A boson ( ) at rest decays isotropically to a massless electron and a massless neutrino.

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

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

Problem

A WW boson (mW=80.4 GeVm_W=80.4\,\mathrm{GeV}) at rest decays isotropically to a massless electron and a massless neutrino. ((a)) Starting from pT=(mW/2)sin⁡θ∗p_T=(m_W/2)\sin\theta^* and dN/dcos⁡θ∗=12\mathrm dN/\mathrm d\cos\theta^*=\tfrac12, derive dN/dpT\mathrm dN/\mathrm dp_T for the electron, and show that it integrates to one over 0<pT<mW/20<p_T<m_W/2. ((b)) Find the fraction of electrons with pTp_T above 0.9 (mW/2)0.9\,(m_W/2), that is in the top tenth of the range, and the value of pTp_T that marks this cut.

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