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Direct $CP$ violation in charmless three-body decays of $B^{\pm}$ mesons

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Abstract

Measurements of $CP$ asymmetries in charmless three-body decays of $B^\pm$ mesons are reported using proton-proton collision data collected by the LHCb detector, corresponding to an integrated luminosity of 5.9$ $fb$^{-1}$. The previously observed $CP$ asymmetry in $B^\pm \to \pi^\pm K^+ K^-$ decays is confirmed, and $CP$ asymmetries are observed with a significance of more than five standard deviations in the $B^\pm \to \pi^\pm \pi^+ \pi^-$ and $B^\pm \to K^\pm K^+ K^-$ decays, while the $CP$ asymmetry of $B^\pm \to K^\pm \pi^+ \pi^-$ decays is confirmed to be compatible with zero. The distributions of these asymmetries are also studied as a function of the three-body phase space and suggest contributions from rescattering and resonance interference processes. An indication of the presence of the decays $B^\pm \to \pi^\pm \chi_{c0}(1P)$ in both $B^\pm \to \pi^\pm \pi^+ \pi^-$ and $B^\pm \to \pi^\pm K^+ K^-$ decays is observed, as is $CP$ violation involving these amplitudes.

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Invariant mass spectra of (a) $ { B ^\pm \rightarrow K ^\pm \pi ^+ \pi ^- }$ , (b) $ { B ^\pm \rightarrow K ^\pm K ^+ K ^- }$ , (c) $ { B ^\pm \rightarrow \pi ^\pm \pi ^+ \pi ^- }$ and (d) $ { B ^\pm \rightarrow \pi ^\pm K ^+ K ^- }$ decays in the mass range [5050--5650] $\text{ Me V /}c^2$ . The left panel in each figure shows the $ B ^- $ candidates and the right panel shows the $ B ^+ $ candidates. The results of the unbinned maximum likelihood fits are overlaid.

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Dalitz plot distributions for (a) $ { B ^\pm \rightarrow \pi ^\pm \pi ^+ \pi ^- }$ , (b) $ { B ^\pm \rightarrow K ^\pm \pi ^+ \pi ^- }$ , (c) $ { B ^\pm \rightarrow \pi ^\pm K ^+ K ^- }$ and (d) $ { B ^\pm \rightarrow K ^\pm K ^+ K ^- }$ decays. The colour scale indicates the number of events.

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Asymmetry distribution in bins of the Dalitz plot for (a) $ { B ^\pm \rightarrow \pi ^\pm \pi ^+ \pi ^- }$ , using 400 bins with approximately 229 events/bin; (b) $ { B ^\pm \rightarrow K ^\pm \pi ^+ \pi ^- }$ , using 1728 bins with approximately 276 events/bin; (c) $ { B ^\pm \rightarrow \pi ^\pm K ^+ K ^- }$ , using 256 bins with approximately 127 events/bin; and (d) $ { B ^\pm \rightarrow K ^\pm K ^+ K ^- }$ , using 729 bins with approximately 461 events/bin.

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(a) Projection of $m^2(\pi^+ \pi^-)_{\textrm{high}}$ for the rescattering region (black region inside the Dalitz plot) with the $ { B ^\pm \rightarrow \pi ^\pm \pi ^+ \pi ^- }$ mass fits for (b) region 1 and (c) region 2 ( $ B ^- $ candidates on the left). Regions are separated by a black vertical line in (a), see Table III.

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(a) $m^2(K^+ \pi^-)$ projection for the rescattering region with the $ { B ^\pm \rightarrow K ^\pm \pi ^+ \pi ^- }$ mass fits for (b) region 1 and (c) region 2 ( $ B ^- $ on the left). Regions are separated by a black vertical line in (a).

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(a) $m^2(K^+ \pi^-)$ projection for the rescattering region with the $ { B ^\pm \rightarrow \pi ^\pm K ^+ K ^- }$ mass fits for (b) region 1 ( $ B ^- $ on the left).

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(a) $m^2(K^+ K^-)_{\textrm{high}}$ projection for the rescattering region with the $ { B ^\pm \rightarrow K ^\pm K ^+ K ^- }$ mass fits for (b) region 1 and (c) region 2 ( $ B ^- $ on the left). Regions are separated by a black vertical line in (a).

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(a) $m^2(K^+ K^-)$ projection in the high-mass region (region 2) for $ { B ^\pm \rightarrow \pi ^\pm K ^+ K ^- }$ decays showing the $\chi_{c0}$ contribution. The mass fit for this region ( $ B ^- $ on the left) is shown in (b).

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(a) $m^2(\pi^+ \pi^-)_{\textrm{high}}$ projection in the high-mass region (region 3) for $ { B ^\pm \rightarrow \pi ^\pm \pi ^+ \pi ^- }$ decays. The mass fit for this region ( $ B ^- $ on the left) is shown in (b).

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Tables and captions

Total signal yields, raw asymmetries and average efficiency ratio $R$ of charmless three-body $ B ^\pm$ decays for the inclusive data set.

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Individual components and total systematic uncertainties related to the mass fit model, efficiency corrections for the integrated phase space and $B^{\pm}$ production asymmetry. The total is the sum in quadrature of these components.

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Definitions of phase-space regions in units of $\text{ Ge V} ^2 /c^4$ . In the $ { B ^\pm \rightarrow K ^\pm K ^+ K ^- }$ channel, the $\phi(1020)$ vector meson is excluded by requiring $m^2(K^+K^-)_{\textrm{low}} > 1.1\text{ Ge V} ^2 /c^4 $.

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Signal yield ($N_{\text{sig}}$), raw asymmetry ($A_{\text{raw}}$) and $ A_{ C P }$ corrected for production and detection asymmetries. The $ A_{ C P }$ uncertainties are statistical, systematic and associated to the control channel, respectively.

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Created on 23 March 2024.