Early this year Yablon spoke in theis group about taking the masses of
electron muon and tau in powers of Sommerfeld alpha (and weinberg
angle) from the electroweak vacuum. It was the first time I read about
relating tau to the eletroweak scale via the fine estructure constant.
Now I find an abstract that predates Jay R. for one year so I think it
is valuable to quote it in the newsgroup:
hep-ph/0302166 version 3
The origin of the first and third generation fermion masses in a
technicolor scenario
A. Doff, A. A. Natale

It was uploaded Wed, 23 Jul 2003 19:43:19 GMT
a later version was uploaded Thu, 22 Jan 2004 20:46:22 GMT

Hi Alejandro:

Interesting article. Thanks for pointing it out.

Yes, especially following electroweak unification and the W and Z boson mass
predictions, Doff and Natale (and others) speculate in general terms that v
= 246 GeV which is an energy expression of the Fermi coupling constant G_F
should have some role in setting the mass scale for Fermion masses as well
(who wouldn't? --if v has no role, then we need a second coupling constant G
in addition to G_F which is inartful, or we need to find a way to have
Newton's Constant i.e., the Planck energy involved, and nobody has a clue at
this time how to do that). And, again if we are to be artful, one would
expect that all the masses should be a general function of v = 246 GeV, the
various interaction couplings, suitable mixing angles (which may be just
another way of representing the interaction couplings), and nothing more.
As we all know, however, it is a long and difficult way from such a general
understanding, to specific mass predictions which are reasonably accurate in
relation to the hand nature has dealt us.

In that context, I don't see how this paper discloses or suggests the
relationship v x a_em = tau mass within about 1% which I found in December
2004 and disclosed early this year. Or, the basis for this relationship in
chiral symmetry and the Yukawa-type couplings I used to get there. Their
couplings appear on perusal to be QCD- or Technicolor-based, and if you look
at their table 1, they end up with a tau mass of 131.2 GeV, a muon of 1.30
Gev, and electron of 5.5 MeV. Where the rubber meets the road, this is not
even in the ballpark!

Best,

Jay.

--
_____________________________
Jay R. Yablon
Email:
wrote in message
oups.com...
Early this year Yablon spoke in theis group about taking the masses of
electron muon and tau in powers of Sommerfeld alpha (and weinberg
angle) from the electroweak vacuum. It was the first time I read about
relating tau to the eletroweak scale via the fine estructure constant.
Now I find an abstract that predates Jay R. for one year so I think it
is valuable to quote it in the newsgroup:
hep-ph/0302166 version 3
The origin of the first and third generation fermion masses in a
technicolor scenario
A. Doff, A. A. Natale

It was uploaded Wed, 23 Jul 2003 19:43:19 GMT
a later version was uploaded Thu, 22 Jan 2004 20:46:22 GMT

Jay R. Yablon wrote:
Hi Alejandro:

Interesting article. Thanks for pointing it out.
I don't see how this paper discloses or suggests the
relationship v x a_em = tau mass within about 1% which I found in December
2004 and disclosed early this year.

Well, the abstract explicitly says about to relate the third generation
of fermions to a mass scale around 250 GeV, and from reading it any
inquisitive author should be tempted to divide the mass of tau between
the 250 GeV in order to see which value should this "alpha" have. Also
the general style of the paper, including drawings, is very close to
some 1970 papers that studied the relation between mass of muon and
mass of electron, particularly reference 23 of the bibliography, Barr
and Zee Phys.Rev.D17:1854,1978.
http://prola.aps.org/abstract/PRD/v17/i7/p1854_1
(which was ref. 13 in the first version of the paper), as well as some
others from Georgi.

Or, the basis for this relationship in
chiral symmetry and the Yukawa-type couplings I used to get there. Their
couplings appear on perusal to be QCD- or Technicolor-based, and if you look
at their table 1, they end up with a tau mass of 131.2 GeV, a muon of 1.30
Gev, and electron of 5.5 MeV. Where the rubber meets the road, this is not
even in the ballpark!

Note that the abstract does appear in the third version of the paper;
compare with versions v1 or v2. It seems to me that during the revision
process they become aware of the relevance of the two jumps, between
electron and muon and between tau and 246 GeV; they stressed it in the
abstract but they were unable to use it to refine their model.

Alejandro

(PS: I received yesterday the PDF of your last work, I will see about
allocating some time to print and read).

Jay R. Yablon wrote:
Yes, especially following electroweak unification and the W and Z boson mass
predictions, Doff and Natale (and others) speculate in general terms that v
= 246 GeV which is an energy expression of the Fermi coupling constant G_F
should have some role in setting the mass scale for Fermion masses as well

Note, also, that the sum of the boson masses (Z, W+, W-), in GeV, is 91
+ 83 + 83, which comes out to 257 GeV, close to the vev.

wrote:
Jay R. Yablon wrote:
Yes, especially following electroweak unification and the W and Z boson mass
predictions, Doff and Natale (and others) speculate in general terms that v
= 246 GeV which is an energy expression of the Fermi coupling constant G_F
should have some role in setting the mass scale for Fermion masses as well

Note, also, that the sum of the boson masses (Z, W+, W-), in GeV, is 91
+ 83 + 83, which comes out to 257 GeV, close to the vev.

Well, 91+83+83+0. But it is not strange because Z is connected to W via
the higgs structure; in the most trivial case, it is just W times
cosine of Weinberg angle. And W is also connected trivially to the vev,
so one can work out the exact number. I will leave it as an exersise.

In any case, this sum was one order of magnitude worse that the
aforementioned fit of Yablon. I suppose Mark was being ironic here, but
some of us have put some effort to see if it is true that random
numerical relationships are abundant, and if you put a decent cutoff
(say, ask for 1% or better accuracy), it is not so easy. We run a year
long thread on this at physicsforums
http://www.physicsforums.com/showthread.php?t=46055
and some notes were produced from them.

Al.Rivero wrote:
Z is just W times cosine of Weinberg angle. And W is also connected
trivially to the vev, so one can work out the exact number.

See for instance Weinberg volume II, formula's 21.3.30 and 21.3.37/38.
where v denotes the vacuum expectation value. Weinberg uses the values
G_e and G_mu as the ratios between the electron/muon mass and the
vacuum expectation value (21.3.31)


Some of Weinberg's own considerations on linking the other masses to
vacuum expectation values or radiative corrections:

"The problem of mass"
http://ccdb3fs.kek.jp/cgi-bin/img/allpdf?197711133

See also section 4, "Where do the small masses come from?"


Regards, Hans

Some of Weinberg's own considerations on linking the other masses to
vacuum expectation values or radiative corrections:

"The problem of mass"
http://ccdb3fs.kek.jp/cgi-bin/img/allpdf?197711133

See also section 4, "Where do the small masses come from?"

especially section 4. The first sections of this paper are widely
quoted, but this las section I am afraid it is not, perhaps because of
the chronological coincidence with the aforementioned Barr and Zee
PhysRev.

Alejandro