View Poll Results: Multiple poll: Check all you agree.  
Logarithms of lepton mass quotients should be pursued.  24  27.91%  
Alpha calculation from serial expansion should be pursued  22  25.58%  
We should look for more empirical relationships  26  30.23%  
Pythagorean triples approach should be pursued.  21  24.42%  
Quotients from distance radiuses should be investigated  16  18.60%  
The estimate of magnetic anomalous moment should be investigated.  26  30.23%  
The estimate of Weinberg angle should be investigated.  21  24.42%  
Jay R. Yabon theory should be investigate.  16  18.60%  
I support the efforts in this thread.  47  54.65%  
I think the effort in this thread is not worthwhile.  30  34.88%  
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All the lepton masses from G, pi, e 
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#361
Sep207, 10:42 PM

P: 2

See:
"Evidence for Detection of a Moving Magnetic Monopole", Price et al., Physical Review Letters, August 25, 1975, Volume 35, Number 8. This was the last of a series of balloon flights, launched in 1973, but not analyzed by myself until 1975, due to higher priority cosmic rays analysis then ongoing. The suggestion that the anomalous track could have been caused by a doubly fractionating normal nucleus is untenable. One would have expected to have seen billions of similar tracks, not quite as closely matched to the expected track of a magnetic monopole, first. No such similar events were ever detected. For further information, contact the administrator who can email me, as I do not regularly post at this forum. Or check www.sciforums.com where I do regularly post, and PM me. Whether the Large Hadron Collider [LHC] will create a magnetic monopole is highly debatable. It might also create miniature black holes, or strangelets. 


#362
Sep2407, 05:48 AM

P: 4

Please see my paper about mass quantization @ arxiv. hepph/0702140



#363
Sep2507, 09:04 AM

PF Gold
P: 2,917

http://www.slac.stanford.edu/spires/...fs?key=7074930 and the list of citations of McGregor http://www.slac.stanford.edu/spires/...=NUCIA,A58,159 are interesting for the topics of this thread. A problem of quantisation of M instead of quantisation of M^2 is that it has some scent of classical group theory, thus one needs to see how many of the relationships are already explained in the quark model and check the extant cases. 


#364
Sep2507, 11:42 PM

P: 4

Thiis paper has been accepted for publication in Modern Physics Letters A.
The important thing is that while the charged pions and muon are related in sense via the decay of former into latter, the neutral pion and muon are not related in any sense. Yet there mass difference serves as a basic mass unit for both leptons and hadrons. 


#365
Sep2607, 06:35 AM

PF Gold
P: 2,917

the question, to me, is not why muon and pion have different mass, but why have they got almost the same mass. A conjecture is SUSY. 


#366
Sep2607, 11:54 PM

P: 4

Here is another surprise
the t lepton mass can be obtained by taking 57 jumps of 29.318 MeV from the muon mass i.e t mass= 57x 29.318. Now this 57 number also helps us to include the electron mass as 57 times electron mass= 29.127 very close to 29.318. This leads us to thing that like in Nambu's and many other cases the basic unit appears from the electron mass. Now this also means the pion muon= 57x electron , tau  muon =57x 29.318 =57x57x electron. which in turn leads to tau pion =56x 29.318 =56 x 57 x electron. Hence the lightest hadron i.e pion and lightest unstable lepton i.e muon , two leptons muon and tau , lightest hadron and heaviest lepton i.e tau are all related through electron mass. 


#367
Sep2807, 04:00 PM

PF Gold
P: 2,917

[tex]{ m_\pi  m_\mu \over m_e}= \sqrt {m_\tau  m_\mu \over m_e}[/tex] It should be nice to have a mathematical (group theoretical) argument for 57. EDIT: It is a bit puzzling that if we fix the mass of tau, mu and electron to the experimental values, the above formula "predicts" 134.88 MeV, to be compared with the mass of the neutral pion (134.976 MeV). Naively one could expect the result to be more related with the mass of the charged pion, which is 4.6 MeV above. EDIT2. Perhaps Krolikowski has some argument for 58/2. Also, Ramanna (eg pg 16 of nuclth/9706063) 


#368
Sep2907, 09:50 AM

PF Gold
P: 2,917

[tex]( m_{\pi_0}  m_\mu )= \sqrt {m_e} \sqrt {m_\tau  m_\mu}[/tex] LHS and RHS still agree within a 0.3 %. No bad. The above comments still apply. On other hand, if I recall correctly, the question about why the mass of the charged pion is higher, and not lower, than the neutral one was a touchy issue decades ago, and it required very high level theoretists to explain it. 


#369
Oct107, 01:44 AM

P: 4

Refering to first version, it ia again amazing that the mass of the neutral pion is deteremined very precisely in terms of the three leptons. Now neutral pion has no relation with the three leptons. it does not decay into any of these particles. On the other hand the charged pion decays into electron and muon. Hence charged pion mass should have been related to lepton masses.



#370
Oct107, 03:55 AM

PF Gold
P: 2,917

To put more intrigue, the mass difference between eta and the average of pion and muon (say, diff=427.2 MeV) also fits roughly in the obvious permuted formulae: [tex] \sqrt {m_\mu} \sqrt {m_\tau  m_e} \approx \sqrt {m_\tau} \sqrt {m_\mu  m_e} \approx \sqrt {m_\tau \pm m_e} \sqrt {m_\mu \pm m_e} \approx \sqrt {m_\mu} \sqrt {m_\tau} = 433.27 MeV [/tex] EDITED: a purpose of the above formulas is to consider the limit [itex]m_\mu \approx m_\tau[/itex] where the former formula cancels and the two first ones in the above become the same. Also, the same cancellation and similarity happens in the other limit [itex]m_e \to 0[/itex]. Simultaneous limit conflicts with Koide's. 


#371
Oct107, 04:12 AM

PF Gold
P: 2,917

My thinking during the last two years was:
initially there is a symmetry where neutrinos have the same mass than neutral mesons and charged leptons have the same mass than charged mesons. Note the count of degrees of freedom. Of course one could also expect the dirac mass of neutrino and charged lepton to coincide. Then seesaw moves the mass of neutrinos out of reach and mixing, including CKM, and/or other unknown mechanism alter the mass eigenvalues of the mesons. The mechanism could be related to a mismatch between isospin in mesons and leptons. Namely, third generation mesons do not exist except bB. 


#372
Oct207, 05:27 AM

PF Gold
P: 2,917

569.32 GeV, so [tex]\eta_8  \pi^0 = 434.34 MeV [/tex] 


#373
Oct207, 03:24 PM

PF Gold
P: 2,917

[tex]m^2_\pi=B_0 (m_u + m_d) [/tex] [tex]m^2_{K^0}=B_0 (m_s + m_d) [/tex] [tex]m^2_{K^\pm}=B_0 (m_s + m_u) [/tex] [tex]m^2_{\eta_8}=\frac 13 B_0 (4 m_s + m_u + m_d ) [/tex] and so on. Asuming isospin, up and down have the same mass, and thus you can get a combination of neutral kaon, pion and eta8. If works well with the neutral particles; it is not only that it does not account for isospin; the idea does not account for EM interactions neither. Old timers extract an extra EM relation via "Dashen's theorem", but I think to remember there was some work of Witten or some other genious about this kind of corrections. EDITED: Indeed we could use the above expressions to reformulate our equations in terms of the mass [itex]m_s[/itex] and [itex]\hat m \equiv m_u = m_d[/itex], with SU(3) flavour breaking to global SU(2) isospin x U(1) as it happened in the papers of 1960s on global symmetries. [tex] m^2_\pi = (m_\mu + \sqrt { m_e (m_\taum_\mu)})^2 = B_0 \hat m[/tex] [tex] m^2_{\eta_8} = (m_\pi + \sqrt { m_\mu (m_\taum_e)})^2 = \frac 23 B_0 (2 m_s + \hat m) [/tex] Here you can see also one of the themes which were debatable in the sixties: the use of mass square instead of plain mass. For instance, it is because of it that our resulting equations do not allow to cancel [itex]B_0[/itex] out. 


#374
Oct407, 03:00 PM

PF Gold
P: 2,917

Dirac gets 53 times the electron mass for the muon, in a paper that has been lately recalled by the guys working on strings and branes. 


#375
Oct507, 05:18 AM

PF Gold
P: 2,917

The traditional current algebra formula for the pion mass(^2) difference puts it in terms of the fine structure constant and the pion decay constant, [itex]e^2 / F_\pi^2[/itex] times some other factors. Entering the octet, we are touching deep problems of the elders. There is a short work of witten in 1983 about how the mass of the charged pion must always be higher than the neutral pion, even if only to avoid tachions in the limit of zero pion mass. Also, the mixing between [itex]\eta_8[\itex] and [itex]\eta_0[\itex] to give [itex]\eta[\itex] and [itex]\eta'[\itex] was the U(1) headache, addressed by t'Hoft, Veneziano and Witten independently, and according Okubo still unclear. I have found even some recent work in the context of strings: Armoni 2004 


#376
Oct1407, 07:55 PM

PF Gold
P: 2,917

http://arxiv.org/abs/0710.2429 (g2)_mu status and prospects



#377
Oct1407, 08:53 PM

P: 2,157

You could try to use the LLL algorithm to find formulae.



#378
Oct1507, 03:38 AM

PF Gold
P: 2,917




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