Cheng & Li's Gauge theory of elementary particle physics has the following formula for the average intensity of neutrino oscillations (Eqs 13.30 and 13.31) on p 411. \begin{align} \langle P_{\nu_e\longrightarrow \nu_e}\rangle &= 1 - 2 c_1^2 s_1^2 -2 s_1^4 c_3^2 s_3^2\nonumber\\ \langle P_{\nu_e\longrightarrow \nu_\mu}\rangle & = 2 c_1^2 s_1^2 c_2^2 + 2 s_1^2 s_3^2 c_3^2 (s_2^2 - c_1^2 c_2^2) + 2 s_1^2 s_2 s_3 c_1 c_2 c_3 (s_3^2 -c_3^2) \cos \delta \nonumber\\ \langle P_{\nu_e\longrightarrow \nu_\tau}\rangle & = 2 c_1^2 s_1^2 s_2^2 + 2 s_1^2 s_3^2 c_3^2 (c_2^2 - c_1^2 s_2^2) + 2 s_1^2 s_2 s_3 c_1 c_2 c_3 (s_3^2 -c_3^2) \cos \delta \end{align} where $c_i = \cos \theta_i$, $s_i = \sin \theta_i$ ($i=1,2,3$) with the $\theta_i$ and $\delta$ the parametrisation of the KM (or PMNS) matrix. $\langle P_{\nu_e\longrightarrow \nu_e}\rangle$ is the probability of having a $\nu_e$ at a distance much larger than the oscillation length when starting from a $\nu_e$, etc.
One would expect these three probabilities to add to one, but this is not the case from the formula above. The terms independent of $\delta$ do indeed sum to one, but there is a term that depends on $\cos \delta$.
Is this a typo in Cheng & Li, or am I missing something?
