Consider a hypothetical neutral particle that decays only to a pion pair,

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

Particle Physics, Ch Decay rates, cross sections and phase space

Problem

Consider a hypothetical neutral particle

X

that decays only to a pion pair,

X \to \pi^+\pi^-

, with

m_{\pi^\pm}c^2 = 139.57\,\mathrm{MeV}

. For a two-body decay the momentum of either product in the

X

rest frame is

p^*c = \tfrac{1}{2}\sqrt{(Mc^2)^2 - 4(m_\pi c^2)^2},

where

M

is the mass of

X

. ((a)) Find

p^*c

, in MeV, for

Mc^2 = 320\,\mathrm{MeV}

. ((b)) Find

p^*c

for

Mc^2 = 290\,\mathrm{MeV}

. ((c)) Find

p^*c

for

Mc^2 = 281\,\mathrm{MeV}

. ((d)) All three hypothetical particles are taken to have exactly the same coupling to

\pi^+\pi^-

. Explain, using the trend in (a)-(c), why the decay rate of the lightest of the three would be far smaller than that of the heaviest, even though the interaction strength has not changed.

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