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Questions of Elementary Particles

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3.13 A pion traveling at speed v decays into a muon and a neutrino, pi^- --> mu^- + v_mu. If the neutrino emerges at 90 degrees to the original pion direction, at what angle does the mu come off?

3.14 Particle A (energy E) hits particle B (at rest), producing particles C_1, C_2, ... A + B --> C_1 + C_2 + ... + C_n. Calculate the threshold (i.e., minimum E) for this reaction, in terms of the various particle masses.

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Let us take units in which the speed of light $c = 1$, and put c back in the final answer, in such cases where it is there, to make it easier to write formulae.

noindent
bf 3.13 rm

Let the incoming pion velocity direction be along X-axis, and neutrino direction be along Y-axis, then the 4-momenta of the pion and neutrino
$$
p_pi = m_pigamma(1, beta, 0, 0),
$$
and
$$
p_nu = ...

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This solution uses step by step calculations and formula to solve the given problems.

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