A detector records decays of the lepton

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Electroweak theory and the Standard Model · Electroweak theory and the Standard Model

Particle Physics, Ch The Standard Model as a table you can predict from

Problem

A detector records 20002000 decays of the τ−\tau^- lepton. Of these, 356356 end as e−νˉeντe^-\bar\nu_e\nu_\tau, 348348 end as μ−νˉμντ\mu^-\bar\nu_\mu\nu_\tau, and the rest contain hadrons. ((a)) Find B(τ−→e−νˉeντ)\mathcal{B}(\tau^-\to e^-\bar\nu_e\nu_\tau), B(τ−→μ−νˉμντ)\mathcal{B}(\tau^-\to\mu^-\bar\nu_\mu\nu_\tau) and the combined branching ratio to hadrons, and check that the three sum to one. ((b)) Someone argues that the τ−\tau^- which decay to hadrons, being the majority, must live for a different length of time from those that decay to an electron. Is that right?

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