0

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
  • 426

2 Answers2

1

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
  • 89,569
  • It should be possible: $\bar u \to W^-\bar d$ on one line, with the $W^-$ connecting to the other quark line, $c W^- \to d \to W^- u$, $W^- \to e^- \bar\nu_e$. – fuenfundachtzig Aug 04 '21 at 19:18
  • @fuenfundachtzig Sure, you can use combinatorics to find second-order (or higher) diagrams that are allowed. But my statement that it's forbidden at "tree level" is correct. For a hint of the nastiness that has to be dealt with in second-order weak decays, have a look into the literature leading up to the paper described here for discussions about the "gamma-Z box diagram," a calculation which delayed that result by a couple of years. – rob Aug 04 '21 at 20:40
  • 1
    I accepted your answer, my comment was only referring to "if it's even possible at all": The decay is possible, but the branching fraction apparently has not been measured (?). – fuenfundachtzig Aug 04 '21 at 20:51
0

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
  • 15,147
  • Thanks for your answer, but note that I am looking for the BRs of $D^0$, not $K^0$. Also, charge-conjugation would give me BR($\bar D^0\to\pi^+e^-\bar\nu_e$), i.e. not $D^0$, wouldn't it? – fuenfundachtzig May 01 '16 at 10:29
  • Sorry K0 was a typo. My reading of the experimental papers is that CC conjugate final states are implied – innisfree May 01 '16 at 10:36
  • But if I look at the decays at quark level (= try to draw quark-level diagrams), this doesn't work without also conjugating the initial state. (That's where I started from arriving at this question.) – fuenfundachtzig May 01 '16 at 10:40
  • My reading of the experimental papers was that an event was tagged by a $\bar D^0$ and the CC related decay modes of the accompanying $D^0$ were measured. I don't know why they don't measure them separately – innisfree May 01 '16 at 10:43
  • Maybe I've misunderstood it, perhaps they mean that they also tag on $D$ and study the CC process on the $\bar D \to e^-\cdots$. – innisfree May 01 '16 at 10:47
  • Another nitpick: The BR you give is missing a factor 0.01 (the notation in the link is misleading: there is a $10^{-2}$ after the value and another one in the table head. Never seen such a notation before :) – fuenfundachtzig May 01 '16 at 10:52