this just out
As you can see, it was actually awake waiting to see if there was some late problem or not (upload was done past yesterday, Fri, 11 Mar 2005 12:35:48 GMT).
It is, I hope, unrelated to "Strings, Branes and QCD"; it is just a point of the long long thread All the lepton masses...
The content of the paper is quite good, but the drafting needs a little work. In addition to a few grammatical errors, the introduction does a poor job of framing the paper.
A better introduction would first have an extended abstract which states, something on the order of: "We derive the value of constants X, Y, . . . . and Z to a precision within the range of experimental error using only A, B, . . . . and C, using an ansantz that draws upon concepts central to the Standard Model of quantum physics."
A good second paragraph of an introduction ought to read something like: "There has been a long history of efforts to derive values for constants such as X, Y . . . . and Z from first principal and A, B, and .... C. The include [name drop], [name drop] and [name drop]. We are aware, however, of no prior effort along these lines that has come to a result within the current experimental error allowed by the current state of experimental knowledge. This effort crosses that threshold."
Then, you can start talking about how the two of you come to your conclusions.
You should also have a final table which shows the experimental results, error bars for that, and your final formulas and results clearly denoted as such, so that a lazy reader can simply go to the table and crib off that without reading the discussion.
I thought it was terrific. The abstract was brief, but effective. It made me want to read the entire paper...
Thanks Chronos! The abstract -I asked a friend for help here- was intentionally vague, to avoid excessive claims but still to insinuate that a browsing across the whole paper could be interesting... Ohwilleke scores in all, or almost all, of his remarks. Yes, time ago I already abandoned any pretension of grammar beyond the concordance of indexes (indices?). Almost every grammatical failure gets at least 9000 hits if you google for it. And well, sometimes even concordance fails 8-(
As for the suggestion for the second paragraph goes, one is tempted to admit it, but there is a pair of caveats. First, that most authors use a precise mathematical scheme, say GUT or Technicolor or Goldstone bosons or whatever, and from there they are a lot more restricted that Hans and me. Second, that we use the values of the mass of W and Z, and the value of tau. Such quantities were not at the reach of model builders in the 1970. When they were, the ball of model building was already in other roofs: SUSY, ETC, string inspired models, &c.
Now, has our numerical observation some relevance beyond Spontaneus Symmetry Breaking? I think it could have. The last equation, having inverse of mass, feels as if it could had some metric information. Remember that mass can be interpreted as inverse of distance; the mass of the Higgs in non commutative geometry models is traditionally related to the separation, in a 5th dimension, between two 4-sheets of space time. Here the broken symmetry bosons could by hinting their own geometrical role, somehow controlled, or controlling, the generation spectra. Still, this formula was obtained from the second order corrections; another ones could fit there too.
ETC: Extended TechniColor
One interesting observation I think is that the pertubative magnetic
anomaly series would more specifically link the masses of the lepton
group to the masses of the EW boson group.
This would, after the left handedness of the weak force, be another
hint to the central role which the spin may play here.
Contgratualtions indeed! So that's "who ordered that!"
(Added:) Ingo Kirsch's new paper, http://arxiv.org/abs/hep-th/0503024, shows that not only lepton masses can come from broken symmetry! This paper has caused some buzz among physicists; arivero submitted it to physics comments ( http://www.physcomments.org/).
Hmm people not reading the other thread could have missed the footnote. The point, guys, is that a semiclassical ansatz on spin drive Hans to calculate the quantity cos X= .8814, so that sin^2 X= 0.2231. And according http://pdg.lbl.gov/2004/reviews/stanmodelrpp.ps, page 23, this quantity is within 1 sigma of "on-shell Weinberg angle". The measurements of Weinberg angle are done differently depending on the renormalisation scheme, so scoring here was not so meaningful and we avoided a deeper remark.
Let me expand on this, because the footnote in the paper was perhaps excessively short. History begins in message 36, where Hans defines a particle radius based on angular momentum.
And then he notices that when taking into account relativity, the speed of the particle does not depend of the rest mass.
It is pretty obvious that you can define this distance for any angular momentum; and then the muonic coincidence happened, and the ansatz explained in the paper drove to try the quotient between the corresponding distances for "spins" 1 and 1/2. This was in message #44:
Now, second column of table 10.5 (page 22) of the pdg report on electroweak parameters gives the most up-to-date measurements of the square of sine weinberg... The all data average is 0.2228(4), the all indirect -not depending on mass of top- is 0.2229(4), and the measurements at Z pole give 0.2231(6). Thus to our surprise, the semiclassical quantity estimated by Hans goes inside the one-sigma of the world average, and right in the middle of the (slighly more diffuse) Z pole estimate.
As for the anomalous moment itself, Hans elaborated a sort of semiclassical argument for it, leaving aside the role of Z and W and concentrating in the before calculated velocities and radious. You can see it at posts 58 and 60.
A question here is if we should say that this quotient is a relativistic or a classical quantity. It uses "c" for the calculation, but it simplifies out!
Separate names with a comma.