# Mixing Parameters of the $D^{0}$ Meson

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.

• Minor comment to the post (v2): In the future please link to abstract pages rather than pdf files. – Qmechanic Sep 15 '18 at 6:51
• @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" – dukwon Sep 22 '18 at 19:11