# What is the speed of a neutral pion and how is it measured?

Alvager et al 1964 purportedly disproved Ritz's emitter theory in an experiment that generated neutral pions with a vellocity of $v =B.c$ where B is slightly smaller than one. How is the velocity of a neutral pion determined? Does the determination invoke special relativity?

Added: Alvager et al (http://mysite.verizon.net/cephalobus_alienus/papers/Alvager_et_al_1964.pdf) beamed a burst of high energy protons at a beryllium crystal and measured arrival times of burst of emitted photons at downstream detectors. Their theory said that the photons were emitted from decay of neutral pions produced from collision of the protons with beryllium and that these pions had a speed of $v = B.c$. Time intervals between output burst being detected at different detectors indicated that photons were travelling at very close to $1.0c$ rather than at a range of values between $c -k.B.c$ and $c + k.B.c$ with $k>0$ which (they said) would have been the case if emission/ballistic/galilean theory/model applied. ( Sorry I dont know where I got my earlier value of $k.B = 0.2$ from).

I pose the question because it seems that Alvager et al were trying to prove special relativity (SR) by assuming pion velocities which were themselves determined assuming SR.

Anna V has answered the question of pion velocity measurement for me (Thankyou!).

Regarding the interpretation of the Alvager experiment the following note is interesting: (http://worldnpa.org/pipermail/memberschat_worldnpa.org/attachments/20090115/db6f6bc5/attachment.pdf).

• Speed in what process? Relative to what? – dmckee Sep 12 '13 at 23:08
• I will add extra info to the question. – steveOw Sep 14 '13 at 19:12

If you go to this link you will see that the lifetime of the pi0 is orders of magnitude shorter than of the charged pions.

8.4 ± 0.6 × 10^−17 seconds, a time characteristic of electromagnetic reactions.

It decays to two photons, which can be measured in the laboratory.

If it is produced with some energy in the laboratory system, its speed can be estimated by measuring the four momenta of the photons and equating the sum to the four momentum of the pi0. Its speed then can be found for that individual measurement. There is no general "speed" of the pi0, as there is no general speed of any elementary particle, their four momenta being dependent of the interaction that produced them and very variable.

To have a speed a fraction of the speed of light any pion or other elementary particle should have an energy given by the relativistic formulae. Have a look here where they calculate the energy necessary for a velocity 1% of the velocity of light for various particles.

• Alvager et al 1964 quote pion energy >6GeV and gamma>45. and pion velocity v of $> 0.99975c$. – steveOw Sep 14 '13 at 20:22
• This is for a specific experiment and a specific reactions studied in their publication. Not for any pion any interaction. One has to find the energy for the pi0 as I outlined above, (experimentally or by a thought experiment), and then see what its speed is with respect to c. – anna v Sep 15 '13 at 2:57
• Thanks, I had realized that these were specific from your answer. I would love to see a detailed example of such a calculation. Could pi0's simply be a fiction invented to rescue SR from photons travelling at non-c velocities? – steveOw Sep 15 '13 at 15:17
• Here is a link dealing in detail with the pi0 decay hep.princeton.edu/~mcdonald/examples/piondecay.pdf . No, they are not fiction, they are measured over and over again and have the same mass as p+ and pi- and are in the same isotopic spin vector. en.wikipedia.org/wiki/Pion – anna v Sep 15 '13 at 15:59
• In a pi0 decay are the two daughter photons produced simultaneously? In the rest frame of the pi0 do these two photons travel in diametrically opposite directions? – steveOw Sep 16 '13 at 19:50