Solution (source code)

= Solution

An experimentally observed example is \b[$K_L\to\pi^+\pi^-$], a decay of the long-lived neutral <kaon> into a CP-even two-pion state. Without <CP violation>, the long-lived state would be CP-odd and this decay would be forbidden.

For the <CKM matrix> mechanism of <CP violation>, \b[three <quark generations> are the minimum]. Rephasings remove every complex phase for one or two generations, while three generations leave one physical <CP-violating phase>. This count concerns weak quark mixing. The <Yang-Mills theta term> in part (c) is a separate possible source of <CP violation> and does not require three generations.