2024-06-07 14:37:09 -04:00
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/-
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Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
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Released under Apache 2.0 license.
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Authors: Joseph Tooby-Smith
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-/
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import HepLean.StandardModel.HiggsBoson.Basic
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2024-06-07 14:40:28 -04:00
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/-!
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# The Two Higgs Doublet Model
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The two Higgs doublet model is the standard model plus an additional Higgs doublet.
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2024-06-08 01:50:39 +02:00
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Currently this file contains the definition of the 2HDM potential.
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2024-06-07 14:40:28 -04:00
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-/
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2024-06-07 14:37:09 -04:00
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namespace TwoHDM
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open StandardModel
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open ComplexConjugate
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noncomputable section
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/-- The potential of the two Higgs doublet model. -/
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def potential (Φ1 Φ2 : higgsField)
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(m11Sq m22Sq lam₁ lam₂ lam₃ lam₄ : ℝ) (m12Sq lam₅ lam₆ lam₇ : ℂ) (x : spaceTime) : ℝ :=
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m11Sq * Φ1.normSq x + m22Sq * Φ2.normSq x
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- (m12Sq * (Φ1.innerProd Φ2) x + conj m12Sq * (Φ2.innerProd Φ1) x).re
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+ 1/2 * lam₁ * Φ1.normSq x ^ 2 + 1/2 * lam₂ * Φ2.normSq x ^ 2
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+ lam₃ * Φ1.normSq x * Φ2.normSq x
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+ lam₄ * ‖Φ1.innerProd Φ2 x‖
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+ (1/2 * lam₅ * (Φ1.innerProd Φ2) x ^ 2 + 1/2 * conj lam₅ * (Φ2.innerProd Φ1) x ^ 2).re
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+ (lam₆ * Φ1.normSq x * (Φ1.innerProd Φ2) x + conj lam₆ * Φ1.normSq x * (Φ2.innerProd Φ1) x).re
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+ (lam₇ * Φ2.normSq x * (Φ1.innerProd Φ2) x + conj lam₇ * Φ2.normSq x * (Φ2.innerProd Φ1) x).re
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end
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end TwoHDM
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