# Pair-production - how come it's always e+e-, never muons or tauons?

1. Mar 17, 2013

### Doofy

Everyone is familiar with photons pair-producing electrons and positrons, but how come it never seems to be a mu+ / mu- or tau+/tau- pair that gets produced, even when the photon is at a sufficient energy to produce any of these?

2. Mar 17, 2013

Staff Emeritus
First, there is no such thing as a "tauon". It's a "tau lepton".

Second, muon pairs are produced - it's just suppressed by a factor of at least 1/40,000.

3. Mar 17, 2013

### Doofy

I thought tau and tauon were interchangeable, I went for tauon to keep consistency with muon and electron.

Anyway, what is the reason for that supression?

4. Mar 17, 2013

Staff Emeritus
They're not. I say again, there is no such thing as a "tauon". It's "tau lepton".

There is a 1/m^2 dependence to the production cross-section, which is 40000x smaller for muons than electrons.

5. Mar 17, 2013

### Doofy

ah right, that's that mystery solved. cheers.

PS. the wiki article on tau leptons reckons tauon is a valid name (1st line):
http://en.wikipedia.org/wiki/Tau_(particle)

6. Mar 17, 2013

### Staff: Mentor

"Tau" is by far the dominant name for the particle. I was in grad school when it was discovered. I wrote a Monte-Carlo simulation of $\nu_\tau + N \rightarrow \tau + X$ followed by $\tau \rightarrow e + \bar \nu_e + \nu_\tau$ decay in an attempt to find tau-neutrino events in the neutrino experiment that I was working with. I don't remember any of the papers that I read, or people I talked to, using the name "tauon." Nor do I specifically remember seeing the name in the 30+ years since then, although I've kept only peripheral touch with the field.

Nevertheless, a search on http://scholar.google.com for "tauon" does turn up a number of hits, including published papers from 2010 and 2011 on the first page. So it's not unheard of.

7. Mar 17, 2013

Staff Emeritus
Spires has 8 records for "tauon"* (and nearly 5000 for "tau"). Four are from one author (and three of those are unpublished) and are only cited by this one author. One was changed to tau by the journal, and one was a thesis. Of the remaining two, they are in the same journal - a journal where the style guide says not to use it.

I think we can safely say that this vocabulary isn't used. At least not by anyone who knows anything - Wikipedia notwithstanding.

* Compare that to a dozen references to "relativistic mass". (Including a lovely paper by Lev Okun, "The virus of relativistic mass in the year of physics")

8. Mar 19, 2013

### Doofy

ah right, well I will abandon the term then. You can blame the British education system, that word has been floating around in my head since I was a GCSE or A-level student and that's definitely where I got it from.

9. Mar 22, 2013

### lpetrich

10. Mar 22, 2013

### Bill_K

No, V50 is right, there's a 1/m2 dependence, even far away from threshold.

To be clear, this is not pair production from photon-photon collisions. This is pair production from a single photon in the Coulomb field of a nucleus. Jauch and Rohrlich give the total cross-section in the high energy limit as

σ = αZ2r02(A ln(ħω/mc2) - B)

where α of course is the fine structure constant, Z is the number of protons in the nucleus, A and B are ugly numerical constants you don't want to look at, and r0 = e2/4πmc2 is the classical electron (or muon!) radius. The r02 is what produces the 1/m2 dependence.

11. Mar 23, 2013

### lpetrich

If A and B are typically O(1), then I concede. But how do they behave at high energies?

12. Mar 23, 2013

### Bill_K

As I said, they are just numerical constants which I didn't want to write down. Oh well, A = 28/9 and B = 218/27.

13. Mar 25, 2013

### belliott4488

When I was in grad school there was an older professor who consistently called it a "tauon". He also consistently referred to the muon as the "mu meson" - as it had originally been called, due to the similarity in pi and mu masses - although by then that was considered to be flat-out wrong, since the mu ain't a meson.

I guess there are all kinds of names that get forgotten - I'm glad you don't see too many references to the "truth" and "beauty" quarks any more; those were still being used by a minority of physicists when I was a student. I'm looking forward to the day when no one remembers that anyone (especially physicists) ever called the Higgs the "god particle". :-)