/-
SMEFTExtension.lean — Standard Model Effective Field Theory

This module formalizes the SMEFT framework for extending the Standard Model
to account for observed anomalies (muon g-2, B→K*μμ, W mass, etc.).

The key equation:
    H_SMEFT = H_SM + Σ_i (C_i^(6)/Λ²) O_i^(6) + Σ_j (C_j^(8)/Λ⁴) O_j^(8)

Where:
  H_SM = Standard Model Hamiltonian
  Λ = energy scale of new physics
  C_i = Wilson coefficients (tuning knobs)
  O_i = higher-dimensional operators (new interactions)

References:
  - arXiv:2505.xxxxx — LHCb B→K*μμ penguin decay anomaly
  - Grzadkowski et al. (2010) — SMEFT operator basis
  - Brivio & Trott (2017) — SMEFT pedagogical review

Part of the OTOM TreeDIAT/PIST family.
-/

import Semantics.FixedPoint
import Semantics.ForceModifiedArrhenius
import Semantics.Q16_16Numerics

namespace Semantics.SMEFTExtension

open Semantics.Q16_16
open Semantics.ForceModifiedArrhenius

-- ═══════════════════════════════════════════════════════════════════════════
-- §1  WILSON COEFFICIENTS
-- ═══════════════════════════════════════════════════════════════════════════

/-- Wilson coefficients for dimension-6 operators.
    These are the "tuning knobs" that encode BSM physics. -/
structure WilsonCoefficients6 where
  C_1  : Q16_16  -- O_1: (L̄γ_μL)(L̄γ^μL) - same-flavor lepton current
  C_2  : Q16_16  -- O_2: (q̄γ_μq)(L̄γ^μL) - quark-lepton current
  C_3  : Q16_16  -- O_3: (q̄γ_μT^Aq)(L̄γ^μT^AL) - color-octet
  C_4  : Q16_16  -- O_4: (q̄γ_μq)(q̄γ^μq) - four-quark
  C_5  : Q16_16  -- O_5: (q̄q̄)(ll) - scalar four-fermion
  C_6  : Q16_16  -- O_6: (q̄q̄)(q̄q) - scalar four-quark
  C_7  : Q16_16  -- O_7: (ēγ_μe)(H†D^μH) - dipole-like
  C_8  : Q16_16  -- O_8: (q̄σ_μνq)(Hσ^μνH) - chromomagnetic
  C_9  : Q16_16  -- O_9: (q̄γ_μq)(ēγ^μe) - vector lepton current ← THE ANOMALOUS ONE
  C_10 : Q16_16  -- O_10: (q̄γ_μq)(ēγ^μγ₅e) - axial lepton current
  deriving Repr

/-- SM values at μ = m_b (approximate). -/
def smWilson : WilsonCoefficients6 :=
  { C_1  := Q16_16.ofRawInt (-196608)  -- ~-3.0
  , C_2  := Q16_16.ofRawInt 13107      -- ~0.2
  , C_3  := Q16_16.zero
  , C_4  := Q16_16.ofRawInt (-65536)   -- ~-1.0
  , C_5  := Q16_16.zero
  , C_6  := Q16_16.zero
  , C_7  := Q16_16.ofRawInt (-69478)   -- ~-0.3
  , C_8  := Q16_16.ofRawInt (-45875)   -- ~-0.7
  , C_9  := Q16_16.ofRawInt 279835     -- ~+4.27 ← SM prediction
  , C_10 := Q16_16.ofRawInt (-262144) } -- ~-4.0

-- ═══════════════════════════════════════════════════════════════════════════
-- §2  BSM DEVIATIONS (what anomalies tell us)
-- ═══════════════════════════════════════════════════════════════════════════

/-- The deviation in Wilson coefficients from BSM physics. -/
structure BSMDelta where
  delta_C7  : Q16_16  -- electromagnetic penguin shift
  delta_C9  : Q16_16  -- vector lepton current shift ← THE 4σ ANOMALY
  delta_C10 : Q16_16  -- axial lepton current shift
  deriving Repr

/-- LHCb fit result: δC_9 ≈ -1.1 ± 0.3. -/
def lhcbAnomaly : BSMDelta :=
  { delta_C7  := Q16_16.ofRawInt 0           -- consistent with 0
  , delta_C9  := Q16_16.ofRawInt (-72089)    -- ≈ -1.1
  , delta_C10 := Q16_16.ofRawInt 0 }         -- consistent with 0

/-- Effective Wilson coefficients with BSM contribution. -/
def effectiveWilson (sm : WilsonCoefficients6) (bsm : BSMDelta) : WilsonCoefficients6 :=
  { sm with
    C_7  := Q16_16.add sm.C_7 bsm.delta_C7
    C_9  := Q16_16.add sm.C_9 bsm.delta_C9
    C_10 := Q16_16.add sm.C_10 bsm.delta_C10 }

-- ═══════════════════════════════════════════════════════════════════════════
-- §3  ENERGY SCALE EXTRACTION
-- ═══════════════════════════════════════════════════════════════════════════

/-- Extract BSM energy scale from Wilson coefficient deviation.
    Λ² ~ g²/(4G_F |V_tb V_ts*| α |δC_9|)
    
    For δC_9 ≈ -1.1: Λ ~ 30-40 TeV -/
def extractEnergyScale (bsm : BSMDelta) : Q16_16 :=
  -- Λ ≈ 35 TeV / √(|δC_9|/1.1) (simplified)
  let abs_DC9 := Q16_16.abs bsm.delta_C9
  let scale_35TeV := Q16_16.ofRawInt 2293760  -- 35 TeV in Q16_16 units
  Q16_16.div scale_35TeV (Semantics.Q16_16Numerics.sqrt abs_DC9)

-- ═══════════════════════════════════════════════════════════════════════════
-- §4  OPERATOR STRUCTURE
-- ═══════════════════════════════════════════════════════════════════════════

/-- The dimension-6 operators as field bilinears.
    O_i = (ψ̄₁Γψ₂)(ψ̄₃Γψ₄) where Γ are Dirac matrices. -/
structure Dimension6Operator where
  name     : String
  fermion1 : String  -- first fermion line
  fermion2 : String  -- second fermion line
  dirac    : String  -- Dirac structure (V, A, S, P, T)
  color    : String  -- color structure (singlet, octet)
  deriving Repr

/-- The key operators for B→K*μμ anomalies. -/
def relevantOps : Array Dimension6Operator :=
  #[ ⟨"O_7", "s_bar", "b", "T", "singlet"⟩
   , ⟨"O_9", "s_bar", "b", "V", "singlet"⟩
   , ⟨"O_10", "s_bar", "b", "A", "singlet"⟩ ]

-- ═══════════════════════════════════════════════════════════════════════════
-- §5  DECAY RATE COMPUTATION
-- ═══════════════════════════════════════════════════════════════════════════

/-- Differential decay rate for B→K*μμ:
    dΓ/dq² ∝ |C_9^eff F_⊥ + (2m_b/q²) C_7 F_T|² + |C_10|² |F_⊥|² -/
def differentialRate (C9eff C7 C10 F_perp F_T mb q2 : Q16_16) : Q16_16 :=
  let term1 := Q16_16.add C9eff (Q16_16.div (Q16_16.mul (Q16_16.ofRawInt 131072) mb) q2)
  let term2 := Q16_16.mul term1 F_perp
  let term3 := Q16_16.mul (Q16_16.div (Q16_16.mul (Q16_16.ofRawInt 131072) mb) q2) (Q16_16.mul C7 F_T)
  let amp_sq := Q16_16.add (Q16_16.mul (Q16_16.add term2 term3) (Q16_16.add term2 term3))
                           (Q16_16.mul (Q16_16.mul C10 C10) (Q16_16.mul F_perp F_perp))
  amp_sq

-- ═══════════════════════════════════════════════════════════════════════════
-- §6  LEPTOQUARK MODEL (BSM candidate)
-- ═══════════════════════════════════════════════════════════════════════════

/-- Leptoquark parameters.
    A scalar leptoquark S₁ mediating b→sμμ. -/
structure Leptoquark where
  mass     : Q16_16  -- M_LQ in TeV
  lambda_b : Q16_16  -- coupling to b quark
  lambda_s : Q16_16  -- coupling to s quark
  deriving Repr

/-- Extract leptoquark mass from δC_9.
    M_LQ = √(π |λ_b λ_s*| / (α |V_tb V_ts*| |δC_9|)) -/
def extractLeptoquarkMass (lq : Leptoquark) (delta_C9 : Q16_16) : Q16_16 :=
  let alpha := Q16_16.ofRawInt 7733  -- α ≈ 1/137
  let vtb_vts := Q16_16.ofRawInt 2687  -- |V_tb V_ts*| ≈ 0.041
  let pi := Q16_16.ofRawInt 205887  -- π in Q16_16
  let numerator := Q16_16.mul pi (Q16_16.abs (Q16_16.mul lq.lambda_b lq.lambda_s))
  let denominator := Q16_16.mul (Q16_16.mul alpha vtb_vts) (Q16_16.abs delta_C9)
  Semantics.Q16_16Numerics.sqrt (Q16_16.div numerator denominator)

-- ═══════════════════════════════════════════════════════════════════════════
-- §7  EXECUTABLE WITNESSES
-- ═══════════════════════════════════════════════════════════════════════════

-- SM Wilson coefficient C_9
#eval smWilson.C_9  -- expect: 279835 (≈ +4.27)

-- Effective C_9 with BSM
def testEff := effectiveWilson smWilson lhcbAnomaly
#eval testEff.C_9  -- expect: 279835 + (-72089) = 207746 (≈ +3.17)

-- Energy scale from anomaly
#eval extractEnergyScale lhcbAnomaly  -- expect: ~35 TeV / √1.0 = ~35 TeV

-- Leptoquark mass (λ = 1, δC_9 = -1.1)
def testLQ : Leptoquark := ⟨Q16_16.ofRawInt 65536, Q16_16.one, Q16_16.one⟩
#eval extractLeptoquarkMass testLQ (Q16_16.ofRawInt (-72089))  -- expect: ~1-10 TeV

end Semantics.SMEFTExtension
