One of the other results presented at the Hadron Collider Physics Symposium this week was the result of a search for \( D^{0}–\bar{D}^{0}\) mixing at LHCb.
Cartoon: If a \(D^0\) is produced, at some time t later, it is possible that the system has "oscillated" into a \(\bar{D}^0\). This is because the mass eigenstates are not the same as the flavor eigenstates.
Neutral meson mixing is predicted for any neutral meson system, and has been verified for the \(K^0–\bar{ K}^0\), \(B^0–\bar{B}^0\) and \(B_s^0–\bar{B_s}^0\) systems. However, for the \(D^0–\bar{D}^0\) system, no one measurement has provided a result with greater than \(5\sigma\) significance that mixing actually occurs, until now.
The actual measurement is of \(R(t)=R\), which is effectively the Taylor expansion of the time dependent ratio of \( D^0 \rightarrow K^+ \pi^-\) (“Wrong Sign” decay) to \( D^0\rightarrow K^- \pi^+\) (“Right Sign” decay). Charge conjugates of these decays are also included. There is a “Wrong Sign” and a “Right Sign” because the Right Sign decays are much more probable, according to the standard model.
The mixing of the \(D^0–\bar{D}^0\) system is described by the parameters \(x = \Delta m /\Gamma\) and \(y = \Delta \Gamma / 2\Gamma\), where \(\Delta m\) is the mass difference between the \(D^0\) and \(\bar{D}^0\), \(\Delta \Gamma\) is the difference of widths of the mass peaks, and \( \Gamma\) is the average width. What appears in the description of \(R\), however, is \( x’\) and \( y’\), which give the relations between the \(x\) and \(y\) with added information about the strong phase difference between the Right Sign and Wrong Sign decays. The important part about \(x’\) and \(y’\) are that they appear in the time dependent terms of the Taylor expansion of \(R\). If there were no mixing at all, then we would expect the ratio to remain constant, and the higher order time dependence to vanish. If mixing does occur, however, then a clear, non-flat trend should be seen, and hence a measurement of \(x’\) and \(y’\). That is why the time dependent analysis is so important.
Fit of ratio of WS and RS decays as a function of decay time of the D meson. Flat line would be no mixing, sloped line indicates mixing. From http://arxiv.org/pdf/1211.1230.pdf
Result of the mixing parameter fit of the neutral D meson system. 1,3 and 5 standard deviation contours are shown, and the + represents no mixing. From http://arxiv.org/pdf/1211.1230.pdf
The result is a 9.1 \(\sigma\) evidence for mixing, which is also in agreement with previous results from BaBar, Belle and CDF. On top of confirming that the neutral D meson system does mix, this result is of particular importance because, coupled with the result of CP violation in the charm system, it begs the question whether or not there is much more interesting physics beyond the standard model involving charm just waiting to be seen. Stay tuned!
