Friday, February 10, 2017

tHWZ - latest formulation

During a discussion at PF, I found the following interesting way to think of these quantities:

mH ~ √2 mZ
mt ~ 2 mZ
Hvev ~ 2 √2 mZ
mW ~ √7 / 3 mZ

The last one may look a little odd, but it allows us to approximate sin2 of the Weinberg angle as 2/9.

The impetus was a comment by @arivero in which he pointed out that a tHWZ mass estimate due to Hans de Vries implies

(mW2 - mH2) / (mZ2 - mt2) = 3/8

Now in many GUTs, at the GUT scale, we have that

mW2 / mZ2 = 3/8

So it's as if (mW2 - mH2) / (mZ2 - mt2) is almost invariant under renormalization group flow, with mH = mt = 0 at the GUT scale.

We could even speculate that my set of four approximations above is an infrared fixed point. (The approximations are not exact, but one could think of these as valid at tree level.)

Unfortunately I don't see how any of this makes sense in terms of Hans de Vries's original physical hypothesis.

Anyway, I find that the LC&P formula also works neatly using the four approximations. And I would remark again that mZ is very close to the standard model's μ parameter


  1. 1) [(Mw)^2+(MH)^2]/[(Mz)^2+(Mt)^2]=ln[sqr(Pi)]

    2) [(Mw)^2+(MH)^2]/[(Mz)^2+(Mt)^2]=(7/e)-2

    3) [(Mw)^2+(MH)^2]/[(Mz)^2+(Mt)^2]= [ln(Pi)]^7-2

    MW = 80.384 Gev
    MH = 125.0901 Gev
    Mz = 91.1876 Gev
    Mt = 173.7 Gev

    (3/8)x [(Mw)^2+(MH)^2]/[(Mz)^2+(Mt)^2] = (cos(13.04°))^2

    13.04° = main cabibo angle , quark matrix mixing

  2. Axiomatization of Unification Theories: the Fundamental Role of the Partition Function of Non-Trivial Zeros (Imaginary Parts) of Riemann's Zeta Function. Two Fundamental Equations that Unify Gravitation with Quantum Mechanics

  3. MH/me = 4(2Pi)^6 x cos(beta)

    MH = higgs boson mass
    me = electron mass
    Beta = 84°(supersimmetry angle )

  4. [(mW2 - mH2) / (mZ2 - mt2)]/[(mW2 -mH2) / (mZ2 + mt2)]=-,lnln(Phi)

    Phi= golden number= (1+sqr(5))/2

    [(mW2 - mH2) / (mZ2 - mt2)]+[(mW2 + mH2) / (mZ2 + mt2)]=sin(84°)

    84°= supetsymmetry angle/ beta

  5. Fascinating stuff. I've been meaning to blog about it when I get a chance, especially the work by Hans de Vries.

  6. (Mtau + Mmuon + Melectron)/Melectron=a



    2*Euler-Mascheroni constant=d

    (alpha)^-1 = 137.035999173

    (alpha)^-1 = 137 + (ln137/137) + (c^2*b)^-1 - (a^2*d)^-1