Amazingly, some parallel development supports Yablon's efforts.

As communicated in s.p.r threads, Jay tries to generate mass for the
leptons from those of the electroweak vacuum, by using a perturbative
expansion on alpha and sin theta_W.

In PhysicsForums, Hans (also a occasional guest of s.p.r.) has hit
upon a amusing transformation of the (arguable) more famous series
expansion of alpha, that of the anomalous magnetic moment. Starting
from the value of m_mu/m_Z, we have noted that the electroweak
calculations for all the three leptons can be very well approached
(0.003%) by quotients of leptons and the electroweak masses.

Of course our question there is "where has the alpha gone?"

The answer can be provided by Yablon-like expansions: the alpha hides
in the lepton mass.

Besides, the thread from de Vries contains a kinematical way to obtain
sin theta_W, if you need it.


Alejandro

Alejandro:

When you say -- as you have said before -- "the alpha hides in the lepton
mass," can you please explain to me or point out something which explains,
exactly what you mean here?

What "problem:" (i.e., where has the alpha gone?) have you and DeVries run
into, and how does a mass expansion in alpha possibly resolve that problem?

Thanks.

Jay.
____________________________
Jay R. Yablon
Email:


"Alejandro" wrote in message
m...
Amazingly, some parallel development supports Yablon's efforts.

As communicated in s.p.r threads, Jay tries to generate mass for the
leptons from those of the electroweak vacuum, by using a perturbative
expansion on alpha and sin theta_W.

In PhysicsForums, Hans (also a occasional guest of s.p.r.) has hit
upon a amusing transformation of the (arguable) more famous series
expansion of alpha, that of the anomalous magnetic moment. Starting
from the value of m_mu/m_Z, we have noted that the electroweak
calculations for all the three leptons can be very well approached
(0.003%) by quotients of leptons and the electroweak masses.

Of course our question there is "where has the alpha gone?"

The answer can be provided by Yablon-like expansions: the alpha hides
in the lepton mass.

Besides, the thread from de Vries contains a kinematical way to obtain
sin theta_W, if you need it.


Alejandro

"Jay R. Yablon" wrote in message . ..

What "problem:" (i.e., where has the alpha gone?) have you and DeVries run
into, and how does a mass expansion in alpha possibly resolve that problem?

Well, for the general public: the problem is obvious. Both DeVries
initial
observations

mm/mZ=0,00115869 (vs ae=0,00115965)
me/mW=0,000006345 (vs am-ae=0,000006269)

As well as my enhancements:

mm/mz + (1/2) (mm/mw)^2= .00115955 (idem vs ae=0,00115965)
me/mw - (1/2) (me*mt/mw^2) = .000006275 (idem vs am-ae=0,000006269)
me/mH+ = .0000075 (vs at-am= .0000078) (*)

should, if they pretend to be a serious approximation to the anomalous
moment of leptons, have a dependence on alpha, if they approach the
QED correction, or in alpha and cos theta_W, if they approach to the
whole electroweak correction. But you see, it is only mass quotients.
No coupling constants!!

The problem dissapears if we can assume that lepton masses are
radiatively produced, or at least produced in some way from the
coupling constants. Moreover, if the expansion happens to have the
electroweak vacuum, we are somehow justified to divide by the
electroweak bosons, which are produced from that vacuum.

BTW, Jay, notice the minus sign in the term entering the tau
contribution. I put it for adjustment, before reading your own
numbers.

Your expansion, although, is not the only solution. Hans is taking a
more fundamental view, connecting mass straightly to the magnetic
moment.

Have a nice guessing weekend!

Alejandro

(*) The value for a_{tau} - a_{mu} is the theoretical calculation,
including electroweak but no hadronic (ie quark driven) corrections.
The value for the charged Higgs, 68 GeV, comes from the events at the
L3 experiment (hep-ex/9909044, hep-ex/0009010, hep-ex/0105057). Note
that if you are willing to believe the ALEPH events for a neutral
scalar, you can also substitute 2mw^2 by H^2 in the equations above.

Hi Alejandro:

OK, now I see exactly what you are saying with the "hiding" of the alpha in
the masses.

I think you and DeVries may also be on to something, and as I can find the
time in the next week or so, I plan to do some calculations to see what
shakes out.

In particular, as I mentioned to you privately, we know that in QED, the
spin 1/2 electrons interact with the photon fields through both their charge
and their magnetic moments. Indeed, one can engage in a Gordon
decomposition of the vector electron current to arrive at the separate
contributions from the charge and the magnetic moment, in a well-known
manner.

I have been revealing mass by having the electrons interact with scalar
bosons (a massless scalar photon with gives me the e = sqrt(alpha) factors
and a massive Higgs which gives me the e sin theta-W factors) through their
charge, but I have ignored the magnetic moments, which likely make small
corrections to the masses (and I could use some very small corrections to
get from within 1% on all three lepton masses where I am now, to something
exact within experimental errors).

It seems to me that I ought to develop a Gordon-type decomposition of the
Fermion mass term as well, and would expect that the observed electron, muon
and tau masses would be a composition of mass due to charge and mass due to
magnetic moments, parallel to Gordon decomposition for vector currents and
bosons. Indeed, if the "charge contribution to mass" and the "magnetic
moment contribution to mass" can be decomposed and separately quantified and
then the total fitted to experimental mass data, it seems that the anomalous
magnetic moments could also be determined, in principle, and thus would give
Devries what he is seeking from a different angle. (I also wonder -- and
this is a guess that may be wrong but it is worth making -- if the neutrino
can gain a tiny mass from its spin interacting with mass-generating scalar
bosons, even though it has no charge.)

I think both a forward and backward calculation will be useful he forward
in the sense of starting with Dirac's equation and doing a Gordon
decomposition as above and seeing how the magnetic moment (even the
non-perturbative g=2) fits in with the mass revelation, and backwards in the
sense of starting with the DeVries relationships and the anomalous magnetic
moment formulas to see if these shed some light on what the perturbative
expansion of the mass ought to be. Hopefully, these two calculations can be
connected somewhere along the line to yield exact result for both masses and
anomalous magnetic moments.

By the way, I do recognize that my "expansion, although, is not the only
solution." It was important to start somewhere with some type of "sensible"
expansion just to get something on the table for further thought, but I have
been keenly aware all along that finding the "right" expansion is crucial.
If the "right" expansion turns out to be hinted at by the anomalous magnetic
moments, and we can take care of the masses and the magnetic moments all in
one fell swoop, so much the better.

Jay.

--
_____________________________
Jay R. Yablon
Email:
"Alejandro" wrote in message
om...
"Jay R. Yablon" wrote in message
. ..

What "problem:" (i.e., where has the alpha gone?) have you and DeVries
run
into, and how does a mass expansion in alpha possibly resolve that
problem?

Well, for the general public: the problem is obvious. Both DeVries
initial
observations

mm/mZ=0,00115869 (vs ae=0,00115965)
me/mW=0,000006345 (vs am-ae=0,000006269)

As well as my enhancements:

mm/mz + (1/2) (mm/mw)^2= .00115955 (idem vs ae=0,00115965)
me/mw - (1/2) (me*mt/mw^2) = .000006275 (idem vs am-ae=0,000006269)
me/mH+ = .0000075 (vs at-am= .0000078) (*)

should, if they pretend to be a serious approximation to the anomalous
moment of leptons, have a dependence on alpha, if they approach the
QED correction, or in alpha and cos theta_W, if they approach to the
whole electroweak correction. But you see, it is only mass quotients.
No coupling constants!!

The problem dissapears if we can assume that lepton masses are
radiatively produced, or at least produced in some way from the
coupling constants. Moreover, if the expansion happens to have the
electroweak vacuum, we are somehow justified to divide by the
electroweak bosons, which are produced from that vacuum.

BTW, Jay, notice the minus sign in the term entering the tau
contribution. I put it for adjustment, before reading your own
numbers.

Your expansion, although, is not the only solution. Hans is taking a
more fundamental view, connecting mass straightly to the magnetic
moment.

Have a nice guessing weekend!

Alejandro

(*) The value for a_{tau} - a_{mu} is the theoretical calculation,
including electroweak but no hadronic (ie quark driven) corrections.
The value for the charged Higgs, 68 GeV, comes from the events at the
L3 experiment (hep-ex/9909044, hep-ex/0009010, hep-ex/0105057). Note
that if you are willing to believe the ALEPH events for a neutral
scalar, you can also substitute 2mw^2 by H^2 in the equations above.

"Alejandro" wrote in message
om...

[snip]

The problem dissapears if we can assume that lepton masses are
radiatively produced,

May I enquire what is meant by lepton masses being radiatively
produced?

[snip]

--
Franz
"A first-rate laboratory is one in which mediocre scientists can
produce outstanding work"
P.M.S. Blackett