Consider mixing in the $D^{0}$ charm meson system as discussed, for example here. Such mixing is characterised by the mixing parameters $x=\frac{\Delta m}{\Gamma}$, and $y=\frac{\Delta\Gamma}{2\Gamma}$. For a given final state $f$, the decay rate is given to first order by the corresponding matrix element squared; $$\Gamma(D^{0}\rightarrow f)(t)=|\langle f|\hat{H}|D^{0}(t)\rangle|^{2}\equiv A_{f}$$ And similarly for the decay of $\bar{D^{0}}$.

I am trying to figure out which combinations of the mixing parameters can be measured for a given decay mode (for example $D^{0}\rightarrow K^{+}K^{-}$). I know that decay rates are measurable, and that's about it.

I'm really not sure how to approach this problem. I know that the $D^{0}$ and $\bar{D^{0}}$ mesons mix, and both can decay to the final state. I'm also able to use the Schrodinger equation to get the time evolution of $\Gamma(D^{0}\rightarrow f)(t)$ and $|D^{0}(t)\rangle$ as well as the mixing probabilities $P(D^{0}\rightarrow \bar{D^{0}})(t)$. I've also tried drawing the relevant Feynman diagrams for this process, but I can't seem to figure out how to convert this information into combinations of the mixing parameters which are measurable.

I'd really appreciate a bit of help, and/or an explanation of what is actually going on here conceptually (I think part of the issue is that I don't really understand what is being asked). In particular I don't know how to figure out which combinations of mixing parameters are measurable for a given decay, and how this changes for different decays.

Thanks in advance, and I'm sorry if this is very basic, I'm really new to experimental particle physics.

  • $\begingroup$ Minor comment to the post (v2): In the future please link to abstract pages rather than pdf files. $\endgroup$ – Qmechanic Sep 15 '18 at 6:51
  • $\begingroup$ @Qmechanic unfortunately very impractical in this case. The PDF is one of many links on this page: pdg.lbl.gov/2014/reviews/contents_sports.html Linking it directly is better than telling the reader to hunt for the one called "D0- Dbar0 Mixing" $\endgroup$ – dukwon Sep 22 '18 at 19:11

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