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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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Please see the attached files for proper formatting.

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.

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),
p_nu = ...

Solution Summary

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