A muon of mass is produced with total momentum at a polar angle to the beam axis.

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Particle Physics & Quantum Fields · Particles, interactions and experiment

Symmetry and Flavour, Ch Four-vectors at work: boosts, invariants and the shape of a final state

Problem

A muon of mass mμ=105.7 MeVm_\mu = 105.7\,\mathrm{MeV} is produced with total momentum p=2.00 GeVp = 2.00\,\mathrm{GeV} at a polar angle θ=45∘\theta = 45^\circ to the beam axis. ((a)) Calculate its pseudorapidity η=−ln⁡tan⁡(θ/2)\eta = -\ln\tan(\theta/2). ((b)) Calculate its rapidity y=12ln⁡ ⁣[E+pzE−pz]y = \tfrac12\ln\!\left[\dfrac{E+p_z}{E-p_z}\right]. ((c)) State whether η\eta may stand in for yy here, and why.

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