A vertex detector records two tracks as Cartesian momentum components (in ): a kaon…

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

Particle Physics, Ch Invariant mass: decays, thresholds and the collider frame

Problem

A vertex detector records two tracks as Cartesian momentum components (in

\mathrm{MeV}/c

): a kaon track

\mathbf p_K = (300, 400, 900)

and a pion track

\mathbf p_\pi = (-200, 100, 1100)

, with

m_K = 493.7\,\mathrm{MeV}/c^2

and

m_\pi = 139.6\,\mathrm{MeV}/c^2

. ((a)) Use the dot product of the two momentum vectors to find the opening angle

\theta

between the tracks, then use the cosine-rule form of the invariant-mass formula to find the mass

M

of whatever decayed to give these two tracks. ((b)) Taking

M

as the parent's mass, use the two-body decay formula to predict the momentum

p^{*}

and the two energies

E_K^{*}

E_\pi^{*}

in the parent's rest frame.

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