 Solution

ID: past-exam-of-the-particle-and-nuclear-physics-course-of-the-university-of-cambridge/2014/paper-1/1/c/solution

Away from thresholds and narrow resonances, photon-mediated annihilation gives one colour copy proportional to

Q_{q}^{2}

relative to the muon cross-section. The accessible flavours are

u, d, s, c

, each with three colours, so

R ≃ 3 q = u, d, s, c \sum Q_{q}^{2} = 3 (\frac{4}{9} + \frac{1}{9} + \frac{1}{9} + \frac{4}{9}) = \frac{10}{3} ≃ 3.3.

Bottom production is closed. QCD radiative corrections raise the leading parton-model result by a relative term beginning at

α_{s} / π

; the requested estimate does not require a supplied value of

α_{s}

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