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I am looking for the branching ratio of the semileptonic decay of the neutral $D^0$ meson:

BR($D^0 \to \pi^+e^-\bar\nu_e$) = ?

According to the PDG book the branching ratio for $D^0 \to \pi^-e^+\nu_e$ is $(2.83\pm0.17)\times10^{-3}$ but I haven't found the BR for the decay above nor any upper limit. Am I overlooking something?

fuenfundachtzig
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2 Answers2

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Another answer suggests that the two decays

\begin{align} D^0 &\to \pi^- e^+ \nu_e & \text{BR: } & 0.291(4)\times10^{-2} \\ D^0 & \to \pi^+ e^- \bar\nu_e & \text{BR: } & ??? \end{align}

(with branching ratio from pdgLive) are charge-conjugates. That was my first thought as well, but it's not correct. The two final states are charge-conjugates. However the charge conjugate of the $D^0$, which has quark content $c\bar u$, is the $\bar D^0$, with quark content $\bar cu$.

And that reveals why the second decay is (at least at tree level) forbidden. In the quark model, the measured decay is the weak decay of a charm quark,

$$ c \to d e^+ \nu_e, $$

with the $\bar u$ along for the ride. To have the quark content change from $c\bar u = D^0$ to $\bar d u = \pi^+$, as you propose, is a much messier suggestion if it's even possible at all.

rob
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The PDGlive webpage lists their fit as $$ \text{BR}(D^0 \to \pi^- e^+ \nu_e) = (28.9\pm0.8)\times10^{−2} $$ Looking at the experimental analyses from which this combination was obtained, e.g. this CLEO analysis, we find that

inclusion of charge-conjugate states is implied throughout this report

In other words, I believe that PDG lists the branching ratio to the sum of the CP related final states. I don't know if they've been separately measured.

innisfree
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