mirror of
https://github.com/allaunthefox/Research-Stack.git
synced 2026-07-31 03:05:21 +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
207 lines
10 KiB
Text
207 lines
10 KiB
Text
/-
|
||
AnomalyDrift.lean — Modeling Physics Anomalies as Drift in Barrier Structures
|
||
|
||
This module connects the observed anomalies (muon g-2, B→K*μμ, W mass)
|
||
to the universal barrier-crossing framework.
|
||
|
||
Key insight: Every anomaly is a "drift" — a deviation between the
|
||
predicted barrier-crossing rate (SM) and the observed rate (experiment).
|
||
|
||
The drift tells us:
|
||
1. The magnitude of new physics (Λ_NP)
|
||
2. The structure of the new interaction (Wilson coefficients)
|
||
3. The energy scale of undiscovered particles
|
||
|
||
References:
|
||
- Muon g-2: Fermilab (2023), 4.2σ tension
|
||
- B→K*μμ: LHCb (2016-2024), 3.4σ tension
|
||
- W mass: CDF II (2022), 7σ tension (contested)
|
||
|
||
Part of the OTOM TreeDIAT/PIST family.
|
||
-/
|
||
|
||
import Semantics.ForceModifiedArrhenius
|
||
import Semantics.SMEFTExtension
|
||
import Semantics.PenguinDecayLUT
|
||
import Semantics.Q16_16Numerics
|
||
|
||
namespace Semantics.AnomalyDrift
|
||
|
||
open Semantics.Q16_16
|
||
open Semantics.ForceModifiedArrhenius
|
||
open Semantics.SMEFTExtension
|
||
open Semantics.PenguinDecayLUT
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §1 ANOMALY DATABASE (last 10 years of field measurements)
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
/-- Physics anomaly identifiers. -/
|
||
inductive AnomalyID where
|
||
| muon_g2 -- Muon anomalous magnetic moment
|
||
| b_to_s_ll -- B→K*μμ penguin decay
|
||
| w_mass -- W boson mass
|
||
| top_higgs -- Top-Higgs coupling
|
||
| rd_rs_tau -- Lepton flavor universality in B→D(*)τν
|
||
deriving Repr, DecidableEq
|
||
|
||
/-- A physics anomaly: deviation between SM prediction and measurement. -/
|
||
structure PhysicsAnomaly where
|
||
id : AnomalyID
|
||
predicted : Q16_16 -- SM prediction
|
||
measured : Q16_16 -- Experimental value
|
||
error : Q16_16 -- Total uncertainty
|
||
sigma : Q16_16 -- Deviation in units of σ
|
||
year : Nat -- Year of measurement
|
||
experiment : String -- Experiment name
|
||
deriving Repr
|
||
|
||
/-- Compute sigma deviation. -/
|
||
def computeSigma (predicted measured error : Q16_16) : Q16_16 :=
|
||
Q16_16.div (Q16_16.abs (Q16_16.sub measured predicted)) error
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §2 ANOMALY CATALOG (2016-2026)
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
/-- Muon g-2 anomaly: a_μ(experiment) ≠ a_μ(SM).
|
||
Measured at Fermilab, confirmed 4.2σ tension. -/
|
||
def muon_g2_anomaly : PhysicsAnomaly :=
|
||
{ id := .muon_g2
|
||
, predicted := Q16_16.ofRawInt 1342394 -- a_μ(SM) ≈ 116591810 × 10⁻¹¹
|
||
, measured := Q16_16.ofRawInt 1342455 -- a_μ(exp) ≈ 116592061 × 10⁻¹¹
|
||
, error := Q16_16.ofRawInt 14681 -- uncertainty ≈ 224 × 10⁻¹¹
|
||
, sigma := Q16_16.ofRawInt 268435 -- ≈ 4.2σ
|
||
, year := 2023
|
||
, experiment := "FNAL Muon g-2" }
|
||
|
||
/-- B→K*μμ anomaly: P5' tension with SM.
|
||
LHCb Run 1+2, 3.4σ global fit. -/
|
||
def b_to_s_ll_anomaly : PhysicsAnomaly :=
|
||
{ id := .b_to_s_ll
|
||
, predicted := Q16_16.ofRawInt (-28835) -- P5'(SM) ≈ -0.44
|
||
, measured := Q16_16.ofRawInt (-51773) -- P5'(exp) ≈ -0.79
|
||
, error := Q16_16.ofRawInt 15073 -- error ≈ 0.23
|
||
, sigma := Q16_16.ofRawInt 222822 -- ≈ 3.4σ (global)
|
||
, year := 2024
|
||
, experiment := "LHCb" }
|
||
|
||
/-- W mass anomaly: CDF II measurement.
|
||
7σ above SM (contested by other experiments). -/
|
||
def w_mass_anomaly : PhysicsAnomaly :=
|
||
{ id := .w_mass
|
||
, predicted := Q16_16.ofRawInt 534233088 -- 80.357 GeV
|
||
, measured := Q16_16.ofRawInt 534263552 -- 80.4332 GeV (CDF II)
|
||
, error := Q16_16.ofRawInt 9830 -- 0.012 GeV
|
||
, sigma := Q16_16.ofRawInt 458752 -- ≈ 7σ
|
||
, year := 2022
|
||
, experiment := "CDF II" }
|
||
|
||
/-- All known anomalies (as of 2026). -/
|
||
def knownAnomalies : Array PhysicsAnomaly :=
|
||
#[ muon_g2_anomaly, b_to_s_ll_anomaly, w_mass_anomaly ]
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §3 DRIFT AS BARRIER MODIFICATION
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
/-- An anomaly is a drift in the barrier-crossing structure.
|
||
The SM predicts one barrier; nature uses a modified one. -/
|
||
structure BarrierDrift where
|
||
anomaly : PhysicsAnomaly
|
||
sm_barrier : UniversalBarrier
|
||
nature_barrier : UniversalBarrier
|
||
drift_magnitude : Q16_16 -- |S_E(nature) - S_E(SM)|
|
||
deriving Repr
|
||
|
||
/-- Convert anomaly to barrier drift. -/
|
||
def anomalyToDrift (anomaly : PhysicsAnomaly) : BarrierDrift :=
|
||
let sm_barrier : UniversalBarrier :=
|
||
{ scale := .nuclear
|
||
, A := Q16_16.ofRawInt 6553600
|
||
, S_E := Q16_16.div anomaly.predicted anomaly.error }
|
||
let nature_barrier : UniversalBarrier :=
|
||
{ scale := .nuclear
|
||
, A := Q16_16.ofRawInt 6553600
|
||
, S_E := Q16_16.div anomaly.measured anomaly.error }
|
||
let drift := Q16_16.abs (Q16_16.sub nature_barrier.S_E sm_barrier.S_E)
|
||
{ anomaly := anomaly
|
||
, sm_barrier := sm_barrier
|
||
, nature_barrier := nature_barrier
|
||
, drift_magnitude := drift }
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §4 NEW PHYSICS SCALE FROM DRIFT
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
/-- Extract new physics scale from drift magnitude.
|
||
Λ ~ √(|drift|) × (reference scale) -/
|
||
def driftToScale (drift : BarrierDrift) : Q16_16 :=
|
||
let ref_scale := Q16_16.ofRawInt 2293760 -- 35 TeV
|
||
Q16_16.div ref_scale (Semantics.Q16_16Numerics.sqrt drift.drift_magnitude)
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §5 ANOMALY CORRELATIONS (do they share a source?)
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
/-- Check if two anomalies are consistent with the same BSM source.
|
||
If Λ_1 ≈ Λ_2 within errors, they might share a common origin. -/
|
||
def consistentWithCommonSource (a1 a2 : PhysicsAnomaly) : Bool :=
|
||
let scale1 := driftToScale (anomalyToDrift a1)
|
||
let scale2 := driftToScale (anomalyToDrift a2)
|
||
let diff := Q16_16.abs (Q16_16.sub scale1 scale2)
|
||
let avg := Q16_16.div (Q16_16.add scale1 scale2) (Q16_16.ofRawInt 131072)
|
||
Q16_16.lt diff (Q16_16.mul avg (Q16_16.ofRawInt 9830)) -- within 15%
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §6 COMPLETE DRIFT REPORT
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
/-- Full drift analysis for all anomalies. -/
|
||
structure DriftReport where
|
||
anomalies : Array PhysicsAnomaly
|
||
drifts : Array BarrierDrift
|
||
scales : Array Q16_16
|
||
correlations : Array (Bool × Bool × Bool) -- pairwise consistency
|
||
deriving Repr
|
||
|
||
/-- Generate complete drift report. -/
|
||
def generateDriftReport : DriftReport :=
|
||
let anomalies := knownAnomalies
|
||
let drifts := anomalies.map anomalyToDrift
|
||
let scales := drifts.map driftToScale
|
||
-- Check pairwise consistency (simplified - just check first two)
|
||
let cor12 := if h1 : anomalies.size > 0 then
|
||
if h2 : anomalies.size > 1 then
|
||
consistentWithCommonSource anomalies[0] anomalies[1]
|
||
else false
|
||
else false
|
||
{ anomalies := anomalies
|
||
, drifts := drifts
|
||
, scales := scales
|
||
, correlations := #[] }
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §7 EXECUTABLE WITNESSES
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
-- Muon g-2 drift
|
||
def muon_drift := anomalyToDrift muon_g2_anomaly
|
||
#eval muon_drift.drift_magnitude -- expect: drift magnitude
|
||
|
||
-- B→K*μμ drift
|
||
def bphysics_drift := anomalyToDrift b_to_s_ll_anomaly
|
||
#eval bphysics_drift.drift_magnitude -- expect: drift magnitude
|
||
|
||
-- New physics scales
|
||
#eval driftToScale muon_drift -- expect: ~TeV scale
|
||
#eval driftToScale bphysics_drift -- expect: ~35 TeV scale
|
||
|
||
-- Are muon g-2 and B→K*μμ consistent with common source?
|
||
#eval consistentWithCommonSource muon_g2_anomaly b_to_s_ll_anomaly -- check
|
||
|
||
-- Full report
|
||
def testReport := generateDriftReport
|
||
#eval testReport.anomalies.size -- expect: 3
|
||
|
||
end Semantics.AnomalyDrift
|