# Quarks and the Fine Structure Constant

1. Sep 4, 2014

In a recent online lecture it was said there is now known releationship between the masses of quarks. My online search seemed to back this up.

My comparison suggests:

Mcharm ≈ Mtop * fine
Mup ≈ Mcharm * fine / 4
Mstrange ≈ Mbottom * fine * 3
Mdown ≈ Mstrange * fine * 7 (corrected for original post)

where fine is the fine structure constant 0.00729735257

these are quite accurate, but are necessarily approximations due to the accuracy of measurement of the quarks with smaller masses

if Mtop = 173.34 GeV
then Mcharm = 1264.92 MeV
and Mup = 2.3076 MeV

if Mbottom = 4.3 GeV
then Mstrange = 94.14 MeV
and Mdown = 4.81 MeV

the bottom - stange - down relationships are my best fit having spotted the much clearer top - charm - up relationships

any ideas as to why they might be related in this way?

Last edited: Sep 4, 2014
2. Sep 4, 2014

### ShayanJ

Simple. You just divide two masses by each other and you get a number. Then you divide that number by the fine structure constant and you get another number. You round that number to an integer and write down those things. Its not saying anything important.

Maybe there are some theories about that. But my point is, the fact that you can write those things, doesn't mean there should be something behind them.

Last edited: Sep 4, 2014
3. Sep 4, 2014

Yes Shyan, I understand that many numerical relationships have no physical significance.

It is why I ask. If this has not been investigated, then I will take some time to look into the maths in more depth, but if it is known already, as I suspect it is, then somebody might have some pointers for me :)

4. Sep 4, 2014

### ShayanJ

There is nothing to be investigated here!

The relationships you wrote, are useless and meaningless by themselves. They can lead you no where. You can't use them to understand anything.
The only point is, maybe from some theory that gives the mass of the quarks, arises a formula that results in your relationships but there are some points about this situation:

1- There is no widely-accepted complete theory in agreement with observations that is able to give the mass of
quarks!

2- Even if you take such a theory and search for such relationships, you're investigation is based on and using that theory. It neither started from these relationships nor gets help from them!

3- It seems very improbable that such relationships can show up in any theory Because they aren't obeying any known pattern about the quarks.

4- $\left. \begin{array} \\ M_{strange}=3\alpha M_{bottom} \\ M_{bottom}=7\alpha M_{strange} \end{array} \right\} \Rightarrow M_{strange}=21 \alpha^2 M_{strange} \Rightarrow 21 \alpha^2=1 \Rightarrow \alpha=\frac{1}{\sqrt{21}}$ Which is a nonsense result and can only mean that these relationships are written with so much error that they should be considered wrong and if any theory gives rise to them, it should be a wrong theory too!

So the only thing you can do with such relationships, is abandoning them!

5. Sep 4, 2014

lol, thanks for 4, the long way of pointed out I had written bottom instead of down in the original post, I corrected that.

6. Sep 4, 2014

### clem

As with most physics, this idea of using alpha was originally proposed by Nambu, but soon discarded by him and everyone else. The numerology is even more impressive when applied to leptons and hadrons.
and Y. Nambu, Progr. Theoret. Phys. (Kyoto) 7, 595 (1952)

7. Sep 4, 2014

Thanks Clem, that was what I expected. I agree entirely with the sceptical of views of American Physical Society (and Shyan on this website).

using this link I also found more recent items:

http://arxiv.org/ftp/hep-ph/papers/0303/0303261.pdf

seems interesting but probably fruitless, though if a relationship of masses could be pinned down it would give us a much more accurate estimate for up and down quark masses, because it appears to be possible to measure the masses of top and bottom quarks with much more accurately.

8. Sep 4, 2014

### arivero

Great, I did not know that reference.

The alpha-fitting game was continued mainly by McGregor, even did a book on the subject. Not only masses, also decay widths.