# Why do particle masses apparently follow a power law?

1. Jul 8, 2012

### Steve Davis

Looking at the known masses of the elementary particles, they appear at first sight to be on some kind of exponential curve. It is certainly attractive for there to be such a simplicity - however, and interestingly ...nothing really lines up exactly. Is there any explanation for this or for the reason for an apparent power law underneath?

PS: Most curiously the biggest "bump" is that the strange quark mass is very close to the mass of the muon.

2. Jul 8, 2012

### mathman

What are the coordinates of the plot - mass vs. ?

3. Jul 8, 2012

### Steve Davis

For simplicity I was thinking a one-dimensional plot - just the masses. What I see is that (mostly!) the differences in mass between each known particle appears to dramatically increase as you go up the energy scale. To get this into a 2d plot I guess you could sort the particles by known mass then assign a "particle number" to each on x and do a plot on y to see what looks like a rather bumpy exponential curve (rather like the "graph of e"). Whichever, it seems hard to ignore the apparent power law that it suggests?

4. Jul 8, 2012

Staff Emeritus
There is no "apparent power law". All you have said is that particles get big in a hurry - true, but that is not the definition of a power law.

5. Jul 8, 2012

### Steve Davis

Thanks for the answers! Let me rephrase the question: is there any explanation for why known particle masses seem to get big in a hurry? Why does it look like an exponential increase, and yet it isn't?

6. Jul 9, 2012

### Staff: Mentor

No, there is not.
A nice distribution on a logarithmic scale could be considered as "natural" in some way, as many things are distributed over many orders of magnitude, but this is not a real argument.

It might follow from a deeper, undiscovered theory.

7. Jul 9, 2012

### Steve Davis

Thanks to all. This problem has inspired me to learn more about the Standard Model. I'm sure that there has to be some explanation for the masses of fundamental particles, and there's a good reason why it isn't obvious as yet. It is however unlikely that I'll appreciate even the question fully until I know more about the math. A good outcome.