Generalize the low-energy char

Generalize the low-energy charged-current effective Lagrangian to include the possibility of a small right-handed–current interaction among the quarks,

where  and  are composite spinors describing uplike and downlike quarks,  is the standard Cabibbo–Kobayashi–Maskawa (left-handed) quark-mixing matrix given by (7.1.27),  is its right-handed analogue, and the factor ε measures the relative strength of right-handed versus left-handed interactions in the low-energy limit. Now consider three independent determinations, within the standard model, of the element |ub|: The inclusive rate for the transition  is proportional to

The exclusive rate for the transition  is governed by the vector current and so is proportional to

The annihilation decay, τ, is mediated by the axial current, so that

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