Studying particle physics I had a doubt that I can't seem to find a solution:

Is possibile in a particle decay to produce some particles with no momentum?

As an example: take the following decay

$$\Upsilon(4S) \rightarrow B+\overline{B} $$

where the particle $\Upsilon (4S)$ is produced by the collision of an electron an a positron beam with different energies (such as in the BaBar experiment), so that $\Upsilon(4S)$ is produced with some momentum.

Or as another example the three body decay

$$K^+ \rightarrow \pi^0 + e^+ + \nu_e $$

where $K^+$ has some momentum. Would it be possible in the laboratory frame to produce the $\pi^0$, for example, with no momentum?

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    $\begingroup$ In some frame, a product with momentum will have none: its rest frame. $\endgroup$ – Cosmas Zachos May 1 '19 at 17:51
  • $\begingroup$ @CosmasZachos Yes, that's clear. But maybe I didn't make it clear: I want to know if in the laboratory frame could be possible! $\endgroup$ – Davide Morgante May 1 '19 at 18:09
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    $\begingroup$ What is so special about the lab frame? go to the rest frame of the pion, Lorentz transform the decaying Kaon, and you have a magic lab frame such that.... $\endgroup$ – Cosmas Zachos May 1 '19 at 18:22
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    $\begingroup$ "What is the minimum lab frame momentum of the kaon such that the pion cannot be produced at rest in the lab?" would be a suitable homework question for a upper-division course in particle physics (for graduate students it would be a warm-up question.), and it thinking about it in those terms might give you a hint. $\endgroup$ – dmckee --- ex-moderator kitten May 1 '19 at 19:29

Suppose you have a proton of energy E hitting another proton. The result is 3 protons and an anti-proton. What is the minimum energy for this to happen?

The answer is 7 times the rest energy of a single proton. But why?

Also consider why pair production doesn't happen in a vacuum even though its always energetically permitted.

  • $\begingroup$ Thanks, I'll think about that! $\endgroup$ – Davide Morgante May 2 '19 at 9:14

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