Particle decays only through one channel

PHYSICS · Subjective · 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

Particle

X

decays only through one channel, with partial width

\Gamma(X\to A) = 3\,\mathrm{MeV}

. Particle

Y

, otherwise identical in mass and interaction type, decays through that same channel with the same partial width

\Gamma(Y\to A) = 3\,\mathrm{MeV}

, but also has a second channel open, with partial width

\Gamma(Y\to B) = 2\,\mathrm{MeV}

. Someone argues: 'Y has more ways to decay than X, so its decays are spread over two channels instead of one; this must make Y live longer than X.' Compute the lifetimes of

X

and

Y

and say whether the argument is correct.

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