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
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10
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