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Search for $CP$ violation in $\Xi^-_b \to p K^- K^-$decays

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Abstract

A search for $CP$ violation in charmless three-body $\Xi_b^- \to p K^- K^-$ decays is performed using $pp$ collision data recorded with the LHCb detector, corresponding to integrated luminosities of $1 \text{fb}^{-1}$ at a centre-of-mass energy $\sqrt{s} = 7 \text{TeV}$, $2 \text{fb}^{-1}$ at $\sqrt{s} = 8 \text{TeV}$ and $2 \text{fb}^{-1}$ at $\sqrt{s} = 13 \text{TeV}$. A good description of the phase-space distribution is obtained with an amplitude model containing contributions from $\Sigma(1385)$, $\Lambda(1405)$, $\Lambda(1520)$, $\Lambda(1670)$, $\Sigma(1775)$ and $\Sigma(1915)$ resonances. The model allows for $CP$-violation effects, which are found to be consistent with zero. The branching fractions of $\Xi_b^- \to \Sigma(1385) K^-$, $\Xi_b^- \to \Lambda(1405) K^-$, $\Xi_b^- \to \Lambda(1520) K^-$, $\Xi_b^- \to \Lambda(1670) K^-$, $\Xi_b^- \to \Sigma(1775) K^-$ and $\Xi_b^- \to \Sigma(1915) K^-$ decays are also reported. In addition, an upper limit is placed on the product of ratios of $\Omega_b^-$ and $\Xi_b^-$ fragmentation fractions and the $\Omega_b^- \to p K^- K^-$ and $\Xi_b^- \to p K^- K^-$ branching fractions.

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Distributions of $ p K ^- K ^- $ invariant mass for $ X ^-_ b $ candidates in (left) Run 1 and (right) Run 2 data with results of the unbinned extended maximum-likelihood fits superimposed. The total fit result is shown as the blue solid curve, with individual components shown as indicated in the legend.

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Distributions of selected candidates from (left) Run 1 and (right) Run 2 data in the (top) Dalitz-plot and (bottom) square Dalitz-plot representations of the phase space.

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Efficiency as a function of square Dalitz-plot position for (left) $\Xi ^-_ b $ and (right) $\overline{ \Xi } {}^+_ b $ decays, for (top) Run 1 and (bottom) Run 2.

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SDP distributions of (top) combinatorial and (bottom) cross-feed background components for (left) Run 1 and (right) Run 2.

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Dalitz-plot distributions from (left) data and (right) the fit model for (top) $\Xi ^-_ b $ and (bottom) $\overline{ \Xi } {}^+_ b $ candidates.

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Distributions of (top) $ m_{\rm low} $ and (bottom) $ m_{\rm high} $ for (left) $\Xi ^-_ b $ and (right) $\overline{ \Xi } {}^+_ b $ candidates, with results of the fits superimposed. The total fit result is shown as the blue solid curve, with contributions from individual signal components and from combinatorial (Comb) and cross-feed (Crsfd) background shown as indicated in the legend.

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Distributions of (top) $ m_{\rm low} $ and (bottom) $ m_{\rm high} $, with $1.43 < m_{\rm low} < 1.60 \text{ Ge V} $, for (left) $\Xi ^-_ b $ and (right) $\overline{ \Xi } {}^+_ b $ candidates, with results of the fits superimposed. The total fit result is shown as the blue solid curve, with contributions from individual signal components and from combinatorial (Comb) and cross-feed (Crsfd) background shown as indicated in the legend.

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Distributions of (top) $ m_{\rm low} $ and (bottom) $ m_{\rm high} $, with $1.6 < m_{\rm low} < 1.8 \text{ Ge V} $, for (left) $\Xi ^-_ b $ and (right) $\overline{ \Xi } {}^+_ b $ candidates, with results of the fits superimposed. The total fit result is shown as the blue solid curve, with contributions from individual signal components and from combinatorial (Comb) and cross-feed (Crsfd) background shown as indicated in the legend.

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Distributions of (top) $ m_{\rm low} $ and (bottom) $ m_{\rm high} $, with $1.8 < m_{\rm low} < 2.2 \text{ Ge V} $, for (left) $\Xi ^-_ b $ and (right) $\overline{ \Xi } {}^+_ b $ candidates, with results of the fits superimposed. The total fit result is shown as the blue solid curve, with contributions from individual signal components and from combinatorial (Comb) and cross-feed (Crsfd) background shown as indicated in the legend.

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Distributions of (top) $ m_{\rm low} $ and (bottom) $ m_{\rm high} $, with $2.2 < m_{\rm low} < 2.8 \text{ Ge V} $, for (left) $\Xi ^-_ b $ and (right) $\overline{ \Xi } {}^+_ b $ candidates, with results of the fits superimposed. The total fit result is shown as the blue solid curve, with contributions from individual signal components and from combinatorial (Comb) and cross-feed (Crsfd) background shown as indicated in the legend.

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Distributions of (top) $ m_{\rm low} $ and (bottom) $ m_{\rm high} $, with $ m_{\rm low} > 2.8 \text{ Ge V} $, for (left) $\Xi ^-_ b $ and (right) $\overline{ \Xi } {}^+_ b $ candidates, with results of the fits superimposed. The total fit result is shown as the blue solid curve, with contributions from individual signal components and from combinatorial (Comb) and cross-feed (Crsfd) background shown as indicated in the legend.

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Distributions of (top) $ m_{\rm low} $ and (bottom) $ m_{\rm high} $, with $ m_{\rm high} < 3.15 \text{ Ge V} $ , for (left) $\Xi ^-_ b $ and (right) $\overline{ \Xi } {}^+_ b $ candidates, with results of the fits superimposed. The total fit result is shown as the blue solid curve, with contributions from individual signal components and from combinatorial (Comb) and cross-feed (Crsfd) background shown as indicated in the legend.

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Distributions of (top) $ m_{\rm low} $ and (bottom) $ m_{\rm high} $, with $3.15 < m_{\rm high} < 3.95 \text{ Ge V} $, for (left) $\Xi ^-_ b $ and (right) $\overline{ \Xi } {}^+_ b $ candidates, with results of the fits superimposed. The total fit result is shown as the blue solid curve, with contributions from individual signal components and from combinatorial (Comb) and cross-feed (Crsfd) background shown as indicated in the legend.

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Distributions of (top) $ m_{\rm low} $ and (bottom) $ m_{\rm high} $, with $ m_{\rm high} > 3.95 \text{ Ge V} $, for (left) $\Xi ^-_ b $ and (right) $\overline{ \Xi } {}^+_ b $ candidates, with results of the fits superimposed. The total fit result is shown as the blue solid curve, with contributions from individual signal components and from combinatorial (Comb) and cross-feed (Crsfd) background shown as indicated in the legend.

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Tables and captions

Yields obtained from fits to the $m( p K ^- K ^- )$ distributions, in the full invariant mass range. The quoted uncertainties are statistical only.

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Summary of the considered $\Lambda ^*$ and $\Sigma ^*$ resonances, ranked either **** or *** by the PDG \cite{PDG2020}. Note that the $ p K ^- $ threshold is at $1432 \text{ Me V} $. Resonances marked $\dagger$ are included in the baseline model, as described in the text. The spin-parity of the $\Sigma (2250)$ is not known and is assumed to be $\frac{3}{2}^+$. For many of these states, the PDG does not report masses and widths with central values and uncertainties, but rather gives real and imaginary parts of the pole position. This reflects the fact that a simple Breit--Wigner parameterisation of these resonances may not fully describe their lineshapes; however, more sophisticated parametrisations are beyond the scope of the current analysis.

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Absolute systematic uncertainties on $\mathcal{R}$, in units of $10^{-3}$, from (top) uncorrelated and (bottom) correlated sources. The total is the sum in quadrature of all contributions.

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Summary of absolute systematic uncertainties, in units of $10^{-2}$, on the results of the amplitude analysis: (top) $ C P$ asymmetry parameters $A^{ C P }$ and fit fractions $\mathcal{F}$, (bottom) interference fit fractions $\mathcal{I}$. The total is the sum in quadrature of all individual sources.

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Results for the $ C P$ -asymmetry parameters. The statistical uncertainties are obtained from pseudoexperiments while the systematic uncertainties are obtained following the procedure described in Sec. ???.

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Results for the fit fractions (diagonal elements) and interference fit fractions (off-diagonal elements) obtained from the amplitude analysis. Identical values for the interference fit fractions in the upper triangle are omitted. All values are in units of $10^{-2}$, with the first uncertainty being statistical and the second systematic.

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Created on 23 March 2024.