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Homework Statement
A rho meson of rest mass 768 MeV/c^2 and total energy of 960 MeV decays into 2 pions, neutral and positive with rest masses 135 and 139.6 MeV/c^2 respectively. Show that the neutral pion has a speed of 0.93588c with respect to the centre of mass frame and that it's momentum, energy and lorentz factor are 735.6 MeV/c, 747.9 MeV and 5.54 respectively.
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Homework Equations
E^2 = p^2 + m^2
E = yM
Vx = [y(dx + bc(dt))]/[y(dt + b(dx)/c)]
E = ymc^2
E = K + m
The Attempt at a Solution
. I found y as 1.25 and therefore b = 0.6. rho moves at 0.6c in the laboratory frame.
Energy and momentum must be conserved. So total energy before = total energy after. Total momentum before = total momentum after.
so p = 576 MeV/c
So now I have momentum and energy at the beginning and they must be the same at the end.
The problem is, the pions are both going to be moving at high speeds.. How do I go about finding their speeds, momentums and energies?
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I really don't know what to do. I need to find the speed of the neutral pion, it's momentum and it's energy. But there are so many equations and the center of mass frame (the rho meson) is also moving at high speed. I'm not asking for a straight answer, just some guidance please.