# I found a lepton mass ratio formula:

1. Jul 25, 2004

### Hans de Vries

I found the following (for what it’s worth):

ln(mu/me) / (2pi-3/pi) = 1.000627
ln(mt/me) / (3pi-4/pi) = 1.00031

me = 0.51099892 MeV (+/-0.00000004)
mu = 105.658369 MeV (+/-0.000009)
mt = 1776.99000 MeV (+0.29 -0.26)

I've not seen it before. There's no theory behind it.
I was trying one, made a bug and stumbled on it.

Regards, Hans

2. Jul 31, 2004

### salsero

Interesting! How did you actually find this?

Any comments from the high-energy people?

3. Jul 31, 2004

### vanesch

Staff Emeritus
And the next in the list is then 29834 MeV ? :tongue2:

cheers,
Patrick.

4. Aug 1, 2004

### arivero

I doubt, but you can check http://pdg.lbl.gov/

It could also be said that the list terminates, because both equations imply a third one, simpler, between 2nd and 3rd generations:
$$\ln {m_\tau \over m_\mu}= \pi - {1 \over \pi}$$

Last edited: Aug 1, 2004
5. Aug 1, 2004

### arivero

On a different side, you could like to use a reference mass of 2444.82 MeV so that all the three masses, when quotiented by this one, have a short expresion in terms of pi. But I can not see where we are going here.

Also we could use sinh(ln(pi)) to put both terms as if it where one,
ie ln(mt/mu)=2 sinh(ln(pi)). It cound hint of some geometric meaning, but it could be nothing. Or it even could be just the first two terms of a series.

Last edited: Aug 2, 2004
6. Aug 17, 2004

### marlon

Hans, how did you find this?
Can you predict the fourth generation. As you know the Standard Model won't like that...

Looks very nive though
marlon

7. Aug 19, 2004

### kurious

I found a formula that predicts all known quark rest masses and says that the mass of
the fourth generation quarks should be 0.08 and 0.16 Gev.Also predicts muon mass to within 1 per cent.Physical review D said that I would need to explain why the decay rate of the z boson isn't greater to convince them of the existence of the fourth generation!

8. Aug 19, 2004

### zefram_c

Phys. Rev. D. makes a good point. The Z boson can directly decay into any quark-antiquark pair whose weak interactions are described by the SM, as long as the mass of the pair is below the mass of the Z. At 0.08 GeV and 0.16GeV, those pairs meet this requirement. The width of the Z boson is directly related to the number of possible decay modes; extra light quarks increase the width. The current experimentally determined width is consistent with the known generations - no more, no less. Also at 0.08/0.16GeV, those quarks would have been detected by now, unless you establish a completely different interaction model for them.

9. Aug 19, 2004

### kurious

I wondered if they just add to the dark energy content of the universe and that's why
they haven't been detected.Can't prove it though!
Also could the mass of the strange quark be so uncertain because sometimes the strange quark is being mistaken for one of the fourth generation quarks?
I suppose the same could be said for uncertainty in the mass of the charm quark.

Last edited: Aug 19, 2004
10. Aug 19, 2004

### zefram_c

Sounds like pure speculation to me. A quark by definition has color and behaves in certain ways. If there were more light quarks we would have seen their bound states by now, even if in nothing else, the widths of decaying mesons. Sounds to me like this fourth generation you're proposing behaves nothing like the current three; which makes it very unlikely to be a continuation of the known ones.
Quark masses are uncertain because they don't exist as free particles, and the theory that describes their bound states (QCD) is extremely difficult to work with so we can't tell how much of a baryon's or meson's mass comes from binding.

11. Aug 25, 2004

### arivero

Laurent Nottale suggested time ago a logarithmic relationship between the mass of Planck and the mass of the electron when the sine squared Weinberg angle takes the -SU(5) inspired- value of 3/8. We have
$$ln({m_P\over m_e})= {3 \over 8} \alpha^{-1}$$
within a 0.3 % according Nottale's webpage.

I am not sure if alpha should be the running fine structure constant or the low energy one. The formula works with the low energy one, 1/137, but on the other side $$\sin^2 \theta_W$$ has the 3/8 value at the unification scale, doesn't it?

Last edited: Aug 25, 2004
12. Aug 25, 2004

### kurious

The existence of a fourth quark family would imply a fourth neutrino but that in turn implies a greater helium abundance in the early universe.So a prediction of a fourth quark family would have to explain why there would be no accompanying neutrino
or why that neutrino has such a small effect on the decay rate of the z boson.

13. Jan 24, 2009

### Hans de Vries

Hi, Taunus. Welcome to Physics Forums.

to collect and archive numerical coincidences which may be of interest
but are not derived from physics.

You're welcome to post your numerical coincidence there. The idea is to use
only this thread and not open any new ones since threads are required to
have an actual (sufficiently mainstream) physical contents.

Typically post should contain the accuracy of the numerical coincidence.
For instance: Your case compares with measured values as 1:1.0000146
which is quite good from a numerical viewpoint.

Regards, Hans

Last edited: Jan 24, 2009