Abstract
Let us now extend the isospin symmetry group to the three light quarks u, d and s. Apart from I 3, strangeness S is also a conserved quantum number in strong interactions. It is often more convenient to use the hypercharge Y as a conserved quantity, with quantum number y related to S through (1.4):
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Notes
- 1.
Note that one needs to move twice around the periphery of the 3∗ triangle to retrieve the original state, e.g. when moving clockwise, \(\overline {u}\to -\overline {s}\to \overline {d}\to -\overline {u}\to \overline {s}\to -\overline {d}\to \overline {u}\).
- 2.
A more involved calculation lifting the assumption m s = m u leads to the results (7.57, 7.58), but with the trigonometric functions multiplied by the factors \(\frac {f_\pi }{f_8}\simeq 0.8\) and \(\frac {f_\pi }{f_1}\simeq 0.95\), respectively, where f π is the pion decay constant and f 8, f 1 are the octet and singlet decay constants [5].
References
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Amsler, C. (2018). SU(3). In: The Quark Structure of Hadrons. Lecture Notes in Physics, vol 949. Springer, Cham. https://doi.org/10.1007/978-3-319-98527-5_7
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