As promised in my last post, today I’ll be talking about one way we measure CP violation. In particular, I’ll be reporting a direct CP asymmetry result which we released for the EPS conference back in July.
Direct CP violation is conceptually the easiest type of CP violation to understand. It is simply when the amplitude of a process differs from its CP conjugate. For instance, it would be when the branching ratio for the process \(B_{d} \rightarrow K^{+} + \pi^{-}\) differs from \(\bar{B}_{d} \rightarrow K^{-} + \pi^{+}\) or the branching ratio for \(B_{s} \rightarrow K^{-} + \pi^{+}\) differs from \(\bar{B}_{s} \rightarrow K^{+} + \pi^{-}\). The diagram below shows the full \(B_{s}\) and \(\bar{B}_{s}\) decays, including their quark components.
And below are the results… The left two plots show the \(K^{+} + \pi^{-}\) final state, while the right two plots show the \(K^{-} + \pi^{+}\) final state. The bottom two plots are the same as the upper two, just with a different \(y\) scale. The dark blue line shows the full fit, the red line is \(B_{d} \rightarrow K + \pi\), the dark red is wrong sign \(B_{d} \rightarrow K + \pi\), the light blue is misidentified \(B_{d} \rightarrow \pi + \pi\), the yellow line is misidentified \(B_{s} \rightarrow K + K\), the green line is \(B_{s} \rightarrow K + \pi\), the grey line is combinatorial background and orange is three-body partially reconstructed decays.
The extra dashed red line and arrow shows the difference between \(B_{d}\) and \(\bar{B}_{d}\) amplitudes while the dashed green line and arrow shows the difference between the \(B_{s}\) and \(\bar{B}_{s}\) amplitudes.
There you have it. The amplitudes are different. Direct CP violation. Nice, isn’t it?
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For the more technically minded out there, we measured the direct CP asymmetries to be:
\(A_{CP}(B_{d} \rightarrow K \pi)=−0.088\pm0.011(stat)\pm0.008(syst)\)
\(A_{CP}(B_{s} \rightarrow \pi K)=0.27\pm0.08(stat)\pm0.02(syst)\)
where the former is the best measurement in the world of that quantity, while the latter is the first evidence of CP violation in that decay.
