Griffiths Introduction to Elementary Particles · Problem 5.18

The Feynman Calculus — David J. Griffiths

Physics — QFT · charmonium-decay-branching-ratios

Problem

Just as positronium, in the triplet configuration, decays to three photons (Problem 5.16), the ψ\psi meson (charmonium in the triplet configuration) decays to three gluons. (The gluons subsequently turn into various combinations of hadrons.) Indeed, the cross section for c+cˉ→3gc + \bar{c} \to 3g is the same as for e++e−→3γe^+ + e^- \to 3\gamma, only with α3→518αs3\alpha^3 \to \frac{5}{18}\alpha_s^3 (the 518\frac{5}{18} is a so-called ``color factor,'' which you'll learn how to calculate in Chapter 9). Use this, together with the formulas in Problems 5.16 and 5.17, and equation (5.82), to determine the ``branching ratios'' Γ(ψ→hadrons):Γ(ψ→e+e−):Γ(ψ→μ+μ−)\Gamma(\psi \to \text{hadrons}):\Gamma(\psi \to e^+e^-):\Gamma(\psi \to \mu^+\mu^-) Compare the experimental results.

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