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Symmetries in particle physics

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<strong>Symmetries</strong><br />

Isosp<strong>in</strong> and scatter<strong>in</strong>g amplitudes<br />

Use isosp<strong>in</strong> for pion-nucleon scatter<strong>in</strong>g amplitudes<br />

Therefore, the cross sections behave like<br />

At a c.m. energy of 1232 MeV there is a dramatic<br />

bump <strong>in</strong> the pion-nucleon scatter<strong>in</strong>g cross section,<br />

first discovered by Fermi <strong>in</strong> 1951. There, the pion<br />

and nucleon form a short-lived resonance state, the<br />

Δ which we know to carry I = 3/2.

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