Over two years ago, a series of posts on tHWZ relations was launched here, starting with the observation that
<ϕ> ~ √2 mt, mt ~ √2 mH
which I was prompted to record, when Andrew Oh-Willeke remarked that
<ϕ> ~ 2 mH
(Where <ϕ>, also often written as v, is the Higgs field "vacuum expectation value".)
Recently a paper appeared on arxiv, noting that first relation, in the form
4 mH2 = 2 mt2 = v2
and Andrew commented that
"I think it is more likely that the observed relationship is really an approximation of the relationships
sum((Fi(^2)=v^2/2 and sum((Bj)^2)=v^2/2 for all fundamental fermion rest masses Fi and fundamental boson rest masses Bj"
which is an aspect of the LC&P sum rule, of which he also says that it is
"quite a bit more profound than the fact that the heaviest fermion by
itself accounts for about half of the Higgs vev squared, or that the
Higgs mass square accounts for about a quarter of the Higgs vev squared."
I agree that the LC&P sum rule looks to be the fundamental thing here. But there is an interesting final twist which he didn't note.
To recapitulate:
1. The sum of the squares of all the fundamental particle masses, is approximately the square of the Higgs VEV.
2. The contributions to this total from bosons and fermions are approximately equal. (Given the love of supersymmetry in the particle physics community, it really is remarkable that this isn't visibly being talked about.)
3. The top quark is responsible for the great majority of the fermion contribution, and thus about half of the total.
4. The Higgs boson is responsible for about half the bosonic contribution, and thus about a quarter of the total.
So where does the rest of the bosonic contribution come from? It comes from the W and Z bosons. So we have a fifth fact:
5. The W and Z bosons are responsible for the other half of the bosonic contribution, and thus for the remaining quarter of the total.
If we write this up as an equation, we get
mH2 ~ mW2 + mZ2 ~ 1/2 mt2
The first part of this equation appeared as a blog comment by S. Vik, who is apparently a retired physicist from Wilfrid Laurier University in Canada. At the time I gave it a low probability of being meaningful, but I did record it. It would be ironic if it is yet another genuine clue to what lies beneath the standard model.
Fair points.
ReplyDeleteThe Higgs Vacuum.The Particles Of The Standard Model And The Compliance With the Energy-Momentum Equation. The Necessary Existence Of the Axion. Stop Quark Mass
ReplyDeleteAuthors: A.Garcés Doz
In this paper it is demonstrated that all the masses of the standard model particles; including the Higgs boson h; with nonzero rest mass, comply with the equation of energy-momentum. The model Higgs vacuum corresponds to a virtual vacuum, for which the contribution of particles with zero rest mass is null (photon, gluon, graviton) .With the best values of the masses of the particles (Particle Data Group), it is found that axion mass has to be extremely small. Also the theoretical model Higgs vacuum, a completely new model based on the lattice R8 and sixteen matrix elements of energy; corresponding to the four solutions of the equation of energy-momentum (isomorphism with the four components of the scalar field. One complex doublet ); to be factored into two factors with real and imaginary components of energy. Of this new model Higgs vacuum; naturally get the beta angle. Stop quark mass is obtained by solving the equation of radiative mass correction Higss boson, h, to one loop. The exact determination of the beta angle, allows calculating the mass of the stop of about 1916 GeV. Similarly, a mass for axion is proposed of around 110 micro eV
http://vixra.org/abs/1408.0162
This said, the values of mH2 ~ mW2 + mZ2 ~ 1/2 mt2 are as follows:
ReplyDeletemH2= 15662.5 (15,562.56-15,750.25) (at best fit value of 125.15 +/- 0.4 GeV) . .
mW2+mZ2= 14,775.47 (using global best fit value for mW of 80.376 GeV and the mV of 91.876 GeV)) or 14776.92 (with a separate world average of 80.385 GeV for mW).
mt/2=14,999.12 (14,860.88-15,138.00)(using global best fit value of 173.2 +/- 0.8 GeV )
The first two are not compatible even at two sigma. The latter can be compatible with either at two sigma, but not with both at the same time.
LC&P sum rule has no mechanism or theoretical model behind it. On the other hand, it is the reflection of the G-string.
ReplyDeleteIn G-string, there should be a vacuum boson {as vacuum [d (blue), -d (-yellow)] quark pair} transformed into vacuum {u (yellow), -u (-blue)}, see http://www.prequark.org/pq11.htm .
This vacuum boson's mass should be:
{Vacuum energy (vev) divided by 2} + {a push over energy (vacuum fluctuation}
The observed vev = 246 Gev.
If the vf (vacuum fluctuation) is about 1% of vev, then
The Vacuum Boson mass = 246/2 + 2.46 = 125.46 Gev.
This above calculation has only two parameters: the vacuum energy and its fluctuation. As a Vacuum Boson, its key feature is having a zero (0) spin. This is not prediction nor postdiction; it is the direct consequence of the G-string language.
Three years after the discovery of this new 125.4 Gev boson, the Higgs mechanism is not verified (see article form Nigel Lockyer, Director of Fermi Lab. at http://www.quantumdiaries.org/2014/04/24/massive-thoughts/ ). That is, the Higgs mechanism is wrong, and of course there is no Higgs boson; it is a Vacuum Boson.
With Vacuum Boson in the G-string, the LC&P sum rule is a good approximation.