavy1 ' 2º2 ° g QE 2º2 -7 ' 2º2 ° g QE ° µ | | ∂ 10 ∑ µ ∂ ∏ ≠ Æ m/H = 0 | | - Production of W bosons is more violent. Ambjorn, Olesen, Phys.Lett.B 218 (1989) 67; Kajantie+, Nucl.Phys.B 544 (1999)CMB 357-373 10-9 ➡ Backreact to Higgs potential 0 10 20 30 40 50 ‣ Induced current N [e-folds] 2 g ˙ Involves gauge coupling running 0 @ E B a B g J Vacuum cont. = t + + 2 ﬁnite terms, i.e., Euler-Heisenberg r ⇥ 4⇡ fa

3 g Q ⇡ Bˆ ⇡m2 1 3 ( ) ˆ ˆ g Q Eˆ gQ J ind = a E B coth e | | 6|⇡2| E|ˆ | H h i | | ✓ ◆ Kyohei Mukaida 30

V.Domcke, Y.Ema, KM, M.Yamada Spontaneous Baryo/Leptogensis 2006.03148 ‣ We can generate baryon asymmetry for almost any SM-ALP couplings. - Complementary to Keisuke and Raymond’s talk

°Y ˙ 1 WS Ye SS Yd u1 Yu 2 cB 24n 22n 21n 18n 18 n q c T = 158 S ° S ° S + S ° ° S B = B √ Yd1 ! f ˙ 24 WS 19 SS 15 Yt 115 W 2 cB L nS nS nS nS qB L = cB L T ° = 261 ° 174 + 58 ° 348 f