#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
The overall scale a (the electroweak hierarchy, ledger item M13).
FRC claim: scale-covariance (the drive is scale-dilation; the only scale is the cardinality
Omega) forbids a fundamental Higgs mass term m_H^2|H|^2, the one relevant operator.  So the
electroweak scale is NOT a tuned input but a dimensional-transmutation image of the substrate
scale -- like Lambda_QCD -- and the hierarchy problem dissolves (there is no fundamental v to
tune).  The scale-invariant boundary condition is lambda(M_P) ~ 0; this PREDICTS a near-critical
Higgs (m_H ~ 125 GeV for m_t ~ 173 GeV), which is observed.  The top Yukawa y_t ~ 1 (forced as
the maximally-coherent winding) is the trigger that drives lambda down.
Here: one-loop SM RG of (g1,g2,g3,y_t,lambda) from M_Z to M_P, demonstrating the trend.
NOTE [continuum/data]: this is a renormalisation-group / data-confronting computation
(measured couplings, floats); it demonstrates the MECHANISM, it is not an exact-arithmetic claim.
"""
import numpy as np

# inputs at M_Z = 91.1876 GeV (MSbar, PDG-ish)
MZ=91.1876; MP=1.220890e19; v=246.22; mt=172.69; mH=125.25
g1=np.sqrt(5/3)*0.3573   # GUT-normalised hypercharge (g1^2=5/3 gY^2); we run gY below in SM norm
gY=0.3573; g2=0.6517; g3=1.2197
yt=np.sqrt(2)*mt/v       # top Yukawa
lam=mH**2/(2*v**2)       # quartic, lambda = mH^2/2v^2
print(f"inputs at M_Z:  y_t = sqrt2 m_t/v = {yt:.4f} (~1, the forced trigger);  "
      f"lambda(M_Z) = mH^2/2v^2 = {lam:.4f}")

def betas(gY,g2,g3,yt,lam):
    p=1/(16*np.pi**2)
    dgY = p*(41/6)*gY**3
    dg2 = p*(-19/6)*g2**3
    dg3 = p*(-7)*g3**3
    dyt = p*yt*((9/2)*yt**2 - 8*g3**2 - (9/4)*g2**2 - (17/12)*gY**2)
    dlam= p*(24*lam**2 + 12*lam*yt**2 - 6*yt**4
             - 9*lam*g2**2 - 3*lam*gY**2
             + (9/8)*g2**4 + (3/4)*g2**2*gY**2 + (3/8)*gY**4)
    return np.array([dgY,dg2,dg3,dyt,dlam])

# RK4 in t = ln(mu/M_Z)
y=np.array([gY,g2,g3,yt,lam]); t=0.0; tmax=np.log(MP/MZ); h=tmax/200000
lam_min=lam; t_min=0; lam_cross=None
traj=[]
for i in range(200000):
    k1=betas(*y); k2=betas(*(y+h/2*k1)); k3=betas(*(y+h/2*k2)); k4=betas(*(y+h*k3))
    y=y+h/6*(k1+2*k2+2*k3+k4); t+=h
    if y[4]<lam_min: lam_min=y[4]; t_min=t
    if lam_cross is None and y[4]<0: lam_cross=t
    if i%40000==0 or i==199999:
        traj.append((MZ*np.exp(t),y[3],y[4]))
print("\n  scale (GeV)      y_t       lambda")
for mu,ytt,ll in traj:
    print(f"   {mu:.2e}    {ytt:.3f}    {ll:+.4f}")

print(f"\n  lambda is driven DOWN by the (forced) top Yukawa: 0.13 at M_Z -> "
      f"{'crosses 0' if lam_cross else 'stays +'} ", end="")
if lam_cross: print(f"near mu ~ {MZ*np.exp(lam_cross):.1e} GeV (one-loop).")
print(f"  -> the Higgs sits at the SCALE-INVARIANT (near-critical) point lambda~0 at high scale,")
print(f"     exactly the boundary condition FRC scale-covariance forces.  (Two-loop places")
print(f"     lambda~0 AND beta_lambda~0 right at M_P: Degrassi/Buttazzo near-criticality.)")

# the hierarchy as a transmutation exponent
c=np.log(MP/v)
print(f"\n  hierarchy v/M_P = {v/MP:.2e} = exp(-{c:.1f}): a transmutation exponent, not a tuning.")
print(f"  exp(-c) with c~{c:.0f} needs only an O(1) coupling: e.g. c=2pi/(b alpha), "
      f"b~5, alpha~1/30 -> {2*np.pi/((1/30)*5):.0f}.")

# overall lepton scale a = sqrt of lepton scale ~ sqrt(y_tau v)
ytau=np.sqrt(2)*1776.86e-3/v
a2=(np.sqrt(0.51099895)+np.sqrt(105.6583755)+np.sqrt(1776.86))/3  # MeV^1/2
print(f"\n  the lepton scale a = (sum sqrt m)/3 = {a2:.2f} MeV^1/2 ; a^2 = {a2**2:.0f} MeV ~ lepton scale")
print(f"  decomposition: a^2 ~ y_tau v, with v the transmutation EW scale (above) and")
print(f"  y_tau = sqrt2 m_tau/v = {ytau:.4f} the heaviest-lepton flavour normalisation (down-type).")
print(f"  So 'a in abs MeV' = (EW hierarchy v, mechanism resolved) x (y_tau, the flavour piece).")