Griffiths Introduction to Elementary Particles · Problem 1.8

Elementary Particle Dynamics — David J. Griffiths

Physics — QFT · omega-minus-decay-metastability

Problem

(a) Analyze the possible decay modes of the

\Omega^-

, just as you did in Problem 1.7 for the

\Delta

\Sigma^*

, and

\Xi^*

. See the problem? Gell-Mann predicted that the

\Omega^-

would be ``metastable'' (i.e., much longer lived than the other members of the decuplet), for precisely this reason. (The

\Omega^-

does in fact decay, but by the much slower weak interaction, which does not conserve strangeness.) (b) From the bubble chamber photograph (Fig.\ 1.11), measure the length of the

\Omega^-

track, and use this to estimate the lifetime of the

\Omega^-

. (Of course, you don't know how fast it was going, but it's a safe bet that the speed was less than the velocity of light; let's say it was going about

0.1c

. Also, you don't know if the reproduction has enlarged or shrunk the scale, but never mind: this is quibbling over factors of 2, or 5, or maybe even 10. The important point is that the lifetime is many orders of magnitude longer than the

10^{-23}

sec characteristic of all other members of the decuplet.)

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