Find the error in the following working

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model · Symmetry, groups and the quark model

Particle Physics, Ch Isospin: a symmetry used as bookkeeping

Problem

Find the error in the following working. "The pions (π+,π0,π−\pi^+,\pi^0,\pi^-) are spin-zero mesons forming an isospin triplet, I=1I=1. The K+K^+ is also a spin-zero meson, with a mass (493.7 MeV/c2493.7\,\mathrm{MeV}/c^2) not enormously different from the pion masses. It should therefore be counted as another member of the same multiplet as the pions, and since K+=usˉK^+ = u\bar s, it is assigned I=1I=1, I3=+1I_3=+1, sitting alongside π+\pi^+." ((a)) Identify what is wrong with this assignment. ((b)) Give the correct isospin quantum numbers and hypercharge of the K+K^+, and state which family it actually belongs to.

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