mirror of
https://github.com/allaunthefox/Research-Stack.git
synced 2026-07-30 18:56:16 +00:00
e5fb0a5f4d
Lean: update Semantics modules, add new numerics/physics data files Hardware: update FPGA bitstreams (tangnano9k_uart_loopback) Infra: k3s-flake tests, netcup-vps configuration, VCN compute substrate Docs: ARCHITECTURE, specs, citation updates
177 lines
9.4 KiB
Text
177 lines
9.4 KiB
Text
/-
|
||
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
|