# Particle decay and momentum

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?

• In some frame, a product with momentum will have none: its rest frame. – Cosmas Zachos May 1 '19 at 17:51
• @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! – Davide Morgante May 1 '19 at 18:09
• 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.... – Cosmas Zachos May 1 '19 at 18:22
• "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. – dmckee --- ex-moderator kitten May 1 '19 at 19:29