Classical Electrodynamics · Problem 11.20

Radiating Systems, Multipole Fields and Radiation — John David Jackson

Physics — E&M · lambda-particle-decay

Problem

The lambda particle (Λ\Lambda) is a neutral baryon of mass M=1115M = 1115 MeV that decays with a lifetime of τ=2.9×10−10\tau = 2.9 \times 10^{-10} s into a nucleon of mass m1≈939m_1 \approx 939 MeV and a pi-meson of mass m2≈140m_2 \approx 140 MeV. It was first observed in flight by its charged decay mode Λ→p+π−\Lambda \to p + \pi^- in cloud chambers. The charged tracks originate from a single point and have the appearance of an inverted vee or lambda. The particles' identities and momenta can be inferred from their ranges and curvature in the magnetic field of the chamber. (a) Using conservation of momentum and energy and the invariance of scalar products of 4-vectors show that, if the opening angle θ\theta between the two tracks is measured, the mass of the decaying particle can be found from the formula M2=m12+m22+2E1E2−2p1p2cos⁡θM^2 = m_1^2 + m_2^2 + 2E_1 E_2 - 2p_1 p_2 \cos\theta where here p1p_1 and p2p_2 are the magnitudes of the 3-momenta. (b) A lambda particle is created with a total energy of 10 GeV in a collision in the top plate of a cloud chamber. How far on the average will it travel in the chamber before decaying? What range of opening angles will occur for a 10 GeV lambda if the decay is more or less isotropic in the lambda's rest frame?

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