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### What does CP violation look like?

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.

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### 10 Responses to “What does CP violation look like?”

1. In the first diagram,

(a) aren’t the quark contents of the pi-minus and pi-plus the wrong way round?

(b) how does B(0)s decay into K+pi-? The PDG decay modes list pi+K- but not pi-K+.

• Anna Phan says:

Thanks for your comment and question. I actually made a mistake in both the image and the equations. Hopefully it’s all correct now.

Cheers,
Anna

Well written short post, and very beautiful diagrams/graphs as well. May I know what software you used to make the first diagram? Thank you.

• Anna Phan says:

Thanks for the comment. It is very nice when a result is clear enough that a couple of equations and a diagram are enough to explain it. I made the decay diagram in Microsoft Powerpoint.

Cheers,
Anna

3. Stephen Brooks says:

A bit confusing that the top two of the four graphs are K+pi- and K-pi+ but the zooms are K-pi+ and K+pi-! (from left to right)

• Anna Phan says:

Dear Stephen,

I didn’t even notice that! I’ve swapped them around now if you think that’s easier to understand. They were in that order in the conference note so that the B_(d,s) were on the left and the anti-B_(d,s) were on the right.

Cheers,
Anna

• Stephen Brooks says:

Thanks! I was just trying to match up the relative sizes of the large red and small green peaks between the plots at the top and the zooms at the bottom when I realised it.

• Stephen Brooks says:

Argh! Now I realise the bottom plots aren’t zooms, they’re completely different plots. So you can ignore my comment, sorry.

• Anna Phan says:

Dear Stephen,

Sorry, I wasn’t very clear in the text. While the plots show the same quantity, they are made with different selections. The upper ones are optimised for the Bd while the lower ones are optimised for the Bs.

Cheers,
Anna

4. Tuan DANG says:

Dear Anna,

Your post is really useful for me. I am studying the B physics @ Belle2 as a junior. Could you please give me some text via my email to understand well CP violation as a beginner?

Bests,