Decaying meson (1 Viewer)

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I've just started an introductory modern physics course, and it's making me ache a bit. I'm unsure about this problem:


A high-speed K0 meson is traveling at a speed of 0.9c when it decays into a pi+ and a pi- meson. What are the greatest and least speeds that the mesons may have?
So, if I calculate the momentum of the two pi mesons in the rest frame of the decaying meson... well... I've gotten that far. I'm not sure if I need to transform the momentum somehow back into the labframe. I know I can transform the velocity, but that doesn't seem useful.



And then I have some inkling that the different velocities depend on the direction of the resulting mesons, but I'm not sure what laws to use to obtain them. It's also not clear to me whether the different speeds are only to be different because they're being measured from the labframe or because they're actually different.

I'd appreciate any advice/help that could be given.
 
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I think I understand that the particles must be going in opposite directions, and that their lowest speed will be when both directions are perpendicular to the direction of motion of the decaying meson. When the directions of motion are parallel to the decaying particle's motion, one pi has to compensate for the other pi's motion against the original direction, and thus it must be going faster.

I'm uncertain about the above, but even if it is so, I'm not sure how to apply the relativistic transforms to the problem.

thanks
 

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