Consequences of Charge Independence in Strong Interactions: A Graphical Method

The hypothesis of charge independence is studied using a simple graphical method. This method is applicable in the common situation when a particle reaction can proceed through several charge channels but only through two isospin channels. The branching ratios of the charge channels are plotted in a two-dimensional diagram which is possible because only two of these ratios are independent. The triangular inequalities are shown to be equivalent to a single inequality, and they determine in the diagram an elliptic boundary curve of a physical region. The plot is also useful for studying isospin properties of intermediate states in the reaction. The method is demonstrated with two examples, the reactions $K^{+}p\to \mathrm{KN}\pi$ and $\pi N\to \pi N$.