Robert Mann - An Introduction to Particle Physics and the Standard Model · Problem 14

Conservation Laws — Robert Mann

Physics — Particle Physics · mandelstam-variables

Problem

Consider a two-body scattering event A+B⟶C+DA + B \longrightarrow C + D. Define the following quantities s=(pA+pB)2t=(pA−pC)2u=(pA−pD)2s = (p_A + p_B)^2 \qquad t = (p_A - p_C)^2 \qquad u = (p_A - p_D)^2 which are a set of variables called Mandelstam variables. (a) Show that the sum of the Mandelstam variables is a Lorentz invariant quantity and compute its value. (b) Find the energy of AA in the lab frame, where particle BB is at rest, in terms of the Mandelstam variables and the rest masses of the particles. (c) Find the center-of-mass energy of AA in terms of the Mandelstam variables and the rest masses of the particles. What is the total energy in this frame?

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