I know in my life at least, there are periods when all I want to do is talk to the public about physics, and then periods where all I would like to do is focus on my work and not talk to anyone. Unfortunately, the last 4 or so months falls into the latter category. Thank goodness, however, I am now able to take some time and write about some interesting physics which had been presented both this year and last. And while polar bears don’t really hibernate, I share the sentiments of this one.

A little while ago, I posted on Dalitz Plots, with the intention of listing a result. Well, now is the time.

At the 7th International Workshop on the CKM Unitarity Triangle, LHCb presented preliminary results

for CP asymmetry in the channels \(B\to hhh\), where \(h\) is either a \(K\) or \(\pi\). Specifically, the presentation was to report on searches for direct CP violation in the decays \(B^{\pm}\to \pi^{\pm} \pi^{+} \pi^{-}\) and \(B^{\pm}\to\pi^{\pm}K^{+}K^{-}\). If CP was conserved in this decay, we would expect decays from \(B^+\) and \(B^-\) to occur in equal amounts. If, however, CP is violated, then we expect a difference in the number of times the final state comes from a \(B^+\) versus a \(B^-\). Searches of this type are effectively “direct” probes of the matter-antimatter asymmetry in the universe.

By performing a sophisticated counting of signal events, CP violation is found with a statistical significance of \(4.2\sigma\) for \(B^\pm\to\pi^\pm\pi^+\pi^-\) and \(3.0\sigma\) for \(B^\pm\to\pi^\pm K^+K^-\). This is indeed evidence for CP violation, which requires a statistical significance >3\(\sigma\).The puzzling part, however, comes when the Dalitz plot of the 3-body state is considered. It is possible to map the CP asymmetry as a function of position in the Dalitz plot, which is shown on the right. It’s important to note that these asymmetries are for both signal and background. Also, the binning looks funny in this plot because all bins are of approximately equal populations. In particular, notice red bins on the top left of the \(\pi\pi\pi\) Dalitz plot and the dark blue and purple section on the left of the \(\pi K K\) Dalitz plot. By zooming in on these regions, specifically \(m^2(\pi\pi_{high})>\)15 GeV/c\(^2\) and \(m^2(K K)<\)3 GeV/c\(^2\), and separating by \(B^+\) and \(B^-\), a clear and large asymmetry is shown (see plots below).

Now, I’d like to put these asymmetries in a little bit of perspective. Integrated over the Dalitz Plot, the resulting asymmetries are

\(A_{CP}(B^\pm\to\pi^\pm\pi^+\pi^-) = +0.120\pm 0.020(stat)\pm 0.019(syst)\pm 0.007(J/\psi K^\pm)\)

and

\(A_{CP}(B^\pm\to\pi^\pm K^+K^-) = -0.153\pm 0.046(stat)\pm 0.019(syst)\pm 0.007(J/\psi K^\pm)\).

Whereas, in the regions which stick out, we find:

\(A_{CP}(B^\pm\to\pi^\pm\pi^+\pi^-\text{region}) = +0.622\pm 0.075(stat)\pm 0.032(syst)\pm 0.007(J/\psi K^\pm)\)

and

\(A_{CP}(B^\pm\to\pi^\pm K^+K^-\text{region}) = -0.671\pm 0.067(stat)\pm 0.028(syst)\pm 0.007(J/\psi K^\pm)\).

These latter regions correspond to a statistical significance of >7\(\sigma\) and >9\(\sigma\), respectively. The interpretation of these results is a bit difficult: the asymmetries are four to five times that of the integrated asymmetries, and are not necessarily associated with a single resonance. We would expect in the \(\rho^0\) and \(f_0\) resonances to appear in the lowest region of \(\pi\pi\pi\) Dalitz plot, in the asymmetry. In the \(K K\pi\) Dalitz plot, there are really no scalar particles which we expect to give us an asymmetry of the kind we see. One possible answer to both these problems is that the quantum mechanical amplitudes are only partially interfering and giving the structure that we see. The only way to check this would be to do a more detailed analysis involving a fit to all of the possible resonances in these Dalitz plots. All I can say is that this result is certainly puzzling, and the explanation is not necessarily clear.

Tags: B meson, B-Physics, b3h, bhhh, CP asymmetry, CPV, LHCb

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